Q: A 2.0 kg textbook is lifted from the floor to a shelf 1.5 m above the ground. What is the change in gravitational potential energy of the textbook? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta U = 2.0\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times 1.5\ \mathrm{m} = 29.4\ \mathrm{J}$$

Q: A 0.5 kg ball is dropped from a height of 10 m. What is its gravitational potential energy relative to the ground just before it is dropped? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$U = 0.5\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times 10\ \mathrm{m} = 49\ \mathrm{J}$$

Q: A 250 g apple is lifted 1.0 m above the ground. What is its gravitational potential energy with respect to the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$U = 0.25\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times 1.0\ \mathrm{m} = 2.45\ \mathrm{J}$$

Q: A roller coaster car of mass 500 kg is at the top of a 30 m hill. What is its gravitational potential energy relative to the bottom of the hill? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$U = 500\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times 30\ \mathrm{m} = 147,000\ \mathrm{J}$$

Q: A hiker lifts a 10 kg backpack from the ground to a height of 2 m, then carries it horizontally for 100 m. What is the total change in gravitational potential energy?

$$\Delta U = 10\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times 2\ \mathrm{m} = 196\ \mathrm{J}$$

Q: If a 3 kg object is raised from 2 m to 5 m above the ground, what is the change in its gravitational potential energy? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta U = 3\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times (5 - 2)\ \mathrm{m} = 88.2\ \mathrm{J}$$

Question 1

Which of the following best describes gravitational potential energy?

Accepted Answer

The energy stored in an object due to its vertical position relative to a chosen reference point.

Question 2

A 2.0 kg textbook is lifted from the floor to a shelf 1.5 m above the ground. What is the change in gravitational potential energy of the textbook? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta U = 2.0\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 1.5\ \mathrm{m} = 29.4\ \mathrm{J}$$

Question 3

Which of the following statements about gravitational potential energy is TRUE?

Accepted Answer

It depends only on the object's mass and its vertical position relative to a reference point.

Question 4

A 0.5 kg ball is dropped from a height of 10 m. What is its gravitational potential energy relative to the ground just before it is dropped? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U = 0.5\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 10\ \mathrm{m} = 49\ \mathrm{J}$$

Question 5

Why is it important to specify a reference level (where $$y=0) $$when calculating gravitational potential energy?

Accepted Answer

Because only changes in gravitational potential energy are physically meaningful, and the reference level determines the zero point.

Question 6

A 250 g apple is lifted 1.0 m above the ground. What is its gravitational potential energy with respect to the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U = 0.25\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 1.0\ \mathrm{m} = 2.45\ \mathrm{J}$$

Question 7

A roller coaster car of mass 500 kg is at the top of a 30 m hill. What is its gravitational potential energy relative to the bottom of the hill? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U = 500\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 30\ \mathrm{m} = 147,000\ \mathrm{J}$$

Question 8

Which of the following is a correct statement about conservative forces?

Accepted Answer

Conservative forces, such as gravity, store energy that can be fully recovered.

Question 9

A hiker lifts a 10 kg backpack from the ground to a height of 2 m, then carries it horizontally for 100 m. What is the total change in gravitational potential energy?

Accepted Answer

$$\Delta U = 10\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 2\ \mathrm{m} = 196\ \mathrm{J}$$

Question 10

If a 3 kg object is raised from 2 m to 5 m above the ground, what is the change in its gravitational potential energy? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta U = 3\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes (5 - 2)\ \mathrm{m} = 88.2\ \mathrm{J}$$

Question 11

Which of the following scenarios best illustrates the conversion of gravitational potential energy to kinetic energy?

Accepted Answer

A ball rolling down a hill, speeding up as it descends.

Question 12

A 1.5 kg object is dropped from a height of 4 m. What is its speed just before hitting the ground? (Assume no air resistance and $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2 	imes 9.8\ \mathrm{m/s^2$} 	imes 4\ \mathrm{m}} = \sqrt{78.4} \approx 8.86\ \mathrm{m/s}$$

Question 13

Which of the following is NOT a property of gravitational potential energy?

Accepted Answer

It depends on the path taken to reach the height.

Question 14

A 0.8 kg object is lifted from the ground to a height of 3 m, then lowered to a height of 1 m. What is the net change in gravitational potential energy from the ground to the final position? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta U = 0.8\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 1\ \mathrm{m} = 7.84\ \mathrm{J}$$

Question 15

If the reference level for gravitational potential energy is changed from the ground to the top of a table, how does this affect the calculated potential energy of an object on the floor?

Accepted Answer

The potential energy of the object on the floor becomes negative.

Question 16

A 5 kg object is lifted vertically at constant speed through a height of 2 m. How much work is done by the lifting force? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = 5\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes 2\ \mathrm{m} = 98\ \mathrm{J}$$

Gravitational Potential Energy: Concepts, Calculations, and Applications

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