Page 103 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 8

Momentum

LINEAR MOMENTUM

Work and energy are scalar quantities that have no directions associated with them. When two or more bodies
interact with one another, or a single body breaks up into two or more others, the various directions of motion
cannot be related by energy considerations alone. The vector quantities called linear momentum and impulse are
important in analyzing such events.
The linear momentum (usually called simply momentum) p of a body of mass m and velocity v is the product
of m and v:

Momentum p = mv
The units of momentum are kilogram-meters per second and slug-feet per second. The direction of the momentum
of a body is the same as the direction in which it is moving.
The greater the momentum of a body, the greater its tendency to continue in motion. Thus a baseball that
is solidly struck by a bat (v large) is harder to stop than a baseball thrown by hand (v small), and an iron shot
(m large) is harder to stop than a baseball (m small) of the same velocity.
Another finding of the theory of relativity, which was mentioned in Chapter 7 as the source of the relationship
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E 0 = mc , is that the momentum of an object of mass m and velocity v increases with increasing v according
to the formula
mv
p = 2 2
1 − v /c
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where c is the velocity of light. Because c = 3 × 10 m/s, this effect is only significant at extremely high
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velocities. When v = 0.01c = 3 × 10 m/s (3 million m/s), for instance, the momentum increase beyond just
mv is only 0.005 percent, which is usually negligible. As v gets closer to c, however, which can be the case
for subatomic particles such as electrons and protons, the difference becomes considerable: for v = 0.9c,itis
229 percent. If v were to equal c, p would be infinite, which is impossible—nothing can have infinite momentum.
This means that no material object can travel as fast or faster than light; c is the ultimate velocity limit in the
universe.

IMPULSE
A force F that acts on a body during time t provides the body with an impulse of Ft:
Impulse = Ft = (force)(time interval)

The units of impulse are newton-seconds and pound-seconds.
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