Question

A railroad freight car, mass 20 000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50 000-kg loaded second car, initially at rest and with brakes released. What percentage of the initial kinetic energy of the 20 000-kg car is preserved in the two-coupled cars after collision?

Question 10 options:

	14%
	23%
	29%
	31%

Answer 1

Mass of the first car = m₁ = 20000 kg

Mass of the second car = m₂ = 50000 kg

Initial speed of the first car = V₁ = 2 m/s

Initial speed of the second car = V₂ = 0 m/s (At rest)

Speed of both the cars after the collision = V₃

By conservation of linear momentum,

m₁V₁ + m₂V₂ = (m₁ + m₂)V₃

(20000)(2) + (50000)(0) = (20000 + 50000)V₃

V₃ = 0.5714 m/s

Initial kinetic energy of the system = KE₁

KE₁ = m₁V₁²/2

KE₁ = (20000)(2)²/2

KE₁ = 40000 J

Final kinetic energy of the system = KE₂

KE₂ = (m₁ + m₂)V₃²/2

KE₂ = (20000 + 50000)(0.5714)²/2

KE₂ = 11427.43 J

Percentage of the initial kinetic energy preserved = P

P = 29%

Percentage of the initial kinetic energy preserved in the two coupled cars after the collision = 29%