Professional Application: A 30,000-kg freight car is coasting at 0.850 m/s with negligible friction under a hopper that dumps 110,000 kg of scrap metal into it. (a) What is the final velocity of the loaded freight car? (b) How much kinetic energy is lost?

Answer:0.182m/s

Explanation:

We assume that the direction of motion of the car be in the positive x-direction.

Before the dump the momentum of the car was in the x-direction with magnitude

p = mv = 30000 x 0.850 = 2.55 x 104 kgm/s.

The x - component of the momentum of the scrap metal was zero,

so the total initial momentum in the x-direction was pi = 2.55*104 kgm/s.

According to the law of conservation of linear momentum. Momentum before collision is equal to momentum after collision and

since no external forces act on the objects in the x-direction, therefore the x-component of the total momentum is conserved.

pfinal = (Mcar + Mmetal) Vfinal

(110,000 + 30000 kg) Vfinal = pinitial

140000Vf = 2.55*104 kgm/s.

vVfinal = (2.55*104 kgm/s) / (140,000 kg)

Ans = 0.182 m/s.