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A collision in an isolated system in which kinetic energy is not conserved throughout the collision. Momentum is conserved, however.

A special case of inelastic collisions is when the colliding objects, deformed from the collision, are stuck together afterwards. The 1-dimensional situation can be described as follows.

Before:

o  --->   <--  o
mA  vA     vB  mB

After:

O  ->
M  v

Legend:
m : mass of object A or B
M : mass of the two objects after the collision
v : velocity of object

We get the following equations.

I) mA*vA + mB*vB = M*v (conservation of momentum)
II) mA + mB = M (conservation of mass)

Example: A car weighing one metric ton (1000 kg) is driving at 100 kph when it hits a 10-ton truck coming towards it at 50 kph. The two collide in an inelastic collision, where they become completely entangled. At what speed and direction will the wreckage move?

Defining:
mA = 10^3 kg
vA = 100 kph
mB = 10^4 kg
vB = -50 kph

Note that positive speed is the direction the car came in, negative speed is the opposite direction.

After the collision, the wreckage has a mass of 11 metric ton (11*10^3). Its velocity is given by (I):

v = (mA*vA + mB*vB) / M
= (10^3 kg * 100 kph + 10*10^3kg * (-50 kph) ) / 11*10^3 kg
= (100 kph - 500 kph) / 11
=~ -36 kph

The two end up driving at 36 kph in the direction the truck was heading.

Thanks to N-Wing for pointing out that ton is a confusing unit.

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