The animation below portrays the inelastic
*collision* between a very massive fish and a less
massive fish. Before the collision, the big fish is in motion with a
velocity of 5 km/hr and the little fish is at rest. The big fish has
four times the mass of the little fish. After the collision, both the
big fish and the little fish move together with the same velocity.
Collisions such as this where the two objects stick together and move
with the same post-collision velocity are referred to as inelastic
collisions. What is the after-*collision* velocity of the two
fish?

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the two fish, the momentum of the big and little fish before the collision equals the momentum of the big and little fish after the collision

The mathematics of this problem is simplified by the fact that
before the collision, there is only one object in motion and after
the collision both objects have the same velocity. That is to say, a
momentum analysis would show that all the momentum was
*concentrated* in the big fish before the collision. And after
the collision, all the momentum was the result of a *single
object* (the combination of the big and little fish) moving at an
easily predictable velocity.

The prediction of the final velocity of the two fish involves
determining the ratio by which the mass which is in motion changed;
and then dividing the initial velocity by that ratio. That is, if the
amount of mass in motion increases by a factor of two, then the
velocity would decrease by a factor of two (divide the original
velocity by two). If the amount of mass in motion increases by a
factor of five, then the velocity would decrease by a factor of five
(divide the original velocity by five). In the case of the animation
above, the amount of mass in motion increased by a factor of 5/4; a
change from say 4 kg for the big fish before the collision to 5 kg
for the combination of the big and little fish after the collision.
(Note that I can make up any numbers for mass as long as they meet
the criteria that the big fish has four times the mass as the little
fish.) Since the amount of mass in motion increased by a factor of
5/4, the velocity at which that mass is in motion must decrease by a
factor of 5/4. That is, the original velocity of 5 km/hr must be
divided by 5/4. The result is 4 km/hr; the big and little fish move
together with a velocity of 4 km/hr after the *collision*.

For more information on physical descriptions of motion, visit The Physics Classroom. Detailed information is available there on the following topics:

Momentum

Other animations can be seen at the Multimedia Physics Studios.

© Tom Henderson, 1996-2007

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