What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

AP Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card AP Physics 1 review of concepts, formulas, graphs, experiments, and reasoning across all eight course units.

Από τον συντάκτη Open Study Contributor

Μελετήστε αυτήν τη δέσμη δωρεάν

Το Nibomo ανοίγει για να ξεκινήσετε τη μελέτη.

Λεπτομέρειες δέσμης

Κάρτες: 400 κάρτες
Έκδοση: 3
Δημοσιεύτηκε: 26 Αυγούστου 2026
Τελευταία ενημέρωση: 10 Σεπτεμβρίου 2026
Άδεια χρήσης: Common knowledge · CC0 1.0
Γλώσσες κοινού: en
Αντικείμενο: Physics
Επίπεδο: AP Physics 1
Ετικέτες: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

Παρόμοιες δέσμες

Σχετικά με αυτήν τη δέσμη

This 400-card deck reviews all eight AP Physics 1 course units: Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs.

The deck does not mechanically reverse every fact. Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded.

The sequence follows Units 1–8 so motion, forces, energy, and momentum become prerequisites for rotation, orbits, oscillations, and fluids. Definitions appear before dependent uses, while related formula, graph, condition, calculation, and contrast prompts are separated where practical to reduce short-range cueing.

Course scope was checked against the official AP Physics 1 course page. Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of physics facts or third-party material.

This is an independently authored, unofficial educational deck. It is not affiliated with, sponsored by, or endorsed by the College Board. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product. No AP exam questions, answer keys, scoring guidelines, curriculum text, logos, or trade dress were copied.

