Question

Q. A 32,000 kg freight car is coasting at 0.550 m/s with negligible friction under a hopper that dumps 140,000 kg of scrap metal into it.

A. What is the final velocity (in m/s) of the loaded freight car? (Enter the magnitude.)

B. How much kinetic energy (in J) is lost?

Answer 1

Mass of the freight car = m₁ = 32000 kg

Mass of the scrap metal dumped in the freight car = m₂ = 140000 kg

Initial velocity of the freight car = V₁ = 0.55 m/s

Final velocity of the loaded freight car = V₂

By conservation of linear momentum,

m₁V₁ = (m₁ + m₂)V₂

(32000)(0.55) = (32000 + 140000)V₂

V₂ = 0.1023 m/s

Initial kinetic energy of the system = KE₁

KE₁ = m₁V₁²/2

KE₁ = (32000)(0.55)²/2

KE₁ = 4840 J

Final kinetic energy of the system = KE₂

KE₂ = (m₁ + m₂)V₂²/2

KE₂ = (32000 + 140000)(0.1023)²/2

KE₂ = 900 J

Kinetic energy lost = KE

KE = KE₂ - KE₁

KE = 900 - 4840

KE = -3940 J

A) Final velocity of the loaded freight car = 0.1023 m/s

B) Kinetic energy lost = -3940 J