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98 CHAPTER 5 FORCE AND MOTION—I

and thus

Defining the mass of Xin this way is useful only if the procedure is consis-

tent. Suppose we apply an 8.0 N force first to the standard body (getting an accel-

eration of 8.0 m/s^2 ) and then to body X(getting an acceleration of 2.0 m/s^2 ). We

would then calculate the mass of Xas

which means that our procedure is consistent and thus usable.

The results also suggest that mass is an intrinsic characteristic of a body—it

automatically comes with the existence of the body. Also, it is a scalar quantity.

However, the nagging question remains: What, exactly, is mass?

Since the word massis used in everyday English, we should have some intu-

itive understanding of it, maybe something that we can physically sense. Is it

a body’s size, weight, or density? The answer is no, although those characteristics

are sometimes confused with mass. We can say only that the mass of a body is

the characteristic that relates a force on the body to the resulting acceleration.Mass

has no more familiar definition; you can have a physical sensation of mass only

when you try to accelerate a body, as in the kicking of a baseball or a bowling ball.

Newton’s Second Law

All the definitions, experiments, and observations we have discussed so far can be

summarized in one neat statement:

mXm 0

a 0

aX

(1.0 kg)

8.0 m/s^2

2.0 m/s^2

4.0 kg,

mXm 0

a 0

aX

(1.0 kg)

1.0 m/s^2

0.25 m/s^2

4.0 kg.

Newton’s Second Law:The net force on a body is equal to the product of the

body’s mass and its acceleration.

In equation form,

(Newton’s second law). (5-1)

Identify the Body. This simple equation is the key idea for nearly all the

homework problems in this chapter, but we must use it cautiously. First, we must

be certain about which body we are applying it to. Then must be the vector

sum of allthe forces that act on thatbody. Only forces that act on thatbody are to

be included in the vector sum, not forces acting on other bodies that might be

involved in the given situation. For example, if you are in a rugby scrum, the net

force on youis the vector sum of all the pushes and pulls on yourbody. It does

not include any push or pull on another player from you or from anyone else.

Every time you work a force problem, your first step is to clearly state the body

to which you are applying Newton’s law.

Separate Axes.Like other vector equations, Eq. 5-1 is equivalent to three

component equations, one for each axis of an xyzcoordinate system:

Fnet,xmax, Fnet,ymay, and Fnet,zmaz. (5-2)

Each of these equations relates the net force component along an axis to the

acceleration along that same axis. For example, the first equation tells us that

the sum of all the force components along the xaxis causes the xcomponentax

of the body’s acceleration, but causes no acceleration in the yandzdirections.

Turned around, the acceleration component axis caused only by the sum of the

F

:

net

F

:

netma

: