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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 3: Work, Energy & PowerTranslational Kinetic Energy & Potential Energy

Translational Kinetic Energy & Potential Energy (College Board AP® Physics 1: Algebra-Based): Exam Questions

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1
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Which of the following statements is correct regarding the translational kinetic energy of an object?

  • The translational kinetic energy of an object depends only on its velocity and is independent of its mass.

  • Translational kinetic energy is a scalar quantity and is directly proportional to the square of the object's velocity.

  • Translational kinetic energy depends on both the magnitude and direction of the velocity of the object.

  • An object's translational kinetic energy remains constant in all reference frames.

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2
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Graph showing gravitational potential energy (J) increasing linearly with height (m);Line begins at (0, 0) and ends at 200 J at 10 m

The graph shows the gravitational potential energy (U subscript g​) of an object as a function of its height (h) above the ground.

Based on the information given in the graph, which of the following statements is correct?

  • The slope of the graph is equal to the mass of the object.

  • The gravitational potential energy is independent of the object's height.

  • The slope of the graph represents the product of the object's mass and the gravitational field strength (m g).

  • The graph represents a quadratic relationship between U subscript g​ and h.

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3
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A graph shows the gravitational potential energy (U subscript g) of a 2 space kg object as a function of its change in height(increment y).

Which of the following expressions represents the value of the gradient when increment y space equals space 15 space straight m?

  • m g

  • m over g

  • 1 half m g

  • 2 m g

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4
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An object of mass m is lifted vertically from an initial height h subscript 1 to a final height h subscript 2​ near the surface of Earth. The object is then dropped from h subscript 2​ and allowed to fall freely under gravity.

Which of the following expressions represents the velocity of the object when it reaches h subscript 1​?

  • square root of 2 g open parentheses h subscript 2 minus h subscript 1 close parentheses end root

  • g open parentheses h subscript 2 space minus space h subscript 1 close parentheses

  • square root of g open parentheses h subscript 2 squared space minus space h subscript 1 squared close parentheses end root

  • 1 half g open parentheses h subscript 2 space minus space h subscript 1 close parentheses

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5
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Which of the following statements correctly describes the behavior of gravitational potential energy between two masses separated by a distance r?

  • If the separation distance between two masses is tripled, the magnitude of gravitational potential energy decreases by a factor of 9.

  • Gravitational potential energy is always positive because it depends on mass, which is always positive.

  • The magnitude of gravitational potential energy increases as the masses move closer together because it is inversely proportional to their separation.

  • If one of the two masses is doubled while the separation remains the same, the gravitational potential energy remains unchanged.

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1
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A baseball is thrown vertically into the sky by a player during a warm up exercise. The ball has an initial velocity, v, and an initial translational kinetic energy, K. Which of the following expressions is correct for the ball when it is halfway through its descent back to the player's hands?

  • v over 4

    fraction numerator K over denominator square root of 2 end fraction

  • v over 4

    K over 2

  • fraction numerator v over denominator square root of 2 end fraction

    K over 2

  • fraction numerator v over denominator square root of 4 end fraction

    fraction numerator K over denominator square root of 2 end fraction

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2
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A satellite of mass 1.6 cross times 10 to the power of 5 space kg is launched from the surface of the Earth to an altitude of 4.3 cross times 10 to the power of 6 space straight m. Given that the Earth has a mass of 5.98 cross times 10 to the power of 24 space kg and a radius of 6.37 cross times 10 to the power of 6 space straight m, which of the following is correct for the change in the gravitational potential energy of the satellite?

  • 4.06 cross times 10 to the power of 12 space straight J

  • 6.04 cross times 10 to the power of 12 space straight J

  • 4.06 cross times 10 to the power of 13 space straight J

  • 6.04 cross times 10 to the power of 13 space straight J

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31 mark

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

Which of the following energy bar charts could represent the gravitational potential energy U subscript g and kinetic energy K of the object when it is one-quarter of the way through its fall?

  • Graph with horizontal axis at zero, labeled "0," and vertical bars under "Ug" and "K" reaching the same level. The y-axis has upward-pointing arrow.
  • Bar chart showing two vertical bars labeled Ug and K on the y-axis, with K being three times taller than Ug.
  • Bar chart showing two bars labeled Ug and K, with Ug being 3 times taller than K.
  • Bar graph showing Ug and K. Ug is 4 lines tall and K is zero.

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41 mark

A particle is thrown vertically upwards to a height h with a speed v. It travels up to the highest point above the ground at point X, and it falls back down through point Y at 3 over 5 h above the ground.

screenshot-2023-08-21-121416

Which of the following values is the correct speed of the particle at point Y?