Κάρτες σε αυτήν τη δέσμη

Κάρτα 1
Ερώτηση
What separates a vector quantity from a scalar quantity?
Απάντηση
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Κάρτα 2
Ερώτηση
When is the point-object model useful in kinematics?
Απάντηση
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Κάρτα 3
Ερώτηση
When may the constant-acceleration kinematic equations be used?
Απάντηση
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Κάρτα 4
Ερώτηση
Why must a velocity statement name or imply a reference frame?
Απάντηση
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Κάρτα 5
Ερώτηση
Why can horizontal and vertical projectile motion be analyzed separately?
Απάντηση
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Κάρτα 6
Ερώτηση
Can an object have zero velocity and nonzero acceleration at one instant?
Απάντηση
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Κάρτα 7
Ερώτηση
A runner completes one lap and returns to the start. How do distance and displacement compare?
Απάντηση
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Κάρτα 8
Ερώτηση
What makes a reference frame convenient for a motion problem?
Απάντηση
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Κάρτα 9
Ερώτηση
How are the components of a launch velocity v at angle θ found?
Απάντηση
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Κάρτα 10
Ερώτηση
What does average velocity measure?
Απάντηση
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Κάρτα 11
Ερώτηση
Do a vector's magnitude and its component use different SI units?
Απάντηση
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Κάρτα 12
Ερώτηση
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Απάντηση
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Κάρτα 13
Ερώτηση
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Απάντηση
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Κάρτα 14
Ερώτηση
What does average acceleration measure?
Απάντηση
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Κάρτα 15
Ερώτηση
What does a negative one-dimensional vector component mean?
Απάντηση
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Κάρτα 16
Ερώτηση
For constant acceleration, what does v = v₀ + at retrieve?
Απάντηση
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Κάρτα 17
Ερώτηση
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Απάντηση
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Κάρτα 18
Ερώτηση
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Απάντηση
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Κάρτα 19
Ερώτηση
What does the slope of a position-versus-time graph represent?
Απάντηση
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Κάρτα 20
Ερώτηση
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Απάντηση
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Κάρτα 21
Ερώτηση
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Απάντηση
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Κάρτα 22
Ερώτηση
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Απάντηση
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Κάρτα 23
Ερώτηση
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Απάντηση
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Κάρτα 24
Ερώτηση
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Απάντηση
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Κάρτα 25
Ερώτηση
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Απάντηση
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Κάρτα 26
Ερώτηση
Why can average speed differ from the magnitude of average velocity?
Απάντηση
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Κάρτα 27
Ερώτηση
What does the slope of a velocity-versus-time graph represent?
Απάντηση
Acceleration. The slope's units are (m/s)/s = m/s².
Κάρτα 28
Ερώτηση
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Απάντηση
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Κάρτα 29
Ερώτηση
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Απάντηση
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Κάρτα 30
Ερώτηση
Can an object have nonzero velocity and zero acceleration?
Απάντηση
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Κάρτα 31
Ερώτηση
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Απάντηση
Position x versus t². Its slope is ½a when the initial velocity is zero.
Κάρτα 32
Ερώτηση
What does signed area under a velocity-versus-time graph represent?
Απάντηση
Displacement. Area below the time axis contributes negative displacement.
Κάρτα 33
Ερώτηση
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Απάντηση
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Κάρτα 34
Ερώτηση
How can a motion sensor test whether a cart moves at constant velocity?
Απάντηση
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Κάρτα 35
Ερώτηση
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Απάντηση
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Κάρτα 36
Ερώτηση
Which constant-acceleration equation connects speed and displacement without using time?
Απάντηση
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Κάρτα 37
Ερώτηση
How could video data test the independence of projectile components?
Απάντηση
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Κάρτα 38
Ερώτηση
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Απάντηση
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Κάρτα 39
Ερώτηση
How can average velocity over a very short interval approximate instantaneous velocity?
Απάντηση
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Κάρτα 40
Ερώτηση
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Απάντηση
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Κάρτα 41
Ερώτηση
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Απάντηση
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Κάρτα 42
Ερώτηση
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Απάντηση
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Κάρτα 43
Ερώτηση
What does signed area under an acceleration-versus-time graph represent?
Απάντηση
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Κάρτα 44
Ερώτηση
How is one-dimensional relative velocity calculated for two objects A and B?
Απάντηση
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Κάρτα 45
Ερώτηση
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Απάντηση
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Κάρτα 46
Ερώτηση
What does choosing a system boundary decide in a mechanics problem?
Απάντηση
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Κάρτα 47
Ερώτηση
What belongs on a free-body diagram for one chosen object?
Απάντηση
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Κάρτα 48
Ερώτηση
What assumptions define the ideal-string model used in introductory algebra-based physics?
Απάντηση
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Κάρτα 49
Ερώτηση
What does translational equilibrium require?
Απάντηση
Zero net force. The object may be at rest or move with constant velocity.
Κάρτα 50
Ερώτηση
In an inertial frame, how does Newton's second law connect force and motion?
Απάντηση
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Κάρτα 51
Ερώτηση
How do mass and weight differ?
Απάντηση
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Κάρτα 52
Ερώτηση
How does static friction choose its magnitude before slipping begins?
Απάντηση
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Κάρτα 53
Ερώτηση
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Απάντηση
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Κάρτα 54
Ερώτηση
What direction does centripetal acceleration point in circular motion?
Απάντηση
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Κάρτα 55
Ερώτηση
What is the gravitational force magnitude between two point masses?
Απάντηση
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Κάρτα 56
Ερώτηση
Why isn't the normal force always equal to an object's weight?
Απάντηση
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Κάρτα 57
Ερώτηση
What determines a friction coefficient in the simple model?
Απάντηση
