Mechanical Engineering Principles

13

Force, mass and acceleration

At the end of this chapter you should be

able to:

• define force and state its unit


• appreciate ‘gravitational force’


• state Newton’s three laws of motion


• perform calculations involving force
  F=ma


• define ‘centripetal acceleration’


• perform calculations involving centripetal

force=

mv^2

r

• define ‘mass moment of inertia’

13.1 Introduction

When an object is pushed or pulled, a forceis
applied to the object. This force is measured in
newtons (N).The effects of pushing or pulling an
object are:

(i) to cause a change in the motion of the object,

and

(ii) to cause a change in the shape of the object.

If a change occurs in the motion of the object,
that is, its velocity changes fromutov, then the
object accelerates. Thus, it follows that acceleration
results from a force being applied to an object. If a
force is applied to an object and it does not move,
then the object changes shape, that is, deformation
of the object takes place. Usually the change in
shape is so small that it cannot be detected by just
watching the object. However, when very sensitive
measuring instruments are used, very small changes
in dimensions can be detected.
A force of attraction exists between all objects.
The factors governing the size of this forceF are

the masses of the objects and the distances between

their centres:

F∝

m 1 m 2

d^2

Thus, if a person is taken as one object and the

Earth as a second object, a force of attraction exists

between the person and the Earth. This force is

called thegravitational forceand is the force that

gives a person a certain weight when standing on

the Earth’s surface. It is also this force that gives

freely falling objects a constant acceleration in the

absence of other forces.

13.2 Newton’s laws of motion

To make a stationary object move or to change the

direction in which the object is moving requires a

force to be applied externally to the object. This

concept is known asNewton’s first law of motion

and may be stated as:

An object remains in a state of rest, or continues in a

state of uniform motion in a straight line, unless it is

acted on by an externally applied force

Since a force is necessary to produce a change of

motion, an object must have some resistance to a

change in its motion. The force necessary to give a

stationary pram a given acceleration is far less than

the force necessary to give a stationary car the same

acceleration on the same surface. The resistance to

a change in motion is called theinertiaof an object

and the amount of inertia depends on the mass of

the object. Since a car has a much larger mass than

a pram, the inertia of a car is much larger than that

of a pram.

Newton’s second law of motionmay be stated as:

The acceleration of an object acted upon by an external

force is proportional to the force and is in the same

direction as the force