The Solar System

CHAPTER 5 | GRAVITY 79

Fundamentals 1). Now imagine that, instead of tossing a

paper clip, someone tosses you a bowling ball. A bowling ball con-

tains much more mass than a paper clip and therefore has much

greater momentum, even though it is moving at the same velocity.

Newton’s second law of motion is about forces. Where

Galileo spoke only of accelerations, Newton saw that an accelera-

tion is the result of a force acting on a mass (Figure 5-5b).

Newton’s second law is commonly written as

F  ma

As always, you must defi ne terms carefully when you look at

an equation. An acceleration is a change in velocity, and a veloc-

ity is a directed speed. Most people use the words speed and veloc-

ity interchangeably, but they mean two diff erent things. Speed is

a rate of motion and does not have any direction associated with

it, but velocity does. If you drive a car in a circle at 55 mph, your

speed is constant, but your velocity is changing because your

direction of motion is changing. An object experiences an accel-

eration if its speed changes or if its direction of motion changes.

Every automobile has three accelerators—the gas pedal, the brake

pedal, and the steering wheel. All three change the car’s velocity.

In a way, the second law is just common sense; you experience

its consequences every day. Th e acceleration of a body is propor-

tional to the force applied to it. If you push gently against a grocery

cart, you expect a small acceleration. Th e second law of motion also

says that the acceleration depends on the mass of the body. If your

grocery cart is fi lled with bricks and you push it gently, you expect

Newton’s fi rst law of motion is really a restatement of
Galileo’s law of inertia. An object continues at rest or in uniform
motion in a straight line unless acted on by some force.
Astronauts drifting in space will travel at constant rates in
straight lines forever if no forces act on them (■ Figure 5-5a).
Newton’s fi rst law also explains why a projectile continues to
move after all forces have been removed—for instance, how an
arrow continues to move after leaving the bowstring. Th e object
continues to move because it has momentum. You can think of
an object’s momentum as a measure of its amount of motion.
An object’s momentum is equal to its velocity times its mass.
A paper clip tossed across a room has low velocity and therefore
little momentum, and you could easily catch it in your hand. But
the same paper clip fi red at the speed of a rifl e bullet would have
tremendous momentum, and you would not dare try to catch it.
Momentum also depends on the mass of an object (Focus on

Mass

O

ne of the most fundamental
parameters in science is mass, a
measure of the amount of matter in
an object. A bowling ball, for example,
contains a large amount of matter and so is
more massive than a child’s rubber ball of the
same size.
Mass is not the same as weight. Your
weight is the force that Earth’s gravity exerts
on the mass of your body. Because gravity
pulls you downward, you press against the
bathroom scale, and you can measure your
weight. Floating in space, you would have no
weight at all; a bathroom scale would be
useless. But your body would still contain the
same amount of matter, so you would still
have the same mass you do on Earth.

Sports analogies illustrate the importance

of mass in dramatic ways. A bowling ball, for

example, must be massive to have a large

effect on the pins it strikes. Imagine trying to

knock down all the pins with a balloon

instead of a bowling ball. In space, where the

bowling ball would be weightless, a bowling

ball would still have more effect on the pins

than a balloon would. On the other hand,

runners want track shoes that have low mass

so that they are easy to move. Imagine trying

to run a 100-meter dash wearing track shoes

that were as massive as bowling balls. It

would be diffi cult to accelerate away from the

starting blocks. Finally, think of the shot put.

It takes muscle because the shot is massive,

not because it is heavy. Imagine throwing the

shot in space where it would have no weight.

It would still be massive, and it would take

great effort to start it moving.

Mass is a unique measure of the amount of

material in an object. Using the metric system

(Appendix A), mass is measured in kilograms.

1

MASS | ENERGY | TEMPERATURE AND HEAT | DENSITY | PRESSURE

Fun

pape

tains

grea

Gali

tion

New

an e

i i

Newton’s fi rst law of motion is really a restatement of
G lil ’ l f i i A bj i i if

■ Table 5-1 ❙ Newton’s Three Laws of

Motion

I. A body continues at rest or in uniform motion in a straight

line unless acted on by some force.

II. The acceleration of a body is inversely proportional to its

mass, directly proportional to the force, and in the same

direction as the force.

III. To every action, there is an equal and opposite reaction.

100

kg

Mass is not the

same as weight.