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.

نوشتهٔ Open Study Contributor

این دسته را رایگان مطالعه کنید

Nibomo باز می‌شود تا بتوانید مطالعه را شروع کنید.

جزئیات دسته

کارت‌ها: ۴۰۰ کارت
نسخه: ۳
منتشرشده: ۴ شهریور ۱۴۰۵
آخرین به‌روزرسانی: ۱۹ شهریور ۱۴۰۵
مجوز: Common knowledge · CC0 1.0
زبان‌های مخاطب: en
موضوع: Physics
سطح: AP Physics 1
برچسب‌ها: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

دسته‌های مشابه

دربارهٔ این دسته

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.

کارت‌های این دسته

کارت ۱
پرسش
What separates a vector quantity from a scalar quantity?
پاسخ
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
کارت ۲
پرسش
When is the point-object model useful in kinematics?
پاسخ
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
کارت ۳
پرسش
When may the constant-acceleration kinematic equations be used?
پاسخ
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
کارت ۴
پرسش
Why must a velocity statement name or imply a reference frame?
پاسخ
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
کارت ۵
پرسش
Why can horizontal and vertical projectile motion be analyzed separately?
پاسخ
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
کارت ۶
پرسش
Can an object have zero velocity and nonzero acceleration at one instant?
پاسخ
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
کارت ۷
پرسش
A runner completes one lap and returns to the start. How do distance and displacement compare?
پاسخ
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
کارت ۸
پرسش
What makes a reference frame convenient for a motion problem?
پاسخ
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
کارت ۹
پرسش
How are the components of a launch velocity v at angle θ found?
پاسخ
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
کارت ۱۰
پرسش
What does average velocity measure?
پاسخ
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
کارت ۱۱
پرسش
Do a vector's magnitude and its component use different SI units?
پاسخ
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
کارت ۱۲
پرسش
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
پاسخ
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.
کارت ۱۳
پرسش
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
پاسخ
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
کارت ۱۴
پرسش
What does average acceleration measure?
پاسخ
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
کارت ۱۵
پرسش
What does a negative one-dimensional vector component mean?
پاسخ
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
کارت ۱۶
پرسش
For constant acceleration, what does v = v₀ + at retrieve?
پاسخ
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
کارت ۱۷
پرسش
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
پاسخ
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.
کارت ۱۸
پرسش
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
پاسخ
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
کارت ۱۹
پرسش
What does the slope of a position-versus-time graph represent?
پاسخ
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
کارت ۲۰
پرسش
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?
پاسخ
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.
کارت ۲۱
پرسش
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
پاسخ
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
کارت ۲۲
پرسش
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
پاسخ
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
کارت ۲۳
پرسش
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
پاسخ
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
کارت ۲۴
پرسش
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
پاسخ
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
کارت ۲۵
پرسش
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
پاسخ
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
کارت ۲۶
پرسش
Why can average speed differ from the magnitude of average velocity?
پاسخ
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
کارت ۲۷
پرسش
What does the slope of a velocity-versus-time graph represent?
پاسخ
Acceleration. The slope's units are (m/s)/s = m/s².
کارت ۲۸
پرسش
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
پاسخ
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
کارت ۲۹
پرسش
Does projectile mass affect the ideal trajectory when air resistance is negligible?
پاسخ
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
کارت ۳۰
پرسش
Can an object have nonzero velocity and zero acceleration?
پاسخ
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
کارت ۳۱
پرسش
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
پاسخ
Position x versus t². Its slope is ½a when the initial velocity is zero.
کارت ۳۲
پرسش
What does signed area under a velocity-versus-time graph represent?
پاسخ
Displacement. Area below the time axis contributes negative displacement.
کارت ۳۳
پرسش
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
پاسخ
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
کارت ۳۴
پرسش
How can a motion sensor test whether a cart moves at constant velocity?
پاسخ
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
کارت ۳۵
پرسش
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
پاسخ
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
کارت ۳۶
پرسش
Which constant-acceleration equation connects speed and displacement without using time?
پاسخ
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
کارت ۳۷
پرسش
How could video data test the independence of projectile components?
پاسخ
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.
کارت ۳۸
پرسش
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
پاسخ
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
کارت ۳۹
پرسش
How can average velocity over a very short interval approximate instantaneous velocity?
پاسخ
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
کارت ۴۰
پرسش
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
پاسخ
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
کارت ۴۱
پرسش
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
پاسخ
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.
کارت ۴۲
پرسش
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
پاسخ
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.
کارت ۴۳
پرسش
What does signed area under an acceleration-versus-time graph represent?
پاسخ
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
کارت ۴۴
پرسش
How is one-dimensional relative velocity calculated for two objects A and B?
پاسخ
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
کارت ۴۵
پرسش
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
پاسخ
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
کارت ۴۶
پرسش
What does choosing a system boundary decide in a mechanics problem?
پاسخ
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
کارت ۴۷
پرسش
What belongs on a free-body diagram for one chosen object?
پاسخ
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
کارت ۴۸
پرسش
What assumptions define the ideal-string model used in introductory algebra-based physics?
