In a railroad switchyard, a 48ton freight car is sent at 7.8mi/h toward a 34ton

Question

In a railroad switchyard, a 48ton freight car is sent at 7.8mi/h toward a 34ton car that is moving in the same direction at 2.2mi/h . What is the speed of the pair after they couple together? Express your answer using two significant figures. What fraction of the initial kinetic energy was lost in the collision? Express your answer using two significant figures.

Explanation / Answer

A)m1 = 48 ton, m2 = 34 ton u1 = 7.8 mi/h, u2 = 2.2 mi/h Let speed after coupling = V Momentum is conserved =>m1u1 + m2u2 = (m1+m2)*V =>V = ((48*7.8)+(34*2.2))/(48+34) = 5.478 mi/hr B)Initial K.E. = (0.5*48*(7.8^2))+(0.5*34*(2.2^2)) = 1542.440 Final K.E. = (0.5*(48+34)*(5.478^2)) = 1230.370 Delta K.E. = 312.070 Delta K.E./K.E._Initial * 100 = (312.070/1542.44)*100 = 20.232 %

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