Answer:
.
Explanation:
KE lost = Total KE before Collision - Total KE after Collision.
For each car, the KE before collision can simply be found with the equation:
, where
is the mass of the car, and
is the speed of the car.
The car would have an initial KE of:
.
The car was initially not moving. Hence, its speed and kinetic energy would zero before the collision.
To find the velocity of the two cars after the collision, apply the conservation of momentum.
The momentum of an object is equal to its mass
times its velocity
. In other words,
.
Let the mass of the two cars be denoted as and
, and their initial speeds
and
. Since the two cars are stuck to each other after the collision, their final speeds would be the same. Let that speed be denotes as
.
Initial momentum of the two-car system:
.
After the collision, both car would have a velocity of (since they were stuck to each other.) As a result, the final momentum of the two-car system would be:
.
Since momentum is conserved during the collision, the momentum of the system after the collision would also be . That is:
.
Solve for :
.
Hence, the total kinetic energy after the collision would be:
.
The amount of kinetic energy lost during the collision would be:
.