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Κάρτα 58
Ερώτηση
What is the centripetal-acceleration magnitude for speed v and radius r?
Απάντηση
a_c = v²/r. It is a kinematic requirement, not a separate force.
Κάρτα 59
Ερώτηση
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Απάντηση
It is greater than the weight. Upward net force requires N - mg > 0.
Κάρτα 60
Ερώτηση
What does a spring constant k measure, and what is its SI unit?
Απάντηση
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Κάρτα 61
Ερώτηση
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Απάντηση
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Κάρτα 62
Ερώτηση
What provides centripetal force?
Απάντηση
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Κάρτα 63
Ερώτηση
How is near-surface gravitational field strength related to weight?
Απάντηση
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Κάρτα 64
Ερώτηση
How is weight resolved on an incline of angle θ measured from horizontal?
Απάντηση
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Κάρτα 65
Ερώτηση
What does Newton's third law say about an interaction between objects A and B?
Απάντηση
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Κάρτα 66
Ερώτηση
What does signed tangential acceleration describe during circular motion?
Απάντηση
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Κάρτα 67
Ερώτηση
What happens to gravitational force if the separation between two point masses doubles?
Απάντηση
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Κάρτα 68
Ερώτηση
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Απάντηση
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Κάρτα 69
Ερώτηση
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Απάντηση
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Κάρτα 70
Ερώτηση
Which tension components act for a conical pendulum?
Απάντηση
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Κάρτα 71
Ερώτηση
What does apparent weight measure for an object supported by one surface?
Απάντηση
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Κάρτα 72
Ερώτηση
How are several forces combined to find net force?
Απάντηση
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Κάρτα 73
Ερώτηση
Why is tension uniform along one continuous ideal string?
Απάντηση
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Κάρτα 74
Ερώτηση
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Απάντηση
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Κάρτα 75
Ερώτηση
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Απάντηση
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Κάρτα 76
Ερώτηση
For the same net force, what happens to acceleration if mass doubles?
Απάντηση
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Κάρτα 77
Ερώτηση
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Απάντηση
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Κάρτα 78
Ερώτηση
How are radial and tangential acceleration combined when circular speed changes?
Απάντηση
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Κάρτα 79
Ερώτηση
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Απάντηση
It is twice as large. Surface field strength follows g = GM/R².
Κάρτα 80
Ερώτηση
Does a force have to point in the direction of motion?
Απάντηση
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Κάρτα 81
Ερώτηση
Where is the center of mass of a uniform object with a symmetric mass distribution?
Απάντηση
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Κάρτα 82
Ερώτηση
How are speed, period, and frequency related in uniform circular motion?
Απάντηση
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Κάρτα 83
Ερώτηση
Why is an object apparently weightless in free fall?
Απάντηση
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Κάρτα 84
Ερώτηση
Can forces balance along one axis while an object accelerates along another?
Απάντηση
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Κάρτα 85
Ερώτηση
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Απάντηση
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Κάρτα 86
Ερώτηση
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Απάντηση
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Κάρτα 87
Ερώτηση
What motion results when the net force on an object is zero in an inertial frame?
Απάντηση
Constant velocity. Rest is the special case with constant velocity equal to zero.
Κάρτα 88
Ερώτηση
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Απάντηση
4 m/s². Use a = ΣF/m = 12/3.
Κάρτα 89
Ερώτηση
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Απάντηση
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Κάρτα 90
Ερώτηση
Does friction in the simple dry-friction model depend on apparent contact area?
Απάντηση
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Κάρτα 91
Ερώτηση
When should Hooke's-law predictions be treated cautiously?
Απάντηση
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Κάρτα 92
Ερώτηση
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Απάντηση
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Κάρτα 93
Ερώτηση
Why do internal forces cancel when finding the net force on a complete system?
Απάντηση
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Κάρτα 94
Ερώτηση
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Απάντηση
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Κάρτα 95
Ερώτηση
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Απάντηση
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Κάρτα 96
Ερώτηση
What does inertia describe?
Απάντηση
An object's resistance to changes in velocity. Mass measures translational inertia.
Κάρτα 97
Ερώτηση
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Απάντηση
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Κάρτα 98
Ερώτηση
Does zero net force mean no forces act?
Απάντηση
No. Several forces can act and cancel vectorially.
Κάρτα 99
Ερώτηση
What is the common model for kinetic-friction magnitude?
Απάντηση
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Κάρτα 100
Ερώτηση
How could hanging masses measure the spring constant of one ideal spring?
Απάντηση
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Κάρτα 101
Ερώτηση
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Απάντηση
It becomes four times as large. F_in = mv²/r depends on speed squared.
Κάρτα 102
Ερώτηση
Where is the center of mass of two point masses on an x-axis?
Απάντηση
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Κάρτα 103
Ερώτηση
Why must net force, rather than one selected force, be used in ΣF = ma?
Απάντηση
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Κάρτα 104
Ερώτηση
Why can tension vary along a hanging chain with nonnegligible mass?
Απάντηση
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Κάρτα 105
Ερώτηση
What makes a reference frame inertial?
Απάντηση
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Κάρτα 106
Ερώτηση
How could carts test the proportionality between acceleration and net force?
Απάντηση
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Κάρτα 107
Ερώτηση
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Απάντηση
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Κάρτα 108
Ερώτηση
Which direction does kinetic friction act?
Απάντηση
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Κάρτα 109
Ερώτηση
What does the slope of a spring-force-versus-displacement graph give?
Απάντηση
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Κάρτα 110
Ερώτηση
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Απάντηση
v_min = √(gr). At the threshold, the support force or tension is zero.
Κάρτα 111
Ερώτηση
What is translational kinetic energy?
Απάντηση
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Κάρτα 112
Ερώτηση
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Απάντηση
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Κάρτα 113
Ερώτηση
What does power measure?
Απάντηση
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Κάρτα 114
Ερώτηση
What does conservation of energy say for an isolated system?
Απάντηση
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Κάρτα 115
