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
m_{A} v_{A} v_{B} m_{B}

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) m_{A}*v_{A} + m_{B}*v_{B} = M*v (conservation of momentum)

II) m_{A} + m_{B} = 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:

m_{A} = 10^3 kg

v_{A} = 100 kph

m_{B} = 10^4 kg

v_{B} = -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 = (m_{A}*v_{A} + m_{B}*v_{B}) / 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.