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.

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การ์ด: 400 การ์ด
เวอร์ชัน: 3
เผยแพร่เมื่อ: 26 สิงหาคม 2569
อัปเดตล่าสุด: 10 กันยายน 2569
สัญญาอนุญาต: Common knowledge · CC0 1.0
ภาษาของผู้เรียน: en
วิชา: Physics
ระดับ: AP Physics 1
แท็ก: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

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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.

การ์ดในเด็คนี้

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

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