Gravitational potential energy
Potential energy is a form of energy that comes from an object’s position. Gravitational potential
energy comes from an object’s height in the presence of gravity. Hand-held objects at heights of one
or two meters have potential energies between 1 and 100 joules. A 6,000 kg helicopter at an altitude
of 1,000 m (1 km) has a potential energy of 60 million joules. Gravitational potential energy depends
linearly on height and mass. For example, increasing the height tenfold will increase the potential
energy by a factor of ten. Note that the value of g remains constant for all objects near Earth’s surface.
E p = mgh
Typical potential energies of everyday objects at typical heights (on/near Earth’s surface):
baseball
baseball
arrow
seagull
diver
helicopter
mass
(kg)
height
(m)
(N/kg)
0.15
0.15
0.01
1.75
1
10
100
50
9.8
9.8
9.8
9.8
1.47
14.7
9.8
857
50
6,000
10
1,000
9.8
9.8
4,900
58,800,000
g
EP
(J)
Applying new knowledge
When calculating the potential energy in problems 1 – 6 below, compare your final answers to the
typical values shown in the table to see if they make sense.
Example: Calculate the potential energy of a 3.0 kg rock at a height of 15 m.
E p = mgh = (3.0 kg)(9.8 N/kg)(15 m) = 441 J
1. Calculate the potential energy of a 5.0 g (0.005 kg) paper airplane 5.0 meters above the ground.
2. Calculate the potential energy of a 6.3 kg eagle flying at a height of 75 m.
3. Calculate the potential energy of a 40 gram sparrow resting on a branch 30 feet above the ground.
(Hint: 1 foot = 0.305 m)
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4. How much potential energy is required to lift a 50 gram arrow to a height of 100 meters?
5. Which has more potential energy: a 1.0 kg ball at a height of 10 m, or a 10 kg ball at a height of
1.0 m?
6. What is the height of a 2.00 kg object if its potential energy is 100 J?
7. A 2.5 kg falcon soaring at a height of 500 meters has a certain potential energy. Now suppose the
falcon were carrying a 1.0 kg snake. What would the new height be if the total potential energy
were to remain the same?
8. Calculate the potential energy of a small plane that weighs 7,200 pounds and is traveling at a speed
of 80 mph at an altitude of 5,500 feet. (Hint: 1 foot = 0.30 m and 1 kg weighs 2.2 lbs. on or near
Earth’s surface)
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