پاسخ
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
کارت ۴۹
پرسش
What does translational equilibrium require?
پاسخ
Zero net force. The object may be at rest or move with constant velocity.
کارت ۵۰
پرسش
In an inertial frame, how does Newton's second law connect force and motion?
پاسخ
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
کارت ۵۱
پرسش
How do mass and weight differ?
پاسخ
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
کارت ۵۲
پرسش
How does static friction choose its magnitude before slipping begins?
پاسخ
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
کارت ۵۳
پرسش
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?
پاسخ
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
کارت ۵۴
پرسش
What direction does centripetal acceleration point in circular motion?
پاسخ
Toward the circle's center. It changes the velocity's direction even when speed is constant.
کارت ۵۵
پرسش
What is the gravitational force magnitude between two point masses?
پاسخ
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
کارت ۵۶
پرسش
Why isn't the normal force always equal to an object's weight?
پاسخ
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
کارت ۵۷
پرسش
What determines a friction coefficient in the simple model?
پاسخ
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
کارت ۵۸
پرسش
What is the centripetal-acceleration magnitude for speed v and radius r?
پاسخ
a_c = v²/r. It is a kinematic requirement, not a separate force.
کارت ۵۹
پرسش
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
پاسخ
It is greater than the weight. Upward net force requires N - mg > 0.
کارت ۶۰
پرسش
What does a spring constant k measure, and what is its SI unit?
پاسخ
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
کارت ۶۱
پرسش
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
پاسخ
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
کارت ۶۲
پرسش
What provides centripetal force?
پاسخ
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
کارت ۶۳
پرسش
How is near-surface gravitational field strength related to weight?
پاسخ
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
کارت ۶۴
پرسش
How is weight resolved on an incline of angle θ measured from horizontal?
پاسخ
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
کارت ۶۵
پرسش
What does Newton's third law say about an interaction between objects A and B?
پاسخ
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
کارت ۶۶
پرسش
What does signed tangential acceleration describe during circular motion?
پاسخ
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.
کارت ۶۷
پرسش
What happens to gravitational force if the separation between two point masses doubles?
پاسخ
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
کارت ۶۸
پرسش
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
پاسخ
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
کارت ۶۹
پرسش
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
پاسخ
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.
کارت ۷۰
پرسش
Which tension components act for a conical pendulum?
پاسخ
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
کارت ۷۱
پرسش
What does apparent weight measure for an object supported by one surface?
پاسخ
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
کارت ۷۲
پرسش
How are several forces combined to find net force?
پاسخ
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
کارت ۷۳
پرسش
Why is tension uniform along one continuous ideal string?
پاسخ
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.
کارت ۷۴
پرسش
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
پاسخ
4 N. F_in = mv²/r = 0.5 × 16 / 2.
کارت ۷۵
پرسش
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
پاسخ
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
کارت ۷۶
پرسش
For the same net force, what happens to acceleration if mass doubles?
پاسخ
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
کارت ۷۷
پرسش
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
پاسخ
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
کارت ۷۸
پرسش
How are radial and tangential acceleration combined when circular speed changes?
پاسخ
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
کارت ۷۹
پرسش
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
پاسخ
It is twice as large. Surface field strength follows g = GM/R².
کارت ۸۰
پرسش
Does a force have to point in the direction of motion?
پاسخ
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
کارت ۸۱
پرسش
Where is the center of mass of a uniform object with a symmetric mass distribution?
پاسخ
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
کارت ۸۲
پرسش
How are speed, period, and frequency related in uniform circular motion?
پاسخ
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
کارت ۸۳
پرسش
Why is an object apparently weightless in free fall?
پاسخ
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
کارت ۸۴
پرسش
Can forces balance along one axis while an object accelerates along another?
پاسخ
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
کارت ۸۵
پرسش
Why don't Newton's third-law forces cancel on one object's free-body diagram?
پاسخ
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
کارت ۸۶
پرسش
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
پاسخ
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
کارت ۸۷
پرسش
What motion results when the net force on an object is zero in an inertial frame?
پاسخ
Constant velocity. Rest is the special case with constant velocity equal to zero.
کارت ۸۸
پرسش
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
پاسخ
4 m/s². Use a = ΣF/m = 12/3.
کارت ۸۹
پرسش
What does the observed equivalence of inertial and gravitational mass imply for free fall?
پاسخ
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
کارت ۹۰
پرسش
Does friction in the simple dry-friction model depend on apparent contact area?
پاسخ
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
کارت ۹۱
پرسش
When should Hooke's-law predictions be treated cautiously?
پاسخ
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
کارت ۹۲
پرسش
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
پاسخ
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
کارت ۹۳
پرسش
Why do internal forces cancel when finding the net force on a complete system?
پاسخ
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
کارت ۹۴
پرسش
An elevator moves downward at constant speed. How does the scale reading compare with weight?
پاسخ
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
کارت ۹۵
پرسش
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
پاسخ
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.
کارت ۹۶
پرسش
What does inertia describe?
پاسخ
An object's resistance to changes in velocity. Mass measures translational inertia.
کارت ۹۷
پرسش
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
پاسخ
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
کارت ۹۸
پرسش
Does zero net force mean no forces act?
