Is the collision elastic or inelastic? Physics

Question

A 1920 kg vehicle going with a speed of 27 m/s collides with the back of 2490 kg truck. The vehicles lock guards.

a) What is the speed of the vehicle and truck together after crash? (accepting 100% of energy stays as KE)

b) What is the Kinetic Energy of the system before the crash?

c) What is the kinetic energy of the system after the collision?

c)Is the collision elastic or inelastic?

Answer 1

Part a can be answered using the conservation of momentum principle, M1V1 = M2V2, the total momentum before collision is equal to the total momentum after collision. The total momentum before the collision is the momentum of the 1920 kg vehicle which is 1920 kg x 27 m/s = 51840 kgm/s. This is equal to the total momentum after collision which is the combined mass of both vehicles x the final velocity.

a. 51840 kgm/s = 4410 kg x V2

Solve for V2 to get 12 m/s

b. The kinetic energy before the crash is the KE of the first vehicle as the 2nd vehicle was not moving.

KE = 1/2 x 1920kg x 27²m²/s² = 7.0 x 10⁵ J.

c. The KE after the collision is

1/2 x 4410 kg x 12² or 3.2 x 10⁵ J

d. As the KE after collision is different from the KE before collision, the collision is inelastic.