Simple Nature - Light and Matter

p/A simplified drawing of an

airgun.

q/The black box does work
by reeling in its cable.

This may not sound like an impressive force, but it’s enough to

supply an electron with a spectacular acceleration. Looking up

the mass of an electron on p. 1068, we find

a=F/m

= 5× 1016 m/s^2.

An air gun example 31

.An airgun, figure p, uses compressed air to accelerate a pellet.

As the pellet moves fromx 1 tox 2 , the air decompresses, so the

force is not constant. Using methods from chapter 5, one can

show that the air’s force on the pellet is given byF =bx-7/5. A

typical high-end airgun used for competitive target shooting has

x 1 = 0.046 m,

x 2 = 0.41 m,

and

b= 4.4 N·m7/5.

What is the kinetic energy of the pellet when it leaves the muzzle?

(Assume friction is negligible.)

.Since the force isn’t constant, it would be incorrect to doF =

∆K/∆x. Integrating both sides of the equation dK = Fdx, we

have

∆K=

∫x 2

x 1

Fdx

=−

5 b

2

(

x 2 -2/5−x 1 -2/5

)

= 22 J

In general, when energy is transferred by a force,^7 we use the

termworkto refer to the amount of energy transferred. This is dif-

ferent from the way the word is used in ordinary speech. If you stand

for a long time holding a bag of cement, you get tired, and everyone

will agree that you’ve worked hard, but you haven’t changed the en-

ergy of the cement, so according to the definition of the physics term,

you haven’t done any work on the bag. There has been an energy

transformation inside your body, of chemical energy into heat, but

this just means that one part of your body did positive work (lost

energy) while another part did a corresponding amount of negative

work (gained energy).

(^7) The part of the definition about “by a force” is meant to exclude the transfer
of energy by heat conduction, as when a stove heats soup.
166 Chapter 3 Conservation of Momentum