Question

a railroad car with a mass of 1.92*10^4kg moving at 3.00 m/s joins with two railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.18m/s.
a. what is the speed of the three joined cars after the collision?
b. what is the decrease in kinetic energy during the collision?

Answer 1

a) let the final speed of the three joined cars after the collision be V m/s

By the conservation of momentum we have

m1u1 + m2u2 = (m1 + m2)V

m*3 + (2m)*1.18 = (m + 2m)*V

V = 1.7867 m/s

so the final speed is 1.7867 m/s

b) initial KE = 0.5m1u1^2 + 0.5m2*u2^2

= 0.5*1.92*10^4*3^2 + 0.5*2*1.92*10^4*1.18^2

= 113134.08 J

Final KE = 0.5(m1 + m2)V^2

= 0.5*(1.92*10^4 + 2*1.92*10^4)*1.7867^2

= 91938.15 J

decrease in KE = 113134.08 - 91938.15 = 21195.93 J = 2.12*10^4 J