Ερώτηση
Can translational kinetic energy be negative?
Απάντηση
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Κάρτα 116
Ερώτηση
What does negative work by a force mean?
Απάντηση
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Κάρτα 117
Ερώτηση
What is the near-surface change in gravitational potential energy?
Απάντηση
ΔU_g = mgΔy. It applies when g can be treated as constant.
Κάρτα 118
Ερώτηση
When is a chosen system's mechanical energy K + U conserved?
Απάντηση
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Κάρτα 119
Ερώτηση
What is the SI unit of power?
Απάντηση
The watt, W. One watt equals one joule per second.
Κάρτα 120
Ερώτηση
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Απάντηση
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Κάρτα 121
Ερώτηση
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Απάντηση
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Κάρτα 122
Ερώτηση
Does choosing a different zero level for potential energy change physical predictions?
Απάντηση
No. Only potential-energy differences enter measurable energy changes.
Κάρτα 123
Ερώτηση
Can an engine do the same work with different average power?
Απάντηση
Yes. Doing the same work in less time requires greater average power.
Κάρτα 124
Ερώτηση
When does a constant nonzero force do zero work over an interval?
Απάντηση
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Κάρτα 125
Ερώτηση
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Απάντηση
No. With only gravity doing work, the potential-energy change depends on height, not path.
Κάρτα 126
Ερώτηση
How does translational kinetic energy change if speed doubles at constant mass?
Απάντηση
It becomes four times as large. Kinetic energy depends on v².
Κάρτα 127
Ερώτηση
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Απάντηση
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Κάρτα 128
Ερώτηση
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Απάντηση
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Κάρτα 129
Ερώτηση
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Απάντηση
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Κάρτα 130
Ερώτηση
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Απάντηση
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Κάρτα 131
Ερώτηση
A machine transfers 600 J in 3 s. What is its average power?
Απάντηση
200 W. Divide energy transferred by elapsed time.
Κάρτα 132
Ερώτηση
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Απάντηση
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Κάρτα 133
Ερώτηση
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Απάντηση
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Κάρτα 134
Ερώτηση
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Απάντηση
They are equal. Kinetic energy uses speed and has no direction.
Κάρτα 135
Ερώτηση
What makes work by a conservative force path independent?
Απάντηση
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Κάρτα 136
Ερώτηση
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Απάντηση
30 J. Here θ = 0, so W = Fd = 10×3.
Κάρτα 137
Ερώτηση
How is total potential energy built for a system with several interacting pairs?
Απάντηση
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Κάρτα 138
Ερώτηση
How should external work appear in an energy equation?
Απάντηση
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Κάρτα 139
Ερώτηση
How does a spring launch problem combine energy forms?
Απάντηση
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Κάρτα 140
Ερώτηση
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Απάντηση
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Κάρτα 141
Ερώτηση
How does translational kinetic energy change if mass triples at constant speed?
Απάντηση
It triples. Kinetic energy is directly proportional to mass.
Κάρτα 142
Ερώτηση
How much net work does a conservative force do around a path that returns to the initial configuration?
Απάντηση
Zero. The initial and final potential energies are the same.
Κάρτα 143
Ερώτηση
Where is stable equilibrium on a potential-energy-versus-position graph?
Απάντηση
At a local minimum. Small displacements produce forces that point back toward the minimum.
Κάρτα 144
Ερώτηση
Which displacement belongs in the work done by a force on a rigid object?
Απάντηση
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Κάρτα 145
Ερώτηση
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Απάντηση
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Κάρτα 146
Ερώτηση
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Απάντηση
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Κάρτα 147
Ερώτηση
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Απάντηση
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Κάρτα 148
Ερώτηση
How can force-sensor data measure work when force changes as its point of application moves?
Απάντηση
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Κάρτα 149
Ερώτηση
Why is potential energy assigned to a system rather than one isolated object?
Απάντηση
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Κάρτα 150
Ερώτηση
How can work by a nonconservative force depend on path?
Απάντηση
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Κάρτα 151
Ερώτηση
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Απάντηση
9 J. K = ½(2)(3²) = 9 J.
Κάρτα 152
Ερώτηση
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Απάντηση
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Κάρτα 153
Ερώτηση
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Απάντηση
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Κάρτα 154
Ερώτηση
Why are energy bar charts useful?
Απάντηση
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Κάρτα 155
Ερώτηση
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Απάντηση
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Κάρτα 156
Ερώτηση
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Απάντηση
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Κάρτα 157
Ερώτηση
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Απάντηση
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Κάρτα 158
Ερώτηση
What does a steep potential-energy graph imply about force magnitude in one dimension?
Απάντηση
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Κάρτα 159
Ερώτηση
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Απάντηση
10 J. U_s = ½(80)(0.50²).
Κάρτα 160
Ερώτηση
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Απάντηση
200 W. P = Fv_point = 50 × 4.
Κάρτα 161
Ερώτηση
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Απάντηση
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Κάρτα 162
Ερώτηση
Does an object's translational kinetic energy depend on the reference frame?
Απάντηση
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Κάρτα 163
Ερώτηση
Why can work depend on the system boundary?
Απάντηση
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Κάρτα 164
Ερώτηση
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Απάντηση
12 J. The signed area is ½×4×6.
Κάρτα 165
Ερώτηση
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Απάντηση
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Κάρτα 166
Ερώτηση
What is the clearest first step in an energy-conservation problem?
Απάντηση
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Κάρτα 167
Ερώτηση
Why can energy methods solve some problems without finding time?
Απάντηση
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Κάρτα 168
Ερώτηση
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Απάντηση
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Κάρτα 169
Ερώτηση
What is the SI unit of kinetic energy?
Απάντηση
The joule, J. One joule equals 1 kg·m²/s².
Κάρτα 170
Ερώτηση
How is work by a conservative force related to potential-energy change?
Απάντηση
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Κάρτα 171
Ερώτηση
Where is unstable equilibrium on a potential-energy-versus-position graph?
Απάντηση
At a local maximum. A small displacement produces a force that pushes the system farther away.
