Mechanical Engineering Principles

12

Linear momentum and impulse

At the end of this chapter you should be

able to:

• define momentum and state its unit


• state Newton’s first law of motion


• calculate momentum given mass and
  velocity


• state Newton’s second law of motion


• define impulse and appreciate when impul-
  sive forces occur


• state Newton’s third law of motion


• calculate impulse and impulsive force


• use the equation of motionv^2 =u^2 + 2 as
  in calculations

12.1 Linear momentum

Themomentumof a body is defined as the product
of its mass and its velocity, i.e.momentum=mu,
wherem=mass (in kg) andu=velocity (in m/s).
The unit of momentum is kg m/s
Since velocity is a vector quantity,momentum
is a vector quantity, i.e. it has both magnitude and
direction.
Newton’s first law of motionstates:

a body continues in a state of rest or in a state of

uniform motion in a straight line unless acted on by

some external force

Hence the momentum of a body remains the same
provided no external forces act on it.
The principle of conservation of momentumfor a
closed system (i.e. one on which no external forces
act) may be stated as:

the total linear momentum of a system is a constant

The total momentum of a system before collision
in a given direction is equal to the total momentum

m 2

m 1

u 1 u 2

Mass

Mass

Figure 12.1

of the system after collision in the same direction.

In Figure 12.1, masses m 1 andm 2 are travelling

in the same direction with velocityu 1 >u 2 .A

collision will occur, and applying the principle of

conservation of momentum:

total momentum before impact

=total momentum after impact

i.e. m 1 u 1 +m 2 u 2 =m 1 v 1 +m 2 v 2

wherev 1 andv 2 are the velocities ofm 1 andm 2

after impact.

Problem 1. Determine the momentum of a

pile driver of mass 400 kg when it is moving

downwards with a speed of 12 m/s.

Momentum=mass×velocity

=400 kg×12 m/s

=4800 kg m/s downwards

Problem 2. A cricket ball of mass 150 g

has a momentum of 4.5 kg m/s. Determine

the velocity of the ball in km/h.

Momentum=mass×velocity,

hence velocity=

momentum

mass

=

4 .5kgm/s

150 × 10 −^3 kg

=30 m/s