Page 53 - Fisika Terapan for Engineers and Scientists

8.5 Power 253

✔ Checkup 8.4

QUESTION 1: The Sun radiates heat and light. Does the Sun consequently suffer a
loss of mass?
QUESTION 2: In the annihilation of matter and antimatter, a particle and an
antiparticle—such as a proton and an antiproton, or an electron and an antielectron—
disappear explosively upon contact, giving rise to an intense flash of light. Is energy
conserved in this reaction? Is mass conserved?
QUESTION 3: You heat a potful of water to the boiling point. If the pot is sealed so
no water molecules can escape, then, compared with the cold water, the mass of the boil-
ing water will:
(A) Increase (B) Decrease (C) Remain the same

8.5 POWER Online
10
Concept
When we use an automobile engine to move a car up a hill or when we use an electric Tutorial
motor to lift an elevator cage, the important characteristic of the engine is not how
much force it can exert, but rather how much work it can perform in a given amount
of time. The force is only of secondary importance, because by shifting to a low gear
we can make sure that even a “weak” engine exerts enough force on the wheels to
propel the automobile uphill. But the work performed in a given amount of time, or
the rate of work, is crucial, since it determines how fast the engine can propel the car
up the hill. While the car moves uphill, the gravitational force takes energy from the
car; that is, it performs negative work on the car. To keep the car moving, the engine
must perform an equal amount of positive work. If the engine is able to perform this
work at a fast rate, it can propel the car uphill at a fast speed.
The rate at which a force does work on a body is called the power delivered by the
force. If the force does an amount of work W in an interval of time
t, then the
average power is the ratio of W and
t:

W
P (8.33) average power
¢t

The instantaneous power is defined by a procedure analogous to that involved in the
definition of the instantaneous velocity. We consider the small amount of work dW
done in the small interval of time dt and take the ratio of these small quantities:

dW
P (8.34) instantaneous power
dt

According to these definitions, the engine of your automobile delivers high power
if it performs a large amount of work on the wheels (or, rather, the driveshaft) in a
short time. The maximum power delivered by the engine determines the maximum
speed of which this automobile is capable, since at high speed the automobile loses
energy to air resistance at a prodigious rate, and this loss has to be made good by the
engine. You might also expect that the power of the engine determines the maximum
acceleration of which the automobile is capable. But the acceleration is determined