پاسخ
No. Several forces can act and cancel vectorially.
کارت ۹۹
پرسش
What is the common model for kinetic-friction magnitude?
پاسخ
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
کارت ۱۰۰
پرسش
How could hanging masses measure the spring constant of one ideal spring?
پاسخ
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.
کارت ۱۰۱
پرسش
For the same object at the same circular radius, how does required inward net force change if speed doubles?
پاسخ
It becomes four times as large. F_in = mv²/r depends on speed squared.
کارت ۱۰۲
پرسش
Where is the center of mass of two point masses on an x-axis?
پاسخ
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
کارت ۱۰۳
پرسش
Why must net force, rather than one selected force, be used in ΣF = ma?
پاسخ
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
کارت ۱۰۴
پرسش
Why can tension vary along a hanging chain with nonnegligible mass?
پاسخ
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.
کارت ۱۰۵
پرسش
What makes a reference frame inertial?
پاسخ
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
کارت ۱۰۶
پرسش
How could carts test the proportionality between acceleration and net force?
پاسخ
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
کارت ۱۰۷
پرسش
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?
پاسخ
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
کارت ۱۰۸
پرسش
Which direction does kinetic friction act?
پاسخ
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
کارت ۱۰۹
پرسش
What does the slope of a spring-force-versus-displacement graph give?
پاسخ
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
کارت ۱۱۰
پرسش
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
پاسخ
v_min = √(gr). At the threshold, the support force or tension is zero.
کارت ۱۱۱
پرسش
What is translational kinetic energy?
پاسخ
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
کارت ۱۱۲
پرسش
How is work by a constant force calculated when its point of application undergoes a straight displacement?
پاسخ
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.
کارت ۱۱۳
پرسش
What does power measure?
پاسخ
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
کارت ۱۱۴
پرسش
What does conservation of energy say for an isolated system?
پاسخ
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
کارت ۱۱۵
پرسش
Can translational kinetic energy be negative?
پاسخ
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
کارت ۱۱۶
پرسش
What does negative work by a force mean?
پاسخ
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.
کارت ۱۱۷
پرسش
What is the near-surface change in gravitational potential energy?
پاسخ
ΔU_g = mgΔy. It applies when g can be treated as constant.
کارت ۱۱۸
پرسش
When is a chosen system's mechanical energy K + U conserved?
پاسخ
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.
کارت ۱۱۹
پرسش
What is the SI unit of power?
پاسخ
The watt, W. One watt equals one joule per second.
کارت ۱۲۰
پرسش
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
پاسخ
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.
کارت ۱۲۱
پرسش
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?
پاسخ
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
کارت ۱۲۲
پرسش
Does choosing a different zero level for potential energy change physical predictions?
پاسخ
No. Only potential-energy differences enter measurable energy changes.
کارت ۱۲۳
پرسش
Can an engine do the same work with different average power?
پاسخ
Yes. Doing the same work in less time requires greater average power.
کارت ۱۲۴
پرسش
When does a constant nonzero force do zero work over an interval?
پاسخ
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
کارت ۱۲۵
پرسش
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
پاسخ
No. With only gravity doing work, the potential-energy change depends on height, not path.
کارت ۱۲۶
پرسش
How does translational kinetic energy change if speed doubles at constant mass?
پاسخ
It becomes four times as large. Kinetic energy depends on v².
کارت ۱۲۷
پرسش
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?
پاسخ
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
کارت ۱۲۸
پرسش
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
پاسخ
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
کارت ۱۲۹
پرسش
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?
پاسخ
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
کارت ۱۳۰
پرسش
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
پاسخ
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
کارت ۱۳۱
پرسش
A machine transfers 600 J in 3 s. What is its average power?
پاسخ
200 W. Divide energy transferred by elapsed time.
کارت ۱۳۲
پرسش
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
پاسخ
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
کارت ۱۳۳
پرسش
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
پاسخ
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
کارت ۱۳۴
پرسش
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
پاسخ
They are equal. Kinetic energy uses speed and has no direction.
کارت ۱۳۵
پرسش
What makes work by a conservative force path independent?
پاسخ
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
کارت ۱۳۶
پرسش
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
پاسخ
30 J. Here θ = 0, so W = Fd = 10×3.
کارت ۱۳۷
پرسش
How is total potential energy built for a system with several interacting pairs?
پاسخ
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
کارت ۱۳۸
پرسش
How should external work appear in an energy equation?
پاسخ
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
کارت ۱۳۹
پرسش
How does a spring launch problem combine energy forms?
پاسخ
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
کارت ۱۴۰
پرسش
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
پاسخ
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
کارت ۱۴۱
پرسش
How does translational kinetic energy change if mass triples at constant speed?
پاسخ
It triples. Kinetic energy is directly proportional to mass.
کارت ۱۴۲
پرسش
How much net work does a conservative force do around a path that returns to the initial configuration?
پاسخ
Zero. The initial and final potential energies are the same.
کارت ۱۴۳
پرسش
Where is stable equilibrium on a potential-energy-versus-position graph?
پاسخ
At a local minimum. Small displacements produce forces that point back toward the minimum.
