Question

a railroad freight car, mass 17000kg, is allowed to coast along a level track at a speed of 3m/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 in the 17000 kg car is preserved in the two coupled cars after collision?

Answer 1

Initial KE = ½mv²
KE = ½(17000 kg)(3.0 m/s)²
KE = 76500 J

Initial Momentum = (17000 kg)*(3.0 m/s) + (50000 kg)*(0 m/s)
Initial Momentum = 51000 kgm/s

Since Initial Momentum = Final Momentum
So,
51000 kgm/s = (17000 + 50000 kg)*v
=> v = 0.76 m/s

KE of the coupled cars :
KE = ½mv²
KE = ½(17000 + 50000 kg)(0.76 m/s)²
KE = 19350 J

percentage of the initial kinetic energy in the 17000 kg car preserved in the two coupled cars after collision = (19350/76500) * 100
= 25.3%