Κάρτα 172
Ερώτηση
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Απάντηση
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Κάρτα 173
Ερώτηση
Why should thermal energy not be written as a force?
Απάντηση
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Κάρτα 174
Ερώτηση
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Απάντηση
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Κάρτα 175
Ερώτηση
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Απάντηση
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Κάρτα 176
Ερώτηση
What is linear momentum?
Απάντηση
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Κάρτα 177
Ερώτηση
How is a multi-object system's total momentum found?
Απάντηση
Add every object's momentum as a vector. In one dimension, add signed values.
Κάρτα 178
Ερώτηση
For a chosen object or system, what is external impulse?
Απάντηση
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Κάρτα 179
Ερώτηση
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Απάντηση
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Κάρτα 180
Ερώτηση
Why can two objects bounce apart yet still collide inelastically?
Απάντηση
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Κάρτα 181
Ερώτηση
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Απάντηση
+12 kg·m/s. p = mv = 3 × 4.
Κάρτα 182
Ερώτηση
Why can momentum be negative while kinetic energy cannot?
Απάντηση
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Κάρτα 183
Ερώτηση
When is a system's total linear momentum conserved?
Απάντηση
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Κάρτα 184
Ερώτηση
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Απάντηση
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Κάρτα 185
Ερώτηση
Can total kinetic energy increase in an explosion?
Απάντηση
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Κάρτα 186
Ερώτηση
How is total momentum related to center-of-mass velocity?
Απάντηση
p_total = Mv_cm. M is the system's total mass.
Κάρτα 187
Ερώτηση
How does a nonzero external impulse affect system momentum?
Απάντηση
It changes total momentum by that impulse. J_external = Δp_system.
Κάρτα 188
Ερώτηση
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Απάντηση
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Κάρτα 189
Ερώτηση
What are equivalent SI units for impulse?
Απάντηση
N·s and kg·m/s. Both represent a change in momentum.
Κάρτα 190
Ερώτηση
What defines an elastic collision?
Απάντηση
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Κάρτα 191
Ερώτηση
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Απάντηση
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Κάρτα 192
Ερώτηση
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Απάντηση
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Κάρτα 193
Ερώτηση
Why must momentum signs be kept through an impulse calculation?
Απάντηση
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Κάρτα 194
Ερώτηση
What defines a perfectly inelastic collision?
Απάντηση
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Κάρτα 195
Ερώτηση
Why can momentum be conserved during a collision even when large forces act?
Απάντηση
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Κάρτα 196
Ερώτηση
Two objects have equal speed. Which has the larger momentum magnitude?
Απάντηση
The object with larger mass. At equal speed, momentum is proportional to mass.
Κάρτα 197
Ερώτηση
How is momentum conservation written for a two-dimensional isolated interaction?
Απάντηση
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Κάρτα 198
Ερώτηση
For a chosen object or system, how is average net external force related to impulse?
Απάντηση
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Κάρτα 199
Ερώτηση
Which conservation law alone can determine the shared final velocity of a sticking collision?
Απάντηση
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Κάρτα 200
Ερώτηση
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Απάντηση
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
400 κάρτες
AP Physics 1 Flashcards: Complete 8-Unit Course Review
Μελετήστε αυτήν τη δέσμη δωρεάν
Το Nibomo ανοίγει για να ξεκινήσετε τη μελέτη.
Κάρτα 201
Ερώτηση
If external impulse during a collision is small but not zero, what should experimental data show?
Απάντηση
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Κάρτα 202
Ερώτηση
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Απάντηση
It does not change. Impulse depends on total signed area, not peak force alone.
Κάρτα 203
Ερώτηση
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Απάντηση
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Κάρτα 204
Ερώτηση
How can a nearly frictionless cart track improve a momentum-conservation test?
Απάντηση
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Κάρτα 205
Ερώτηση
How does an object's momentum change if its speed doubles at constant mass?
Απάντηση
Its momentum magnitude doubles. Momentum depends linearly on speed.
Κάρτα 206
Ερώτηση
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Απάντηση
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Κάρτα 207
Ερώτηση
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Απάντηση
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Κάρτα 208
Ερώτηση
Why is sticking evidence of an inelastic collision?
Απάντηση
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Κάρτα 209
Ερώτηση
Can a moving two-object system have zero total momentum?
Απάντηση
Yes. Equal and opposite momenta cancel even though each object is moving.
Κάρτα 210
Ερώτηση
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Απάντηση
3 N·s in the force direction. Multiply the net external force by the interaction time.
Κάρτα 211
Ερώτηση
What does a momentum-versus-velocity graph's slope represent for one object?
Απάντηση
Its mass. The relationship p = mv is linear through the origin.
Κάρτα 212
Ερώτηση
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Απάντηση
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Κάρτα 213
Ερώτηση
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Απάντηση
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Κάρτα 214
Ερώτηση
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Απάντηση
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Κάρτα 215
Ερώτηση
What remains conserved in an isolated inelastic collision?
Απάντηση
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Κάρτα 216
Ερώτηση
Why does choosing both colliding objects as the system simplify momentum analysis?
Απάντηση
Their contact forces become internal. Only external impulse can change the system total.
Κάρτα 217
Ερώτηση
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Απάντηση
Net external force. A steeper slope means a larger force in the slope's signed direction.
Κάρτα 218
Ερώτηση
Why do airbags reduce injury force during a stop?
Απάντηση
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Κάρτα 219
Ερώτηση
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Απάντηση
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Κάρτα 220
Ερώτηση
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Απάντηση
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Κάρτα 221
Ερώτηση
What is angular displacement?
Απάντηση
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Κάρτα 222
Ερώτηση
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Απάντηση
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Κάρτα 223
Ερώτηση
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Απάντηση
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Κάρτα 224
Ερώτηση
What does rotational inertia measure?
Απάντηση
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Κάρτα 225
Ερώτηση
What is the lever arm in a torque calculation?
Απάντηση
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Κάρτα 226
Ερώτηση
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Απάντηση
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Κάρτα 227
Ερώτηση
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Απάντηση
