Question

A 100kg cart moving at 25m/s rear-ends a 75kg cart moving at 10m/s. The two carts stick together, but during the collision a 10kg wheel on the 100kg cart breaks off and continues moving forward at 20m/s. Show work for all problems.

1) How fast are the carts going after the collision? (Be sure that your answer(s) clearly indicate direction as well as speed.)

2) Is this collision elastic? If yes, explain. If not, calculate the percentage of the initial kinetic energy that was lost.

Answer 1

Given,

m1 = 100 kg ; m2 = 75 kg

u1 = 25 m/s ; u2 = 10 m/s ;

1)Both the carts are moving in the same direction. Let V be the speed after collision.

from the conservation of momentum

Pi = Pf

m1u1 + m2u2 = [ (m1 - 10) + m2 ] V + 10 x 20

100 x 25 + 75 x 10 = (90 + 75)V + 200 => V = 18.48 m/s

Hence, V = 18.48 m/s.

2)The collision is ineastic, since the two masses sticks and energy is not conserved.

KEi = KE1 + KE2

KEi = 1/2 x 100 x 25 x 25 + 1/2 x 75 x 10 x 10 = 35000 J

KEf = 1/2 x 165 x 18.48 x 18.48 + 1/2 x 10 x 20 x20 = 30175 J

Delta KE = 30175 - 35000 = 4825 J

Hence, delta KE = 4825 J was lost.