Question

4 railway truck a moves along a horizontal track and collides with a stationary truck b. the two join together in the collision. immediately before the collision, truck a has a speed of 5.0 m/s. immediately after the collision, the speed of the trucks is v. the mass of truck a is 800 kg and the mass of truck b is 1200 kg. (i) Calculate the value of v. (ii) Calculate the total kinetic energy lost during the collision.

Answer 1

The final velocity v after the collision is 2.0 m/s and the total kinetic energy lost during the collision is 6,000 J.

Step-by-step explanation:

When railway truck A, which has a mass of 800 kg and is moving at 5.0 m/s, collides with the stationary truck B with a mass of 1200 kg and they stick together, to find the final velocity v we must use the conservation of momentum:

Momentum before collision = Momentum after collision

(800 kg × 5.0 m/s) + (1200 kg × 0 m/s) = (800 kg + 1200 kg) × v

4000 kg·m/s = 2000 kg × v

v = 4000 kg·m/s / 2000 kg

v = 2.0 m/s

The total kinetic energy lost during the collision is calculated by finding the difference in kinetic energy before and after the collision.

KE initial = (1/2) × 800 kg × (5.0 m/s)² = 10,000 J

KE final = (1/2) × 2000 kg × (2.0 m/s)² = 4,000 J

Total KE lost = KE initial - KE final = 10,000 J - 4,000 J = 6,000 J