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Κάρτα 228
Ερώτηση
How is rotational inertia found for a collection of point masses?
Απάντηση
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Κάρτα 229
Ερώτηση
What determines the magnitude of torque from one force about a chosen axis?
Απάντηση
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Κάρτα 230
Ερώτηση
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Απάντηση
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Κάρτα 231
Ερώτηση
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Απάντηση
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Κάρτα 232
Ερώτηση
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Απάντηση
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Κάρτα 233
Ερώτηση
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Απάντηση
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Κάρτα 234
Ερώτηση
How are clockwise and counterclockwise torques combined?
Απάντηση
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Κάρτα 235
Ερώτηση
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Απάντηση
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Κάρτα 236
Ερώτηση
Why must an axis be named when stating rotational inertia?
Απάντηση
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Κάρτα 237
Ερώτηση
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Απάντηση
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Κάρτα 238
Ερώτηση
Why is torque's unit N·m not called a joule?
Απάντηση
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Κάρτα 239
Ερώτηση
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Απάντηση
4 rad/s². |α| = |Στ_external|/I = 8/2.
Κάρτα 240
Ερώτηση
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Απάντηση
At the object's center of mass. That single force gives the same net gravitational force and torque.
Κάρτα 241
Ερώτηση
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Απάντηση
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Κάρτα 242
Ερώτηση
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Απάντηση
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Κάρτα 243
Ερώτηση
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Απάντηση
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Κάρτα 244
Ερώτηση
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Απάντηση
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Κάρτα 245
Ερώτηση
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Απάντηση
The hoop. More of its mass lies far from the axis.
Κάρτα 246
Ερώτηση
Why can a rigid object have zero net external force but nonzero net external torque?
Απάντηση
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Κάρτα 247
Ερώτηση
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Απάντηση
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Κάρτα 248
Ερώτηση
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Απάντηση
4 N·m. τ = rF for a perpendicular force.
Κάρτα 249
Ερώτηση
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Απάντηση
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Κάρτα 250
Ερώτηση
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Απάντηση
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Κάρτα 251
Ερώτηση
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Απάντηση
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Κάρτα 252
Ερώτηση
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Απάντηση
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Κάρτα 253
Ερώτηση
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Απάντηση
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Κάρτα 254
Ερώτηση
Does moving the chosen pivot change an individual force's torque?
Απάντηση
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Κάρτα 255
Ερώτηση
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Απάντηση
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Κάρτα 256
Ερώτηση
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Απάντηση
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Κάρτα 257
Ερώτηση
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Απάντηση
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Κάρτα 258
Ερώτηση
How could a meterstick experiment test torque balance?
Απάντηση
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Κάρτα 259
Ερώτηση
For uniform rotation at frequency f, what is the angular-speed magnitude?
Απάντηση
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Κάρτα 260
Ερώτηση
Why is choosing the pivot at an unknown support force often useful?
Απάντηση
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Κάρτα 261
Ερώτηση
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Απάντηση
The parallel axis through the center of mass. Any offset adds the positive term Md².
Κάρτα 262
Ερώτηση
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Απάντηση
It becomes one-third as large. For each stated system, α = Στ_external/I.
Κάρτα 263
Ερώτηση
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Απάντηση
3 m/s. v_t = r|ω| = 0.50 × 6.
Κάρτα 264
Ερώτηση
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Απάντηση
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Κάρτα 265
Ερώτηση
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Απάντηση
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Κάρτα 266
Ερώτηση
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Απάντηση
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Κάρτα 267
Ερώτηση
How does moving mass farther from a rotation axis affect rotational inertia?
Απάντηση
It increases rotational inertia strongly. For a point mass, I = mr².
Κάρτα 268
Ερώτηση
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Απάντηση
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Κάρτα 269
Ερώτηση
Why must angular displacement be in radians for Δs = rΔθ?
Απάντηση
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Κάρτα 270
Ερώτηση
When does a nonzero force produce zero torque about an axis?
Απάντηση
When its line of action passes through the axis. The lever arm is then zero.
Κάρτα 271
Ερώτηση
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Απάντηση
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Κάρτα 272
Ερώτηση
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Απάντηση
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Κάρτα 273
Ερώτηση
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Απάντηση
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Κάρτα 274
Ερώτηση
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Απάντηση
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Κάρτα 275
Ερώτηση
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Απάντηση
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Κάρτα 276
Ερώτηση
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Απάντηση
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Κάρτα 277
Ερώτηση
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Απάντηση
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Κάρτα 278
Ερώτηση
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Απάντηση
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Κάρτα 279
Ερώτηση
What is a rigid body's rotational kinetic energy about a fixed axis?
Απάντηση
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Κάρτα 280
Ερώτηση
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Απάντηση
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Κάρτα 281
Ερώτηση
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Απάντηση
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Κάρτα 282
Ερώτηση
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Απάντηση
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Κάρτα 283
Ερώτηση
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Απάντηση
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Κάρτα 284
Ερώτηση
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Απάντηση
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Κάρτα 285
Ερώτηση
Does angular-momentum conservation require rotational kinetic-energy conservation?
Απάντηση
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Κάρτα 286
