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216 CHAPTER 7 Work and Energy

ignore friction, then the only force that does work on the water particles is gravity.
This work is positive, so the kinetic energy of the water increases and it attains a
maximum value at the lower end of the channel (where its speed is greatest). The
stream of water emerges from this channel with high kinetic energy and hits the
blades of the waterwheel. The water pushes on the wheel, turns it, and gives up its
kinetic energy while doing work—and the wheel runs the millstones and does useful
work on them. Thus, the work that gravity does on the descending water is ulti-
mately converted into useful work, with the kinetic energy playing an intermediate
role in this process.
The unit of kinetic energy is the joule, the same as the unit of work.Table 7.1 lists
some typical kinetic energies.

During a baseball game, the pitcher throws the ball with a speed
EXAMPLE 5
of 30 m/s (Fig. 7.17).The mass of the ball is 0.15 kg. What is
the kinetic energy of the ball when it leaves his hand? How much work did his
hand do on the ball during the throw?
SOLUTION: The final speed of the ball, when it leave the hand at the end of the
throwing motion, is v 30 m/s. The final kinetic energy of the ball is
2
1
2
1
2
K mv 0.15 kg (30 m s) 68 J (7.26)
2 2 2 2
According to the work–energy theorem [Eq. (7.25)], the work done by the hand
on the ball equals the change of kinetic energy. Since the initial kinetic energy at
the beginning of the throwing motion is zero (v 0), the change of kinetic energy
1
equals the final kinetic energy, and the work is
W K K 68 J 0 68 J
2 1
Note that for this calculation of the work we did not need to know the (compli-
cated) details of how the force varies during the throwing motion.The work–energy
theorem gives us the answer directly.

FIGURE 7.17 Pitcher throwing a ball.
The ball leaves his hand with a speed of
30 m/s.

TABLE 7.1 SOME KINETIC ENERGIES

33
Orbital motion of Earth 2.6 10 J
9
Ship Queen Elizabeth (at cruising speed) 9 10 J
9
Jet airliner (Boeing 747 at maximum speed) 7 10 J
5
Automobile (at 90 km/h) 5 10 J
3
Rifle bullet 4 10 J
Person walking 60 J
Falling raindrop 4 10 5 J
Proton from large accelerator (Fermilab) 1.6 10 7 J
Electron in atom (hydrogen) 2.2 10 18 J
Air molecule (at room temperature) 6.2 10 21 J