  • square root of fraction numerator 2 g h over denominator 5 end fraction end root

  • 2 square root of fraction numerator g h over denominator 5 end fraction end root

  • 4 square root of fraction numerator g h over denominator 5 end fraction end root

  • square root of fraction numerator 3 g h over denominator 5 end fraction end root

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1
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A box of mass m is pushed up an inclined slope with an applied force F. Which of the following energy bar charts is correct for the gravitational potential energy, U subscript g, kinetic energy, K, and elastic potential energy, U subscript s , of the object whilst it is in motion if the system is defined as only the box?

  • Graph with labeled regions Ug, K, and Us on the horizontal axis. Vertical axis starts at 0. K is 4 lines tall, Ug and Us are zero.
  • Bar graph with three bars labeled Ug, K, and Us. Ug is zero, K is 3 lines tall, and Us is 1 line tall.
  • Bar graph showing values for Ug, K, and Us on the vertical axis against a horizontal axis with intervals. Ug is 2.5 lines tall, K is 1.5 lines tall, Us is zero.
  • Graph showing energy levels with shaded bars. Ug is 2 lines tall, K is zero, Us is 2 lines tall.

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2
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The following table provides data for four different springs, showing their spring constants (k) and compression distances (increment x).

Spring

k space open parentheses straight N divided by straight m close parentheses

increment x space open parentheses straight m close parentheses

A

2.0 cross times 10 to the power of negative 3 end exponent

4.0 cross times 10 to the power of negative 2 end exponent

B

3.0 cross times 10 to the power of negative 4 end exponent

7.0 cross times 10 to the power of negative 2 end exponent

C

1.5 cross times 10 to the power of negative 2 end exponent

2.5 cross times 10 to the power of negative 3 end exponent

D

5.0 cross times 10 to the power of negative 3 end exponent

3.0 cross times 10 to the power of negative 2 end exponent

Which of the following correctly ranks the elastic potential energies stored in the springs from greatest to least?

  • U subscript D space greater than space U subscript B space greater than space U subscript C space greater than space U subscript A

  • U subscript A space greater than space U subscript B space greater than space U subscript C space greater than space U subscript D

  • U subscript D space greater than space U subscript A space greater than space U subscript B space greater than space U subscript C

  • U subscript B space greater than space U subscript D space greater than space U subscript A space greater than space U subscript C

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3
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The table below provides data for three pairs of objects, showing their masses (m subscript 1​, m subscript 2) and the separation distances (r) between their centers of mass.

Pair

m subscript 1 space open parentheses kg close parentheses

m subscript 2 space open parentheses kg close parentheses

r space open parentheses straight m close parentheses

X

2.0 cross times 10 cubed

4.0 cross times 10 cubed

8.0 cross times 10 cubed

Y

5.0 cross times 10 squared

1.0 cross times 10 cubed

2.0 cross times 10 cubed

Z

1.0 cross times 10 cubed

2.0 cross times 10 cubed

1.0 cross times 10 to the power of 4

Which pair has the greatest magnitude of gravitational potential energy?

  • Pair X

  • Pair Y

  • Pair Z

  • All pairs have the same gravitational potential energy.

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4
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A spacecraft of mass m is traveling at a constant velocity v subscript S​ relative to an observer on Earth. Another observer, moving with velocity v subscript O​ relative to Earth in the same direction as the spacecraft, measures the spacecraft’s velocity as v apostrophe.

Which of the following correctly expresses the kinetic energy of the spacecraft as measured by the moving observer?

  • 1 half m v subscript S squared space minus fraction numerator space 1 over denominator 2 end fraction m v subscript O squared

  • 1 half m open parentheses v subscript S space minus space v subscript O close parentheses squared

  • 1 half m open parentheses v subscript S space plus space v subscript O close parentheses squared

  • 1 half m v subscript S squared space plus fraction numerator space 1 over denominator 2 end fraction m v subscript O squared

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51 mark
Energy bar chart showing three bars: Us has a value of 4, K is at zero, and Ug has a value of 1.

The energy bar chart shows the spring potential energy, U subscript s, translational kinetic energy, K, and gravitational potential energy, U subscript g, for a bungee jumper at the lowest point in their motion.

Which of the following correctly defines the system?

  • The person only.

  • The person and the rope.

  • The rope and the Earth.

  • The person and the Earth.

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61 mark

A car of mass m is moving at a constant velocity v subscript 0​ relative to the ground. A truck of mass 3 m is moving in the same direction with velocity v subscript rrelative to the ground. An observer inside the truck measures the car's kinetic energy as K apostrophe.

Which of the following correctly describes the relationship between K apostrophe and the kinetic energy of the truck as measured from the reference frame of the ground, K subscript 0​?

  • K apostrophe space less than space K subscript 0

  • K apostrophe space greater than space K subscript 0

  • K apostrophe space equals space K subscript 0

  • There is not enough information to determine the relative translational kinetic energy.

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