# Worksheet: Gravitational Potential Energy

In this worksheet, we will practice calculating the potential energy of an object due to its displacement from a given point in a uniform gravitational field.

Q1:

How much work is done against the gravitational force on a briefcase of mass 5.00 kg when it is carried from the ground floor to the roof of the Empire State Building, a vertical climb of 380 m?

Q2:

A cat’s crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3.0 m/s. Assume, in this problem, that air drag is negligible.

What is the kinetic energy of the ball as it leaves the hand?

How much work is done by the gravitational force during the ball’s rise to its peak?

What is the change in the gravitational potential energy of the ball during the rise to its peak?

If the gravitational potential energy is taken to be zero at the point where the ball leaves the hand, what is the gravitational potential energy when it reaches the maximum height?

If the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand?

What is the maximum height the ball reaches?

Q3:

Suppose a 350 g kookaburra (a large kingfisher bird) picks up a 75 g snake and raises it 2.5 m from the ground to a branch.

How much work did the bird do on the snake?

How much work did the bird do to raise its own center of mass to the branch?

Q4:

Find the change in energy of a payload of mass kg taken from rest at the surface of Earth and placed at rest on the surface of the Moon, assuming that all the kinetic energy involved in moving the payload could be recovered. Use a value of kg for the mass of Earth and a value of kg for the mass of the Moon; use a value of m for the radius of Earth and a value of m for the radius of the Moon; and use a value of m for the distance between the center of mass of Earth and the center of mass of the Moon.

• A J
• B J
• C J
• D J
• E J

Q5:

A person of mass 62.0 kg climbs stairs, moving 1.14 m vertically upward. Find the work done by the person.

Q6:

An elevator car of mass kg is pulled 40.0 m vertically upward at constant speed by its cable. An average friction force of 100 N resists the motion of the elevator car.

What work is done on the elevator car by the cable?

What work is done on the elevator car by the force of gravity?

What is the total work done on the elevator car?

Q7:

A cruise ship is docked in a harbour. The level of the dock is 2.15 m above the water line. A woman on the cruise ship stands on a deck 55.5 m above the water line. She pushes a 36.0-g-mass pebble off the deck. A man standing on the dock holds out a net 1.20 m above the top of the dock and catches the pebble in the net. Assume that vertically upward motion corresponds with positive displacement.

How much work is done by gravity on the pebble?

How much does the gravitational potential energy of the pebble change?

Taking gravitational potential energy at the water line to be zero, what is the gravitational potential energy of the pebble on the deck of the cruise ship?

Taking gravitational potential energy at the water line to be zero, what is the gravitational potential energy of the pebble when it is caught in the net?

Taking gravitational potential energy at the water line to be 21.5 J, what is the gravitational potential energy of the pebble on the deck of the cruise ship?

Taking gravitational potential energy at the water line to be 21.5 J, what is the gravitational potential energy of the pebble when it is caught in the net?

Q8:

The Great Pyramid of Giza has a mass of kg, and its center of mass is 34.7 m above the surrounding ground. How much gravitational potential energy is stored in the pyramid?

• A J
• B J
• C J
• D J
• E J

Q9:

A hydroelectric power facility converts the gravitational potential energy of water behind a dam to electric energy. What is the gravitational potential energy relative to the generators of a lake of volume 50.0 km3 and a mass of kg, given that the lake has an average height of 40.0 m above the generators?

• A
• B
• C
• D
• E

Q10:

There is a 250 m high cliff at Half Dome in Yosemite National Park in California. Suppose a boulder breaks loose from the top of this cliff.

How fast will it be going when it strikes the ground?

Assuming a reaction time of 0.300 s, how long a time will a tourist at the bottom have to get out of the way after hearing the sound of the rock breaking loose (neglecting the height of the tourist, which would become negligible anyway if hit)? The speed of sound is 335.0 m/s on this day.

Q11:

The awe-inspiring Great Pyramid of Giza was built more than 4,500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres and was 146 m high, with a mass of about kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging.) Historians estimate that 20,000 workers spent 20 years to construct it, working 12 hours per day and 330 days per year.

Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

• A J
• B J
• C J
• D J
• E J

Only a fraction of the workers lifted blocks; most of them were involved in support services, such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1,000 of them and they consumed food energy at the rate of 300 kcal/h. Use a value of 4,184 for the number of joules per kilocalorie.

• A5.26%
• B2.51%
• C11.5%
• D1.82%
• E14.4%

Calculate the mass of food that had to be supplied each day, assuming that the average worker required 3 600 kcal per day and that their diet was 5% protein, 60% carbohydrate, and 35% fat. 1 g of protein contains approximately 4.10 kcal, 1 g of carbohydrate contains approximately 4.10 kcal, and 1 g of fat contains approximately 9.30 kcal.

• A kg
• B kg
• C kg
• D kg
• E kg

Q12:

The summit of the Great Blue Hill in Milton, Massachusetts, is 147 m above its base and has an elevation above sea level of 195 m, as shown in the diagram. A hiker of mass 75.0 kg ascends from the hill’s base to its summit. Gravitational potential energy is taken as being zero at the base of the hill.

What is the gravitational potential energy of the hiker at the base of the hill?

What is the gravitational potential energy of the hiker at the summit?

What is the gravitational potential energy of the hiker when they have descended to sea level?

What is the gravitational potential energy of the hiker at the base of the hill if sea level is taken as being at zero gravitational potential energy?

What is the gravitational potential energy of the hiker at the summit of the hill if sea level is taken as being at zero gravitational potential energy?

What is the gravitational potential energy of the hiker at sea level if sea level is taken as being at zero gravitational potential energy?

Q13:

A very large book that weighs 20 N is lowered vertically downward a distance of 1 m by a librarian. He then carries the book to a table a horizontal distance of 3 m from the shelf along path a as shown in the diagram. After the librarian reads the book, he returns it to the shelf by walking in its direction while slowly raising the book vertically upward as he approaches the shelf such that the book travels along the line of path b from the tabletop to the shelf.

Calculate the work done by gravity on the book due to its displacement from the shelf to the table.

Find the work done by gravity on the book due to its net displacement from the shelf to the table and back to the shelf.