کارت ۱۴۴
پرسش
Which displacement belongs in the work done by a force on a rigid object?
پاسخ
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
کارت ۱۴۵
پرسش
What happens to mechanical energy when kinetic friction acts inside the chosen system?
پاسخ
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
کارت ۱۴۶
پرسش
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?
پاسخ
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
کارت ۱۴۷
پرسش
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
پاسخ
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.
کارت ۱۴۸
پرسش
How can force-sensor data measure work when force changes as its point of application moves?
پاسخ
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.
کارت ۱۴۹
پرسش
Why is potential energy assigned to a system rather than one isolated object?
پاسخ
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
کارت ۱۵۰
پرسش
How can work by a nonconservative force depend on path?
پاسخ
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
کارت ۱۵۱
پرسش
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
پاسخ
9 J. K = ½(2)(3²) = 9 J.
کارت ۱۵۲
پرسش
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?
پاسخ
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
کارت ۱۵۳
پرسش
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
پاسخ
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
کارت ۱۵۴
پرسش
Why are energy bar charts useful?
پاسخ
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
کارت ۱۵۵
پرسش
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?
پاسخ
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.
کارت ۱۵۶
پرسش
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
پاسخ
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
کارت ۱۵۷
پرسش
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
پاسخ
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
کارت ۱۵۸
پرسش
What does a steep potential-energy graph imply about force magnitude in one dimension?
پاسخ
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
کارت ۱۵۹
پرسش
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?
پاسخ
10 J. U_s = ½(80)(0.50²).
کارت ۱۶۰
پرسش
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?
پاسخ
200 W. P = Fv_point = 50 × 4.
کارت ۱۶۱
پرسش
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
پاسخ
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
کارت ۱۶۲
پرسش
Does an object's translational kinetic energy depend on the reference frame?
پاسخ
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
کارت ۱۶۳
پرسش
Why can work depend on the system boundary?
پاسخ
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.
کارت ۱۶۴
پرسش
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?
پاسخ
12 J. The signed area is ½×4×6.
کارت ۱۶۵
پرسش
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
پاسخ
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
کارت ۱۶۶
پرسش
What is the clearest first step in an energy-conservation problem?
پاسخ
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
کارت ۱۶۷
پرسش
Why can energy methods solve some problems without finding time?
پاسخ
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
کارت ۱۶۸
پرسش
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
پاسخ
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.
کارت ۱۶۹
پرسش
What is the SI unit of kinetic energy?
پاسخ
The joule, J. One joule equals 1 kg·m²/s².
کارت ۱۷۰
پرسش
How is work by a conservative force related to potential-energy change?
پاسخ
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
کارت ۱۷۱
پرسش
Where is unstable equilibrium on a potential-energy-versus-position graph?
پاسخ
At a local maximum. A small displacement produces a force that pushes the system farther away.
کارت ۱۷۲
پرسش
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
پاسخ
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.
کارت ۱۷۳
پرسش
Why should thermal energy not be written as a force?
پاسخ
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
کارت ۱۷۴
پرسش
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
پاسخ
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.
کارت ۱۷۵
پرسش
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
پاسخ
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
کارت ۱۷۶
پرسش
What is linear momentum?
پاسخ
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
کارت ۱۷۷
پرسش
How is a multi-object system's total momentum found?
پاسخ
Add every object's momentum as a vector. In one dimension, add signed values.
کارت ۱۷۸
پرسش
For a chosen object or system, what is external impulse?
پاسخ
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
کارت ۱۷۹
پرسش
What experimental uncertainty matters strongly when comparing collision kinetic energies?
پاسخ
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
کارت ۱۸۰
پرسش
Why can two objects bounce apart yet still collide inelastically?
پاسخ
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
کارت ۱۸۱
پرسش
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
پاسخ
+12 kg·m/s. p = mv = 3 × 4.
کارت ۱۸۲
پرسش
Why can momentum be negative while kinetic energy cannot?
پاسخ
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
کارت ۱۸۳
پرسش
When is a system's total linear momentum conserved?
پاسخ
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
کارت ۱۸۴
پرسش
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
پاسخ
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
کارت ۱۸۵
پرسش
Can total kinetic energy increase in an explosion?
پاسخ
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.
کارت ۱۸۶
پرسش
How is total momentum related to center-of-mass velocity?
پاسخ
p_total = Mv_cm. M is the system's total mass.
کارت ۱۸۷
پرسش
How does a nonzero external impulse affect system momentum?
پاسخ
It changes total momentum by that impulse. J_external = Δp_system.
کارت ۱۸۸
پرسش
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
پاسخ
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
کارت ۱۸۹
پرسش
What are equivalent SI units for impulse?
پاسخ
N·s and kg·m/s. Both represent a change in momentum.
کارت ۱۹۰
پرسش
What defines an elastic collision?
پاسخ
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
کارت ۱۹۱
پرسش
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
پاسخ
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.
کارت ۱۹۲
پرسش
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
پاسخ
Left. The person and boat acquire opposite momenta so total momentum remains zero.
کارت ۱۹۳
پرسش
Why must momentum signs be kept through an impulse calculation?
پاسخ
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
کارت ۱۹۴
پرسش
What defines a perfectly inelastic collision?
پاسخ
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
کارت ۱۹۵
پرسش
Why can momentum be conserved during a collision even when large forces act?
پاسخ
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.
کارت ۱۹۶
پرسش
Two objects have equal speed. Which has the larger momentum magnitude?
پاسخ
The object with larger mass. At equal speed, momentum is proportional to mass.
کارت ۱۹۷
پرسش
How is momentum conservation written for a two-dimensional isolated interaction?
پاسخ
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.
کارت ۱۹۸
پرسش
For a chosen object or system, how is average net external force related to impulse?
پاسخ
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
کارت ۱۹۹
پرسش
Which conservation law alone can determine the shared final velocity of a sticking collision?
پاسخ
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
کارت ۲۰۰
پرسش
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
پاسخ
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
۴۰۰ کارت
AP Physics 1 Flashcards: Complete 8-Unit Course Review
این دسته را رایگان مطالعه کنید
Nibomo باز می‌شود تا بتوانید مطالعه را شروع کنید.
کارت ۲۰۱
پرسش
If external impulse during a collision is small but not zero, what should experimental data show?
پاسخ
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
کارت ۲۰۲
پرسش
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
پاسخ
It does not change. Impulse depends on total signed area, not peak force alone.
کارت ۲۰۳
پرسش
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?
پاسخ
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.
کارت ۲۰۴
پرسش
How can a nearly frictionless cart track improve a momentum-conservation test?
پاسخ
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
کارت ۲۰۵
پرسش
How does an object's momentum change if its speed doubles at constant mass?
پاسخ
Its momentum magnitude doubles. Momentum depends linearly on speed.
کارت ۲۰۶
پرسش
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
پاسخ
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.
کارت ۲۰۷
پرسش
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?
پاسخ
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
کارت ۲۰۸
پرسش
Why is sticking evidence of an inelastic collision?
پاسخ
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
کارت ۲۰۹
پرسش
Can a moving two-object system have zero total momentum?
پاسخ
Yes. Equal and opposite momenta cancel even though each object is moving.
کارت ۲۱۰
پرسش
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
پاسخ
3 N·s in the force direction. Multiply the net external force by the interaction time.
کارت ۲۱۱
پرسش
What does a momentum-versus-velocity graph's slope represent for one object?
پاسخ
Its mass. The relationship p = mv is linear through the origin.
کارت ۲۱۲
پرسش
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?
پاسخ
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
کارت ۲۱۳
پرسش
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?
پاسخ
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.
کارت ۲۱۴
پرسش
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
پاسخ
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
کارت ۲۱۵
پرسش
What remains conserved in an isolated inelastic collision?
پاسخ
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
کارت ۲۱۶
پرسش
Why does choosing both colliding objects as the system simplify momentum analysis?
پاسخ
Their contact forces become internal. Only external impulse can change the system total.
کارت ۲۱۷
پرسش
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
پاسخ
Net external force. A steeper slope means a larger force in the slope's signed direction.
کارت ۲۱۸
پرسش
Why do airbags reduce injury force during a stop?
پاسخ
They increase the stopping time for roughly the same momentum change. That lowers the average force.
کارت ۲۱۹
پرسش
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?
پاسخ
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
کارت ۲۲۰
پرسش
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
پاسخ
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.
کارت ۲۲۱
پرسش
What is angular displacement?
پاسخ
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
کارت ۲۲۲
پرسش
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
پاسخ
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
کارت ۲۲۳
پرسش
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
پاسخ
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
کارت ۲۲۴
پرسش
What does rotational inertia measure?
پاسخ
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
کارت ۲۲۵
پرسش
What is the lever arm in a torque calculation?
پاسخ
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
کارت ۲۲۶
پرسش
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
پاسخ
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
کارت ۲۲۷
پرسش
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
پاسخ
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
کارت ۲۲۸
پرسش
How is rotational inertia found for a collection of point masses?
پاسخ
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
کارت ۲۲۹
پرسش
What determines the magnitude of torque from one force about a chosen axis?
پاسخ
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.
کارت ۲۳۰
پرسش
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
پاسخ
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
کارت ۲۳۱
پرسش
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
پاسخ
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.
کارت ۲۳۲
پرسش
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?
پاسخ
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.
کارت ۲۳۳
پرسش
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
پاسخ
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
کارت ۲۳۴
پرسش
How are clockwise and counterclockwise torques combined?
پاسخ
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
کارت ۲۳۵
پرسش
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?
پاسخ
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
کارت ۲۳۶
پرسش
Why must an axis be named when stating rotational inertia?
پاسخ
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
کارت ۲۳۷
پرسش
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
پاسخ
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
کارت ۲۳۸
پرسش
Why is torque's unit N·m not called a joule?
پاسخ
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
کارت ۲۳۹
پرسش
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?
پاسخ
4 rad/s². |α| = |Στ_external|/I = 8/2.
کارت ۲۴۰
پرسش
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
پاسخ
At the object's center of mass. That single force gives the same net gravitational force and torque.
کارت ۲۴۱
پرسش
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
پاسخ
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.
