Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

260 Chapter 10 Force and Force-Related Parameters

the mass of the object being pushed, while keeping the magnitude of the force constant, the

object did not move as quickly and had a smaller rate of change of speed. Thus, Newton noticed

that there was a direct relationship between the push (the force), the mass of the object being

pushed, and the acceleration of the object. He also noticed that there was a direct relationship

between the direction of the force and the direction of the acceleration. Newton’s second law

of motion simply states that the net effect of unbalanced forces is equal to mass times acceler-

ation of the object, which is given by the expression

(10.5)

where the symbol (sigma) means summation,Frepresents the forces in units of newton,

mis the mass of the object in kg, andais the resulting acceleration of the mass center of the

object in m/s

2

. In Equation (10.5), a summation of forces is used to allow for application of
more than one force on an object.

Newton’s Third Law

Returning to our example of a book resting on a desk, as shown in Figure 10.9, because the

weight of the book is pushing down on the desk, simultaneously the desk also pushes up on the

book. Otherwise, the desk won’t be supporting the book. Newton’s third law states that for

every action there exists a reaction, and the forces of action and reaction have the same magni-

tude and act along the same line, but they have opposite directions.

Newton’s Law of Gravitation

The weight of an object is the force that is exerted on the mass of the object by the earth’s grav-

ity. Newton discovered that any two masses,m 1 andm 2 , attract each other with a force that is

equal in magnitude and acts in the opposite direction, as shown in Figure 10.10, according to

the following relationship:

F (10.6)

Gm 1 m 2

r

2

g

a^ F

!

ma

!

Weight of

the book

Force from

the table

supporting

the book

■Figure 10.9 The forces of action and reaction; they have the same magnitude and the same line of action,

but they act in opposite directions.

r

m 2

m 1 F

F

■Figure 10.10

The gravitational attraction of

two masses.

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