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.

Tác giả Open Study Contributor

Về bộ thẻ này

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.

Thẻ trong bộ này

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

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

400 thẻ