کارت ۲۴۲
پرسش
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
پاسخ
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
کارت ۲۴۳
پرسش
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?
پاسخ
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.
کارت ۲۴۴
پرسش
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?
پاسخ
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
کارت ۲۴۵
پرسش
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?
پاسخ
The hoop. More of its mass lies far from the axis.
کارت ۲۴۶
پرسش
Why can a rigid object have zero net external force but nonzero net external torque?
پاسخ
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
کارت ۲۴۷
پرسش
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
پاسخ
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
کارت ۲۴۸
پرسش
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
پاسخ
4 N·m. τ = rF for a perpendicular force.
کارت ۲۴۹
پرسش
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
پاسخ
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.
کارت ۲۵۰
پرسش
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?
پاسخ
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
کارت ۲۵۱
پرسش
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
پاسخ
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
کارت ۲۵۲
پرسش
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?
پاسخ
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
کارت ۲۵۳
پرسش
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
پاسخ
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
کارت ۲۵۴
پرسش
Does moving the chosen pivot change an individual force's torque?
پاسخ
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
کارت ۲۵۵
پرسش
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
پاسخ
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
کارت ۲۵۶
پرسش
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
پاسخ
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
کارت ۲۵۷
پرسش
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
پاسخ
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.
کارت ۲۵۸
پرسش
How could a meterstick experiment test torque balance?
پاسخ
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
کارت ۲۵۹
پرسش
For uniform rotation at frequency f, what is the angular-speed magnitude?
پاسخ
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
کارت ۲۶۰
پرسش
Why is choosing the pivot at an unknown support force often useful?
پاسخ
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
کارت ۲۶۱
پرسش
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
پاسخ
The parallel axis through the center of mass. Any offset adds the positive term Md².
کارت ۲۶۲
پرسش
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?
پاسخ
It becomes one-third as large. For each stated system, α = Στ_external/I.
کارت ۲۶۳
پرسش
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
پاسخ
3 m/s. v_t = r|ω| = 0.50 × 6.
کارت ۲۶۴
پرسش
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?
پاسخ
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
کارت ۲۶۵
پرسش
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
پاسخ
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.
کارت ۲۶۶
پرسش
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
پاسخ
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
کارت ۲۶۷
پرسش
How does moving mass farther from a rotation axis affect rotational inertia?
پاسخ
It increases rotational inertia strongly. For a point mass, I = mr².
کارت ۲۶۸
پرسش
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
پاسخ
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
کارت ۲۶۹
پرسش
Why must angular displacement be in radians for Δs = rΔθ?
پاسخ
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
کارت ۲۷۰
پرسش
When does a nonzero force produce zero torque about an axis?
پاسخ
When its line of action passes through the axis. The lever arm is then zero.
کارت ۲۷۱
پرسش
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
پاسخ
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
کارت ۲۷۲
پرسش
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?
پاسخ
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
کارت ۲۷۳
پرسش
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?
پاسخ
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
کارت ۲۷۴
پرسش
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?
پاسخ
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.
کارت ۲۷۵
پرسش
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
پاسخ
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
کارت ۲۷۶
پرسش
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
پاسخ
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.
کارت ۲۷۷
پرسش
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
پاسخ
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.
کارت ۲۷۸
پرسش
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
پاسخ
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
کارت ۲۷۹
پرسش
What is a rigid body's rotational kinetic energy about a fixed axis?
پاسخ
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
کارت ۲۸۰
پرسش
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)?
پاسخ
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)).
کارت ۲۸۱
پرسش
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
پاسخ
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.
کارت ۲۸۲
پرسش
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?
پاسخ
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
کارت ۲۸۳
پرسش
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?
پاسخ
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
کارت ۲۸۴
پرسش
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?
پاسخ
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.
کارت ۲۸۵
پرسش
Does angular-momentum conservation require rotational kinetic-energy conservation?
پاسخ
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
کارت ۲۸۶
پرسش
Why do astronauts feel weightless in orbit even though gravity acts on them?
پاسخ
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
کارت ۲۸۷
پرسش
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
پاسخ
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
کارت ۲۸۸
پرسش
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
پاسخ
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
کارت ۲۸۹
پرسش
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?
پاسخ
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
کارت ۲۹۰
پرسش
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
پاسخ
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
کارت ۲۹۱
پرسش
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?
پاسخ
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
کارت ۲۹۲
پرسش
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?
پاسخ
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.
کارت ۲۹۳
پرسش
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
پاسخ
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.
کارت ۲۹۴
پرسش
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?
پاسخ
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.
کارت ۲۹۵
پرسش
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
پاسخ
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
کارت ۲۹۶
پرسش
How does rotational kinetic energy change if angular speed doubles at fixed I?
پاسخ
It becomes four times as large. Rotational kinetic energy depends on ω².
کارت ۲۹۷
پرسش
Why should external torque be evaluated about the same axis used for angular momentum?
پاسخ
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
کارت ۲۹۸
پرسش
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?
پاسخ
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.
کارت ۲۹۹
پرسش
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
پاسخ
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.
کارت ۳۰۰
پرسش
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?
پاسخ
v = √(GM/r). Gravity supplies the inward net force.
