A railroad car with a mass of 5.4 105 kg collides with a stationary railroad car

Question

A railroad car with a mass of 5.4 105 kg collides with a stationary railroad car of equal mass. After the collision, the two cars lock together and move off at 3.5 m/s, as shown in Figure 11-21.

Figure 11-21
(a) Before the collision, the first railroad car was moving at 7.0 m/s. What was its momentum?
kg·m/s
(b) What was the total momentum of the two cars after the collision?
kg·m/s
(c) What were the kinetic energies of the two cars before and after the collision?
J (before the collision)
J (after the collision)

(d) Account for the loss of kinetic energy.

Explanation / Answer

a)using conservation of momentum mu = 2m*3.5 u = 7 m/s momentum = mu = 37.8 x 10^5 kg.m/s b) momentum is conserved after collision total momentum = 37.8 x 10^5 kg.m/s c) Before collision KE = .5mu^2 = 132.3 x 10^5 J after collision KE = .5(2m)(u/2)^2 = 66.15 x 10^5 J d) loss of KE = 132.3 x 10^5 - 66.15 x 10^5 = 66.15 x 10^5 during the collision heat is lost in the form of heat and sound energies

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