Name:
Class:
Date:
GRAVITATIONAL POTENTIAL ENERGY WORD PROBLEMS (A)
Introduction:
Gravitational potential energy (GPE) is the energy an object has because of its position above the
ground. The energy is stored due to the attraction of object towards the Earth because of the force of
gravity. To calculate the GPE, use the following formula:
GPE = Mass x Gravity Constant x Height
Where…
Mass:
Gravity:
Height:
GPE:
or… GPE = mgh
measured in kilograms (kg)
gravity constant on Earth = 9.8 m/s2
measured in meters (m)
measured in Joules (J) or kilojoules (kJ)
It may be useful to use a formula triangle, such as the ones on the right, to
help you remember the equations for GPE, M, G, or H. To use the triangle,
simply cover the quantity you want to find out and the triangle will show you
the correct formula.
Special Note:
To earn full points when solving word problems, you MUST SHOW ALL OF YOUR WORK.
STEP 1
STEP 2
STEP 3
STEP 4
Full formula
Correct values inserted into
formula – rough work
Answer rounded to the
correct number of sig figs
Correct metric units stated
in the answer
Sample Problem:
A tennis player holds a tennis ball with a mass of 0.30 kg. If the player holds the ball above the ground
at a height of 2.0 m to serve, what is its gravitational potential energy (GPE)?
Known Values:
m = 0.30 kg
h = 2.0 m
Unknown Values:
Relevant Formula:
GPE = __________
GPE = mgh
Rough Work:
GPE
= mgh
GPE
= 0.3 kg x 9.8 m/s2 x 2.0 m
= 5.88 (not rounded)
GPE
= 5.9 J (2 significant figures)
Questions:
1. Determine the gain in gravitational potential energy when a 4.00 kg rock is raised 18.000 m.
2. A leopard with a mass of 55.00 kg climbs 12.0 m up a tree. What is its gain in GPE?
3. An aircraft is taking a group of skydivers up into the air. Evan is dressed in his parachuting outfit,
which brings his mass to a total of 90.0 kg. The aircraft takes the group to a height of 5000.00 m
before the jump. How much GPE does Evan gain before jumping?
4. An owl has a mass of 4.00 kg. It dives to catch a mouse, losing 800.00 J of its GPE. What was the
starting height of the owl, in meters?
5. The moon has a different gravity constant than Earth. An astronaut with a mass of 110.0 kg climbs
5.0 m up a ladder, increasing his GPE by 880.0 J. What is the strength of gravity on the Moon?
6. One of the tallest radio towers is in Fargo, North Dakota. The tower is 629.9 m tall. If a bird lands on
top of the tower, so that the gravitational potential energy associated with the bird is 2033.76 J, what
is its mass, in kilograms?
7. The largest sea turtle found in the U.S. had a mass of 860.24 kg. If the GPE associated with the
turtle as it was being lifted onto a ship was 20,320.7 J, how high above the water was the turtle?
8. The most massive piece of equipment ever carried by a plane was a 12,400.05-kg generator in 1993.
How far above the ground was the generator when the GPE associated with it was 91,700,000.00 J?
Name:
Class:
Date:
GRAVITATIONAL POTENTIAL ENERGY WORD PROBLEMS (A) (KEY)
1. Determine the gain in gravitational potential energy when a 4.00 kg block is raised 18.000 m.
Known Values:
m = 47.0 kg
h = 18.000 m
GPE =?
GPE = mgh
GPE = 4.00 kg x 9.8 m/s2x x 18.000 m
GPE =705.6 J
GPE = 706 J (3 significant figures)
2. A leopard with a mass of 55.00 kg climbs 12.0 m up a tree. What is its gain in GPE?
Known Values:
m = 55.00 kg
h = 12.00 m
GPE =?
GPE = mgh
GPE =55.00 kg x 9.8 m/s2 x 12.0 m
GPE = 6468.0
GPE = 6470 J or 6.47 kJ (3 significant figures)
3. An aircraft is taking a group of skydivers up into the air. Evan is dressed in his parachuting gear,
which brings his mass to a total of 90.0 kg. The aircraft takes the group to a height of 5000.00 m
before the jump. How much GPE does Evan gain?
Known Values:
m = 90.0 kg
h = 5000.00 m
GPE =?
GPE = mgh
GPE = 90.0 kg x 9.8 m/s2x 5000.00 m
GPE = 4,410,000.00
GPE = 4,410,000 J or (3 significant figures)
4. An owl has a mass of 4.00 kg. It dives to catch a mouse, losing 800.00 J of its GPE. How high was
the owl to begin with?
Known Values:
GPE = mgh
m = 4.00 kg
GPE = 800.00 J
REARRANGED… h = GPE / mg
h = 800.0 J / (4.00 kg) (9.8 m/s2)
h = 800.0 J / 39.2
h = 20.408
h = 20.4 m (3 significant figures)
h =?
5. The moon has a different gravity constant than Earth. An astronaut with a mass of 110.0 kg climbs
5.0 m up a ladder, increasing his GPE by 880.0 J. What is the strength of gravity on the Moon?
Known Values:
m = 110.0 kg
GPE = mgh
REARRANGED…
GPE = 880.0 J
h =5.0 m
g =?
g = GPE / mh
g = 880.0 J / (110.0 kg) (5.0 m)
g = 880.0 / 550.0
g = 1.6 m/s2 (2 significant figures)
6. One of the tallest radio towers is in Fargo, North Dakota. The tower is 629.9 m tall. If a bird lands on
top of the tower, so that the gravitational potential energy associated with the bird is 2033.76 J, what
is its mass, in kilograms?
Known Values:
GPE = mgh
h = 629.9 m
GPE = 2033.76 J
m =?
REARRANGED… m = GPE / gh
m = 2033.76 J / (9.8 m/s2) (629.9 m)
m = 2033.76 / 6173.02
m = 0.3294594
m = 0.3295 kg (4 significant figures)
7. The largest sea turtle found in the U.S. had a mass of 860.24 kg. If the GPE associated with the
turtle as it was being lifted onto a ship was 20,320.7 J, how high above the water was the turtle?
Known Values:
GPE = mgh
m = 860.24 kg
GPE = 20,320.7 J
REARRANGED…
h =?
h = GPE / mg
h = 20,320.7 J / (860.24 kg) (9.8 m/s )
2
h = 20,320.7 / 8430.35
h = 2.4104218
h = 2.4104 m (5 significant figures)
8. The most massive piece of equipment ever carried by a plane was a 12,400.05 kg generator in 1993.
How far above the ground was the generator when the GPE associated with it was 91,700,000.00 J?
Known Values:
GPE = mgh
m = 12,400.05 kg
REARRANGED…
GPE = 91,700,000.01 J
h = GPE / mg
h = 91,700,000.00 J / (12,400.05 kg) (9.8 m/s2)
h = 91,700,000.00 J /121,520.49
h = 754.605252
h = 754.6053 m (7 significant figures)
h =?