کارت ۳۰۱
پرسش
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?
پاسخ
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.
کارت ۳۰۲
پرسش
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?
پاسخ
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
کارت ۳۰۳
پرسش
Why can't the rolling condition alone prove that friction points uphill or downhill?
پاسخ
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
کارت ۳۰۴
پرسش
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?
پاسخ
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
کارت ۳۰۵
پرسش
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?
پاسخ
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
کارت ۳۰۶
پرسش
What makes simple harmonic motion a special kind of periodic motion?
پاسخ
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
کارت ۳۰۷
پرسش
What does the amplitude of an SHM displacement graph represent?
پاسخ
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
کارت ۳۰۸
پرسش
How are period and frequency related?
پاسخ
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
کارت ۳۰۹
پرسش
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
پاسخ
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
کارت ۳۱۰
پرسش
For one-dimensional SHM, what is the equilibrium position?
پاسخ
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.
کارت ۳۱۱
پرسش
How far apart in phase are displacement and velocity in SHM?
پاسخ
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
کارت ۳۱۲
پرسش
When can a simple pendulum be modeled as SHM?
پاسخ
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
کارت ۳۱۳
پرسش
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
پاسخ
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
کارت ۳۱۴
پرسش
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
پاسخ
U_s = ½kx². It has the same value at +x and -x.
کارت ۳۱۵
پرسش
At the equilibrium position of SHM, is the oscillator necessarily at rest?
پاسخ
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
کارت ۳۱۶
پرسش
How does a spring oscillator's period change if k becomes four times as large?
پاسخ
The period is halved. T is proportional to 1/√k.
کارت ۳۱۷
پرسش
How are acceleration and displacement related along the SHM coordinate?
پاسخ
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.
کارت ۳۱۸
پرسش
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
پاسخ
E = ½kA². It stays constant when dissipative effects are negligible.
کارت ۳۱۹
پرسش
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
پاسخ
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
کارت ۳۲۰
پرسش
How can frequency be read from an oscillation-versus-time graph?
پاسخ
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
کارت ۳۲۱
پرسش
Why does an ideal mass–spring oscillator exhibit SHM?
پاسخ
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.
کارت ۳۲۲
پرسش
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?
پاسخ
1 J. E = ½(50)(0.20²).
کارت ۳۲۳
پرسش
At maximum positive displacement in SHM, what are velocity and acceleration?
پاسخ
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
کارت ۳۲۴
پرسش
How does a spring oscillator's period change if its mass becomes four times as large?
پاسخ
The period doubles. T is proportional to √m.
کارت ۳۲۵
پرسش
Why isn't uniform circular motion itself one-dimensional SHM?
پاسخ
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
کارت ۳۲۶
پرسش
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
پاسخ
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
کارت ۳۲۷
پرسش
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
پاسخ
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
کارت ۳۲۸
پرسش
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
پاسخ
No within the ideal SHM model. The period depends on system parameters, not amplitude.
کارت ۳۲۹
پرسش
How is maximum speed related to amplitude and angular frequency in SHM?
پاسخ
v_max = ωA. Maximum speed occurs at equilibrium.
کارت ۳۳۰
پرسش
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
پاسخ
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
کارت ۳۳۱
پرسش
How far apart in phase are displacement and acceleration in SHM?
پاسخ
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
کارت ۳۳۲
پرسش
What is the period of a small-angle simple pendulum of length L when damping is negligible?
پاسخ
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.
کارت ۳۳۳
پرسش
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
پاسخ
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.
کارت ۳۳۴
پرسش
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
پاسخ
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
کارت ۳۳۵
پرسش
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
پاسخ
Both are positive. Motion and restoring acceleration point right toward equilibrium.
کارت ۳۳۶
پرسش
How does a pendulum's period change if its length becomes nine times as large?
پاسخ
The period triples. T is proportional to √L.
کارت ۳۳۷
پرسش
If SHM starts at maximum positive displacement, what equation gives its position?
پاسخ
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
کارت ۳۳۸
پرسش
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
پاسخ
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
کارت ۳۳۹
پرسش
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
پاسخ
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
کارت ۳۴۰
پرسش
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
پاسخ
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
کارت ۳۴۱
پرسش
What makes a substance a fluid?
پاسخ
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
کارت ۳۴۲
پرسش
What is mass density?
پاسخ
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
کارت ۳۴۳
پرسش
For pressure that is uniform over a surface patch, how is it related to normal force and area?
پاسخ
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
کارت ۳۴۴
پرسش
What is volume flow rate?
پاسخ
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
کارت ۳۴۵
پرسش
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
پاسخ
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
کارت ۳۴۶
پرسش
What conditions support the basic Bernoulli model used here?
پاسخ
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.
کارت ۳۴۷
پرسش
Under the ideal model, how does average density predict whether a free object floats or sinks?
پاسخ
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.
کارت ۳۴۸
پرسش
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
پاسخ
Q = Av. This gives the volume crossing a completely filled pipe section per time.
کارت ۳۴۹
پرسش
How does a static fluid exert force on a surface?
پاسخ
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
کارت ۳۵۰
پرسش
How does pressure change with depth in a static uniform fluid?
