Inelastic Collision Energy Loss

## Question:

hi, i have a problem that says: a 0.400-kg toy truck moving at an
initial speed of 0.100 m/s collides head-on with a 0.300-kg toy
car at rest. The collision is perfectly inelastic, so the two
toys stick together. Calculate how much kinetic energy was lost
in the collision.
i have already figured out the final velocity which is 0.0571
m/s, but i have no idea how to get the KE, or how much was lost.
could u explain the process of solving this problem?

## Answer:

We need to take the total kinetic energy before the collision and
subtract from that the total kinetic energy after the collision.
The difference will be the amount lost.
Kinetic energy is determined from the mass and velocity of an
object. It is a scalar quantity so to get the total for the two
vehicles we just need to calculated it for each and add them up.
The formula for kinetic energy is 1/2*m*v^{2}. In the
pre-collision situation for the truck this is
1/2*.4*.1^{2} = .2*.01 = .002 Joules. For the car,
before the collision this is
1/2*.3*0^{2} = 0. So the total kinetic energy is
that of the truck = .002.

After the collision both vehicles will have the same velocity.
Even in inelastic collisions, momentum is conserved. The momentum
before the collision was the mass of the truck times its velocity
or .4*.1 = .04. After the collision this
value must be the same so the total mass of the toys times the
final velocity must be .04. The final velocity then is .04
divided by the total mass of .7kg as you already figured out to
be .0571.

Next we calculate the final kinetic energy. That is 1/2*(.4+.3)*.0571^{2} = .35*.0033 =
.00116. This we subtract from .002 to get the mechanical
energy lost to heat in the collision. The answer is .002-.00116 = .00084 Joules.

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