than the net effect of other forces acting on them, so we may ignore these other forces.
Elastic and inelastic are two terms used to define types of collisions. These types of
collisions differ in whether the total amount of kinetic energy in the system stays
constant or is reduced by the collision. In any collision, the system’s total amount of
energy must be the same before and after, because the law of conservation of energy
must be obeyed. But in an inelastic collision, some of the kinetic energy is transformed
by the collision into other types of energy, so the total kinetic energy decreases.
For example, a car crash often results in dents. This means some kinetic energy
compresses the car permanently; other KE becomes thermal energy, sound energy
and so on. This means that an inelastic collision reduces the total amount of KE.
In contrast, the total kinetic energy is the same before and after an elastic collision.
None of the kinetic energy is transformed into other forms of energy. The game of pool
provides a good example of nearly elastic collisions. The collisions between balls are
almost completely elastic and little kinetic energy is lost when they collide.
In both elastic and inelastic collisions occurring within an isolated system, momentum is
conserved. This important principle enables you to analyze any collision.
We will mention a third type of collision briefly here: explosive collisions, such as what
occurs when a bomb explodes. In this type of collision, the kinetic energy is greater
after the collision than before. However, since momentum is conserved, the explosion
does not change the total momentum of the constituents of the bomb.Inelastic collision
Kinetic energy is not conserved
Either type of collision
Momentum is conserved
7.9 - Sample problem: elastic collision in one dimension
The picture and text above pose a classic physics problem. Two balls collide in an elastic collision. The balls collide head on, so the second
ball moves away along the same line as the path of the first ball. The balls’ masses and initial velocities are given. You are asked to calculate
their velocities after the collision. The strategy for solving this problem relies on the fact that both the momentum and kinetic energy remain
unchanged.
VariablesWhat is the strategy?- Set the momentum before the collision equal to the momentum after the collision.
- Set the kinetic energy before the collision equal to the kinetic energy after the collision.
- Use algebra to solve two equations with two unknowns.
Physics principles and equations
Since problems like this one often ask for values after a collision, it is convenient to state the following conservation equations with the final
values on the left.
Conservation of momentum
m 1 vf1 + m 2 vf2 = m 1 vi1 + m 2 vi2The small purple ball strikes the
stationary green ball in an elastic
collision. What are the final velocities
of the two balls?
ball 1 (purple) ball 2 (green)
mass m 1 = 2.0 kg m 2 = 3.0 kginitial velocity vi1 = 5.0 m/s vi2 = 0 m/s
final velocity vf1 vf2
(^152) Copyright 2007 Kinetic Books Co. Chapter 07