پاسخ
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
کارت ۳۵۱
پرسش
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
پاسخ
F_B = mg. The object's weight equals the weight of the fluid it displaces.
کارت ۳۵۲
پرسش
What is the continuity equation for steady incompressible flow in one filled pipe?
پاسخ
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
کارت ۳۵۳
پرسش
Why does a static fluid produce an upward buoyant force?
پاسخ
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
کارت ۳۵۴
پرسش
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
پاسخ
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
کارت ۳۵۵
پرسش
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?
پاسخ
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
کارت ۳۵۶
پرسش
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
پاسخ
0.060 m³/s. Q = Av = 0.020×3.
کارت ۳۵۷
پرسش
What does the slope of a mass-versus-volume graph represent for one uniform material?
پاسخ
Density. Since m = ρV, the line's slope is ρ.
کارت ۳۵۸
پرسش
How do gauge pressure and absolute pressure differ?
پاسخ
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
کارت ۳۵۹
پرسش
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
پاسخ
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
کارت ۳۶۰
پرسش
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
پاسخ
It doubles. Continuity keeps Av constant.
کارت ۳۶۱
پرسش
When does a fluid element's velocity change?
پاسخ
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
کارت ۳۶۲
پرسش
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
پاسخ
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
کارت ۳۶۳
پرسش
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?
پاسخ
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
کارت ۳۶۴
پرسش
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
پاسخ
It becomes four times as large. Area is proportional to radius squared.
کارت ۳۶۵
پرسش
What does Pascal's principle say for a confined incompressible fluid at rest?
پاسخ
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
کارت ۳۶۶
پرسش
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
پاسخ
ρg. For known g, the slope can determine fluid density.
کارت ۳۶۷
پرسش
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?
پاسخ
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
کارت ۳۶۸
پرسش
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?
پاسخ
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
کارت ۳۶۹
پرسش
What physical quantity does each term in P + ½ρv² + ρgy share?
پاسخ
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
کارت ۳۷۰
پرسش
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
پاسخ
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
کارت ۳۷۱
پرسش
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?
پاسخ
0.75, or 75%. Use the density ratio for floating equilibrium.
کارت ۳۷۲
پرسش
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
پاسخ
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
کارت ۳۷۳
پرسش
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?
پاسخ
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
کارت ۳۷۴
پرسش
Why does the same force create more pressure on a smaller area?
پاسخ
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
کارت ۳۷۵
پرسش
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
پاسخ
3.0×10³ kg/m³. Divide mass by volume.
کارت ۳۷۶
پرسش
What conservation law underlies the continuity equation for incompressible flow?
پاسخ
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
کارت ۳۷۷
پرسش
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?
پاسخ
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.
کارت ۳۷۸
پرسش
What is the SI unit of pressure?
پاسخ
The pascal, Pa. One pascal equals 1 N/m².
کارت ۳۷۹
پرسش
How do pressures compare at the same horizontal level in one connected static fluid?
پاسخ
They are equal. Container shape does not change pressure at a fixed elevation.
کارت ۳۸۰
پرسش
What does specific gravity compare?
پاسخ
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
کارت ۳۸۱
پرسش
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
پاسخ
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
کارت ۳۸۲
پرسش
How does the particle model distinguish a fluid from a rigid solid?
پاسخ
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
کارت ۳۸۳
پرسش
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
پاسخ
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
کارت ۳۸۴
پرسش
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?
پاسخ
200 N. F_B = ρgV = 1000×10×0.020.
کارت ۳۸۵
پرسش
Why can a steel ship float even though steel is denser than water?
پاسخ
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
کارت ۳۸۶
پرسش
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
پاسخ
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
کارت ۳۸۷
پرسش
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
پاسخ
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
کارت ۳۸۸
پرسش
What does incompressible mean in the introductory ideal-fluid model?
پاسخ
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
کارت ۳۸۹
پرسش
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
پاسخ
Pressure is lower at the higher point. P + ρgy remains constant.
کارت ۳۹۰
پرسش
How can water displacement measure an irregular solid's volume?
پاسخ
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.
کارت ۳۹۱
پرسش
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
پاسخ
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
کارت ۳۹۲
پرسش
How can scale readings in air and water determine buoyant force?
پاسخ
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.
کارت ۳۹۳
پرسش
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
پاسخ
30,000 Pa. P_gauge = ρgh = 1000×10×3.
کارت ۳۹۴
پرسش
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
پاسخ
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
کارت ۳۹۵
پرسش
For a chosen fluid element in a horizontal region, what can a pressure difference do?
پاسخ
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.
کارت ۳۹۶
پرسش
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
پاسخ
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.
کارت ۳۹۷
پرسش
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
پاسخ
5,000 Pa. P = F/A = 200/0.040.
کارت ۳۹۸
پرسش
Why doesn't a hydraulic lift multiply energy?
پاسخ
The large-force piston moves a shorter distance. Ideally, input work equals output work.
کارت ۳۹۹
پرسش
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?
پاسخ
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
کارت ۴۰۰
پرسش
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
پاسخ
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.

۴۰۰ کارت