Game Development Reference
In-Depth Information
One area where the principle of conservation of linear momentum of a system of objects
appears is in the analysis of two-body linear collisions—a subject we will explore a little later in
the chapter.
Elastic and Inelastic Collisions
An analysis of the collision between two objects depends on the momentum of the objects, but
collisions can also be analyzed in terms of energy. Consider the sphere falling to the ground in
Figure 6-1. Just before the sphere collides with the ground, it has a velocity,
v
. The kinetic energy of
the sphere as it hits the ground is equal to
1/2mv
2
.
½
mv
2
E
KE
=
Figure 6-1.
An elastic collision conserves kinetic energy.
If the sphere bounces off the ground with the same velocity magnitude (in the opposite
direction) as the impact velocity, then the kinetic energy of the sphere will be the same before and
after the collision. A collision in which kinetic energy is conserved is called an
elastic collision
.
On the other hand, if a ball of string is dropped to the ground, it may only bounce a little.
Because the post-collision velocity of the ball of string is less than the pre-collision velocity,
kinetic energy is not conserved in this instance. A collision in which part or all of the kinetic
energy is lost is called an
inelastic collision
. If you're wondering where the kinetic energy goes
in an inelastic collision, the answer is work. Inelastic collisions usually involve the deformation
of one or both colliding objects. When the force of collision moves part of an object a certain
distance, work is performed.
If both colliding objects are moving at the time of collision, the element to look at when
evaluating the collision is the relative velocity between the two objects. Figure 6-2 shows two
objects just before they collide. The relative velocity between the two objects just before the
collision is equal to
v
2
- v
1
. If the magnitude of the relative velocity between the objects is the
same after the collision as it is before the collision, then kinetic energy is conserved and the
collision is elastic.