Ερώτηση
Why do astronauts feel weightless in orbit even though gravity acts on them?
Απάντηση
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Κάρτα 287
Ερώτηση
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Απάντηση
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Κάρτα 288
Ερώτηση
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Απάντηση
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Κάρτα 289
Ερώτηση
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Απάντηση
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Κάρτα 290
Ερώτηση
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Απάντηση
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Κάρτα 291
Ερώτηση
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Απάντηση
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Κάρτα 292
Ερώτηση
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Απάντηση
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Κάρτα 293
Ερώτηση
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Απάντηση
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Κάρτα 294
Ερώτηση
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Απάντηση
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Κάρτα 295
Ερώτηση
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Απάντηση
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Κάρτα 296
Ερώτηση
How does rotational kinetic energy change if angular speed doubles at fixed I?
Απάντηση
It becomes four times as large. Rotational kinetic energy depends on ω².
Κάρτα 297
Ερώτηση
Why should external torque be evaluated about the same axis used for angular momentum?
Απάντηση
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Κάρτα 298
Ερώτηση
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Απάντηση
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Κάρτα 299
Ερώτηση
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Απάντηση
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Κάρτα 300
Ερώτηση
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Απάντηση
v = √(GM/r). Gravity supplies the inward net force.
Κάρτα 301
Ερώτηση
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Απάντηση
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Κάρτα 302
Ερώτηση
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Απάντηση
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Κάρτα 303
Ερώτηση
Why can't the rolling condition alone prove that friction points uphill or downhill?
Απάντηση
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Κάρτα 304
Ερώτηση
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Απάντηση
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Κάρτα 305
Ερώτηση
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Απάντηση
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Κάρτα 306
Ερώτηση
What makes simple harmonic motion a special kind of periodic motion?
Απάντηση
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Κάρτα 307
Ερώτηση
What does the amplitude of an SHM displacement graph represent?
Απάντηση
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Κάρτα 308
Ερώτηση
How are period and frequency related?
Απάντηση
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Κάρτα 309
Ερώτηση
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Απάντηση
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Κάρτα 310
Ερώτηση
For one-dimensional SHM, what is the equilibrium position?
Απάντηση
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Κάρτα 311
Ερώτηση
How far apart in phase are displacement and velocity in SHM?
Απάντηση
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Κάρτα 312
Ερώτηση
When can a simple pendulum be modeled as SHM?
Απάντηση
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Κάρτα 313
Ερώτηση
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Απάντηση
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Κάρτα 314
Ερώτηση
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Απάντηση
U_s = ½kx². It has the same value at +x and -x.
Κάρτα 315
Ερώτηση
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Απάντηση
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Κάρτα 316
Ερώτηση
How does a spring oscillator's period change if k becomes four times as large?
Απάντηση
The period is halved. T is proportional to 1/√k.
Κάρτα 317
Ερώτηση
How are acceleration and displacement related along the SHM coordinate?
Απάντηση
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Κάρτα 318
Ερώτηση
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Απάντηση
E = ½kA². It stays constant when dissipative effects are negligible.
Κάρτα 319
Ερώτηση
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Απάντηση
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Κάρτα 320
Ερώτηση
How can frequency be read from an oscillation-versus-time graph?
Απάντηση
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Κάρτα 321
Ερώτηση
Why does an ideal mass–spring oscillator exhibit SHM?
Απάντηση
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Κάρτα 322
Ερώτηση
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Απάντηση
1 J. E = ½(50)(0.20²).
Κάρτα 323
Ερώτηση
At maximum positive displacement in SHM, what are velocity and acceleration?
Απάντηση
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
Κάρτα 324
Ερώτηση
How does a spring oscillator's period change if its mass becomes four times as large?
Απάντηση
The period doubles. T is proportional to √m.
Κάρτα 325
Ερώτηση
Why isn't uniform circular motion itself one-dimensional SHM?
Απάντηση
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
Κάρτα 326
Ερώτηση
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Απάντηση
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
Κάρτα 327
Ερώτηση
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Απάντηση
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
Κάρτα 328
Ερώτηση
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Απάντηση
No within the ideal SHM model. The period depends on system parameters, not amplitude.
Κάρτα 329
Ερώτηση
How is maximum speed related to amplitude and angular frequency in SHM?
Απάντηση
v_max = ωA. Maximum speed occurs at equilibrium.
Κάρτα 330
Ερώτηση
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Απάντηση
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
Κάρτα 331
Ερώτηση
How far apart in phase are displacement and acceleration in SHM?
Απάντηση
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
Κάρτα 332
Ερώτηση
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Απάντηση
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
Κάρτα 333
Ερώτηση
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Απάντηση
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
Κάρτα 334
Ερώτηση
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Απάντηση
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
Κάρτα 335
Ερώτηση
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Απάντηση
Both are positive. Motion and restoring acceleration point right toward equilibrium.
Κάρτα 336
Ερώτηση
How does a pendulum's period change if its length becomes nine times as large?
Απάντηση
The period triples. T is proportional to √L.
Κάρτα 337
Ερώτηση
If SHM starts at maximum positive displacement, what equation gives its position?
Απάντηση
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
Κάρτα 338
Ερώτηση
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Απάντηση
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
Κάρτα 339
Ερώτηση
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Απάντηση
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
Κάρτα 340
Ερώτηση
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Απάντηση
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
Κάρτα 341
Ερώτηση
What makes a substance a fluid?
Απάντηση
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
Κάρτα 342
Ερώτηση
What is mass density?
Απάντηση
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
Κάρτα 343
Ερώτηση
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Απάντηση
