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220 CHAPTER 7 Work and Energy

whenever gravity performs negative work on the particle ( y y , an ascending par-
1 2
ticle), the “amount of mgy” increases. Thus, the quantity mgy represents the amount of
stored, or latent, gravitational work; that is, it represents the gravitational potential energy.
We will adopt the notation U for the gravitational potential energy:
gravitational potential energy U mgy (7.29)

This potential energy is directly proportional to the height y, and it has been chosen
to be zero at y 0 (see Fig. 7.21).

U

39.2

29.4

19.6 Gravitational
For a 1-kg potential energy
mass, U = increases linearly
1 kg g y. 9.8 with height.

U = 0 is chosen 0
here to occur 0 1 2 3 4 m y
at y = 0.
FIGURE 7.21 Plot of the gravitational potential energy
of a mass of 1 kg as a function of height y.

In terms of the gravitational potential energy, Eq. (7.28) for the work done by
gravity becomes
W U U (7.30)
2 1
Since U U U is the change in potential energy, Eq. (7.30) says that the work
2 1
equals the negative of the change in potential energy,
W U (7.31)

What is the kinetic energy and what is the gravitational potential
EXAMPLE 7
energy (relative to the ground) of a jet airliner of mass 73000 kg
cruising at 240 m/s at an altitude of 9000 m?

SOLUTION: The kinetic energy is
4
2
2
1
9
1
K mv 7.3 10 kg (240 m s) 2.1 10 J
2
2
The gravitational potential energy is U mgy. If we measure the y coordinate
from the ground level, then y 9000 m for our airliner, and
4 2 3 9
U mg y 7.3 10 kg 9.81 m s 9.0 10 m 6.4 10 J
We see that the airliner has about three times more potential energy than kinetic
energy.