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AP Physics 1: Algebra-Based Practice Quiz: Potential Energy

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 12 questions to check your progress.

Question 1 of 12

Which of the following best describes potential energy?

All Questions (12)

Which of the following best describes potential energy?

A) A scalar quantity associated with the configuration of objects in a system.

B) A vector quantity representing the energy of motion.

C) A property of a single, isolated object.

D) The energy an object has due to its temperature.

Correct Answer: A

Based on the provided content, potential energy is described as a property of a system (composed of two or more objects) and is a scalar quantity associated with the position of objects within that system.

Under which condition can potential energy be defined for a system of two or more objects?

A) When the objects interact through any type of force.

B) When the objects interact only through conservative forces.

C) When the objects are in motion relative to each other.

D) When the total energy of the system is zero.

Correct Answer: B

The provided content explicitly states that a system has potential energy if the objects within that system only interact with each other through conservative forces.

How is the zero point for potential energy (U=0) determined for a given system?

A) It is a universal constant for all systems.

B) It is determined by the total mass of the system.

C) It is defined by the international standard for energy.

D) It is chosen by the observer to simplify the analysis of the situation.

Correct Answer: D

The provided content states that the definition of zero potential energy for a given system is a decision made by the observer to simplify or otherwise assist in analysis.

An ideal spring with a spring constant k is stretched a distance Δx from its equilibrium position, storing potential energy U. If the spring is then stretched further to a total distance of 2Δx from equilibrium, what is the new elastic potential energy stored in the spring?

A) U

B) 2U

C) 4U

D) U/2

Correct Answer: C

The elastic potential energy is given by U_s = (1/2)k(Δx)^2. The original energy is U = (1/2)k(Δx)^2. The new energy is U_new = (1/2)k(2Δx)^2 = (1/2)k(4(Δx)^2) = 4 * [(1/2)k(Δx)^2] = 4U. The energy is four times as large.

A book of mass m is lifted from the floor to a shelf at a height Δy above the floor. If the floor is defined as the zero potential energy level (U_g=0), what is the change in the gravitational potential energy of the book-Earth system?

A) -mgΔy

B) mgΔy

C) (1/2)m(Δy)^2

D) 0

Correct Answer: B

The change in gravitational potential energy is given by the equation ΔU_g = mgΔy. Since the book is lifted, its vertical position increases, resulting in a positive change in potential energy.

An ideal spring is first stretched by a distance Δx from its equilibrium and then compressed by the same distance Δx from its equilibrium. How does the elastic potential energy stored in the stretched case compare to the compressed case?

A) The energy is greater when stretched.

B) The energy is greater when compressed.

C) The energy is the same in both cases.

D) The energy is positive when stretched and negative when compressed.

Correct Answer: C

The formula for elastic potential energy is U_s = (1/2)k(Δx)^2. The displacement term (Δx) is squared, so the energy stored is the same whether the displacement is positive (stretched) or negative (compressed), as long as the magnitude of the displacement is the same.

A 2 kg object is moved from a height of 3 m to a height of 5 m above the ground. An observer sets the zero potential energy level at the 3 m mark. What is the change in gravitational potential energy (ΔU_g) for the object-Earth system during this movement? (Use g ≈ 10 m/s²)

A) 0 J

B) 20 J

C) 40 J

D) 60 J

Correct Answer: C

The change in potential energy, ΔU_g = mgΔy, depends only on the change in height, not on the choice of the zero level. Here, Δy = 5 m - 3 m = 2 m. So, ΔU_g = (2 kg)(10 m/s²)(2 m) = 40 J. The choice of the zero point does not affect the change in potential energy.

An ideal spring has a spring constant of 200 N/m. How much elastic potential energy is stored in the spring when it is compressed by 0.1 meters from its equilibrium position?

A) 1 J

B) 2 J

C) 10 J

D) 20 J

Correct Answer: A

Using the formula for elastic potential energy, U_s = (1/2)k(Δx)^2. Plugging in the values: U_s = (1/2)(200 N/m)(0.1 m)^2 = (1/2)(200)(0.01) = 1 J.

Why is potential energy considered a property of a system rather than a single object?

A) Because energy must always be shared between at least two objects.

B) Because it is a scalar quantity associated with the relative positions of interacting objects.

C) Because a single object can only have kinetic energy.

D) Because the zero point of energy is arbitrary.

Correct Answer: B

The provided content indicates that potential energy arises from the interaction between two or more objects and depends on their configuration (position relative to each other). Therefore, it is a property of the system of interacting objects, not a single object in isolation.

A box is lifted from the ground to a height h. The change in gravitational potential energy is ΔU_g. If a second box with twice the mass is lifted to half the height, what is the change in its gravitational potential energy?

A) (1/2)ΔU_g

B) ΔU_g

C) 2ΔU_g

D) 4ΔU_g

Correct Answer: B

The initial change is ΔU_g = mgh. For the second box, the mass is 2m and the height change is h/2. The new change is ΔU_new = (2m)g(h/2) = mgh = ΔU_g. The change in potential energy is the same.

A student is analyzing the change in gravitational potential energy of a ball as it is thrown upwards. Which of the following statements correctly identifies a key property of this energy?

A) The change in potential energy is a vector pointing upwards.

B) The change in potential energy is a scalar quantity.

C) The potential energy depends on the ball's velocity.

D) The potential energy is always negative.

Correct Answer: B

The provided content states that potential energy is a scalar quantity. This applies to all forms of potential energy discussed, including gravitational potential energy.

Which of the following statements about potential energy is NOT supported by the provided principles?

A) The change in gravitational potential energy of an object-planet system depends on the vertical displacement of the object.

B) The choice of where U_g = 0 affects the calculated value of ΔU_g.

C) Potential energy is a characteristic of a system where objects interact via conservative forces.

D) The energy stored in a spring is proportional to the square of its displacement from equilibrium.

Correct Answer: B

The content states that the definition of zero potential energy is an arbitrary choice made by the observer. However, the change in potential energy (ΔU_g = mgΔy) depends only on the change in position (Δy), not on the chosen zero point. The choice of zero affects the value of U at a specific point, but not the value of ΔU between two points.