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
Κάρτα 344
Ερώτηση
What is volume flow rate?
Απάντηση
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
Κάρτα 345
Ερώτηση
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Απάντηση
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
Κάρτα 346
Ερώτηση
What conditions support the basic Bernoulli model used here?
Απάντηση
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
Κάρτα 347
Ερώτηση
Under the ideal model, how does average density predict whether a free object floats or sinks?
Απάντηση
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
Κάρτα 348
Ερώτηση
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Απάντηση
Q = Av. This gives the volume crossing a completely filled pipe section per time.
Κάρτα 349
Ερώτηση
How does a static fluid exert force on a surface?
Απάντηση
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
Κάρτα 350
Ερώτηση
How does pressure change with depth in a static uniform fluid?
Απάντηση
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
Κάρτα 351
Ερώτηση
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Απάντηση
F_B = mg. The object's weight equals the weight of the fluid it displaces.
Κάρτα 352
Ερώτηση
What is the continuity equation for steady incompressible flow in one filled pipe?
Απάντηση
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
Κάρτα 353
Ερώτηση
Why does a static fluid produce an upward buoyant force?
Απάντηση
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
Κάρτα 354
Ερώτηση
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Απάντηση
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
Κάρτα 355
Ερώτηση
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Απάντηση
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
Κάρτα 356
Ερώτηση
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Απάντηση
0.060 m³/s. Q = Av = 0.020×3.
Κάρτα 357
Ερώτηση
What does the slope of a mass-versus-volume graph represent for one uniform material?
Απάντηση
Density. Since m = ρV, the line's slope is ρ.
Κάρτα 358
Ερώτηση
How do gauge pressure and absolute pressure differ?
Απάντηση
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
Κάρτα 359
Ερώτηση
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Απάντηση
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
Κάρτα 360
Ερώτηση
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Απάντηση
It doubles. Continuity keeps Av constant.
Κάρτα 361
Ερώτηση
When does a fluid element's velocity change?
Απάντηση
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
Κάρτα 362
Ερώτηση
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Απάντηση
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
Κάρτα 363
Ερώτηση
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Απάντηση
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
Κάρτα 364
Ερώτηση
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Απάντηση
It becomes four times as large. Area is proportional to radius squared.
Κάρτα 365
Ερώτηση
What does Pascal's principle say for a confined incompressible fluid at rest?
Απάντηση
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
Κάρτα 366
Ερώτηση
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Απάντηση
ρg. For known g, the slope can determine fluid density.
Κάρτα 367
Ερώτηση
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Απάντηση
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
Κάρτα 368
Ερώτηση
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Απάντηση
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
Κάρτα 369
Ερώτηση
What physical quantity does each term in P + ½ρv² + ρgy share?
Απάντηση
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
Κάρτα 370
Ερώτηση
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Απάντηση
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
Κάρτα 371
Ερώτηση
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Απάντηση
0.75, or 75%. Use the density ratio for floating equilibrium.
Κάρτα 372
Ερώτηση
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Απάντηση
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
Κάρτα 373
Ερώτηση
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Απάντηση
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
Κάρτα 374
Ερώτηση
Why does the same force create more pressure on a smaller area?
Απάντηση
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
Κάρτα 375
Ερώτηση
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Απάντηση
3.0×10³ kg/m³. Divide mass by volume.
Κάρτα 376
Ερώτηση
What conservation law underlies the continuity equation for incompressible flow?
Απάντηση
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
Κάρτα 377
Ερώτηση
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Απάντηση
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
Κάρτα 378
Ερώτηση
What is the SI unit of pressure?
Απάντηση
The pascal, Pa. One pascal equals 1 N/m².
Κάρτα 379
Ερώτηση
How do pressures compare at the same horizontal level in one connected static fluid?
Απάντηση
They are equal. Container shape does not change pressure at a fixed elevation.
Κάρτα 380
Ερώτηση
What does specific gravity compare?
Απάντηση
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
Κάρτα 381
Ερώτηση
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Απάντηση
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
Κάρτα 382
Ερώτηση
How does the particle model distinguish a fluid from a rigid solid?
Απάντηση
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
Κάρτα 383
Ερώτηση
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Απάντηση
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
Κάρτα 384
Ερώτηση
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Απάντηση
200 N. F_B = ρgV = 1000×10×0.020.
Κάρτα 385
Ερώτηση
Why can a steel ship float even though steel is denser than water?
Απάντηση
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
Κάρτα 386
Ερώτηση
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Απάντηση
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
Κάρτα 387
Ερώτηση
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Απάντηση
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
Κάρτα 388
Ερώτηση
What does incompressible mean in the introductory ideal-fluid model?
Απάντηση
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
Κάρτα 389
Ερώτηση
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Απάντηση
Pressure is lower at the higher point. P + ρgy remains constant.
Κάρτα 390
Ερώτηση
How can water displacement measure an irregular solid's volume?
Απάντηση
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
Κάρτα 391
Ερώτηση
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Απάντηση
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
Κάρτα 392
Ερώτηση
How can scale readings in air and water determine buoyant force?
Απάντηση
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
Κάρτα 393
Ερώτηση
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Απάντηση
30,000 Pa. P_gauge = ρgh = 1000×10×3.
Κάρτα 394
Ερώτηση
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Απάντηση
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
Κάρτα 395
Ερώτηση
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Απάντηση
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
Κάρτα 396
Ερώτηση
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Απάντηση
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
Κάρτα 397
Ερώτηση
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Απάντηση
5,000 Pa. P = F/A = 200/0.040.
Κάρτα 398
Ερώτηση
Why doesn't a hydraulic lift multiply energy?
Απάντηση
The large-force piston moves a shorter distance. Ideally, input work equals output work.
Κάρτα 399
Ερώτηση
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Απάντηση
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
Κάρτα 400
Ερώτηση
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Απάντηση
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

An orange sphere traces an orbital path between a wave, a rotating disc, and a fluid ripple on a dark grid.

400 κάρτες