LINEAR MOMENTUM AND IMPULSE 139
- Calculate the momentum of a car of
mass 750 kg moving at a constant veloc-
ity of 108 km/h. [22500 kg m/s]
- A football of mass 200 g has a momen-
tum of 5 kg m/s. What is the velocity of
the ball in km/h. [90 km/h]
- A wagon of mass 8 t is moving at a
speed of 5 m/s and collides with another
wagon of mass 12 t, which is stationary.
After impact, the wagons are coupled
together. Determine the common veloc-
ity of the wagons after impact.
[2 m/s]
- A car of mass 800 kg was stationary
when hit head-on by a lorry of mass
2000 kg travelling at 15 m/s. Assuming
no brakes are applied and the car and
lorry move as one, determine the speed
of the wreckage immediately after colli-
sion. [10.71 m/s]
- A body has a mass of 25 g and is moving
with a velocity of 30 m/s. It collides with
a second body which has a mass of 15 g
and which is moving with a velocity of
20 m/s. Assuming that the bodies both
have the same speed after impact, deter-
mine their common velocity (a) when
the speeds have the same line of action
and the same sense, and (b) when the
speeds have the same line of action but
are opposite in sense.
[(a) 26.25 m/s (b) 11.25 m/s]
- A ball of mass 40 g is moving with a
velocity of 5 m/s when it strikes a sta-
tionary ball of mass 30 g. The velocity
of the 40 g ball after impact is 4 m/s
in the same direction as before impact.
Determine the velocity of the 30 g ball
after impact. [1.33 m/s]
- Three masses, X, Y andZ, lie in a
straight line.Xhas a mass of 15 kg and
is moving towardsYat 20 m/s.Y has
a mass of 10 kg and a velocity of 5 m/s
and is moving towardsZ.MassZis sta-
tionary.Xcollides withY,andXandY
then collide withZ. Determine the mass
ofZassuming all three masses have a
common velocity of 4 m/s after the col-
lision ofXandYwithZ. [62.5 kg]
12.2 Impulse and impulsive forces
Newton’s second law of motionstates:
the rate of change of momentum is directly proportional
to the applied force producing the change, and takes
place in the direction of this force
In the SI system, the units are such that:
the applied force
= rate of change of momentum
=
change of momentum
time taken
( 12. 1 )
When a force is suddenly applied to a body due
to either a collision with another body or being hit
by an object such as a hammer, the time taken
in equation (12.1) is very small and difficult to
measure. In such cases, the total effect of the force is
measured by the change of momentum it produces.
Forces that act for very short periods of time
are calledimpulsive forces. The product of the
impulsive force and the time during which it acts
is called theimpulseof the force and is equal to the
change of momentum produced by the impulsive
force, i.e.
impulse=applied force×time
=change in linear momentum
Examples where impulsive forces occur include
when a gun recoils and when a free-falling mass hits
the ground. Solving problems associated with such
occurrences often requires the use of the equation
of motion:v^2 =u^2 + 2 as, from Chapter 11.
When a pile is being hammered into the ground,
the ground resists the movement of the pile and this
resistance is called aresistive force.
Newton’s third law of motionmay be stated as:
for every action there is an equal and opposite reaction
The force applied to the pile is the resistive force;
the pile exerts an equal and opposite force on the
ground.
In practice, when impulsive forces occur, energy
is not entirely conserved and some energy is changed
into heat, noise, and so on.
