Question

Three identical train cars, coupled together are rolling east at 2.0 m/s.  A fourth car traveling east at 4.0 m/s catches up with the three and couples to make a fourcar train.  A moment later the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five car train.  What is the speed of the five car train?  Answer in m/s.

Answer 1

Consider the mass of each train car as m, because the three train cars are identical т — т, 3D т, %3D т The three identical train cars are travelling with same speed towards east, then the initial speed of the three train cars is, и, 3 и, — и, 3 2.0 m/s The mass of the fourth train car is, т, The initial speed of the fourth car is, u4 = 4.0 m/s The mass of the fifth train car is, The fifth car is initially at rest, then the initial speed of the fifth train car is, s 0 After Collison of the four train cars with fifth car, the final speed of five cars is same V4 = v5 = v V2 3 The expression for the law of conservation of momentum is, ти, + ти, +т,и, + т,и, + т,u, — ту, + т,V2 + mv; + mv,+ m;V; 44 4

Calculate the final speed of the five-car train as follows: ти, + ти, +ти, +ти, + т,us — ту, + т,V2 + m,V; t mavt m;vs (u, +и, +u, +uи,) + т(0): m ту + my +ту+тy+mу т (и, +и, +и, +и,) %— 5v -С.- -@еоы 1 (и, +и, +и, +и, 5 у%3 (2.0 m/s +2.0 m/s 2.0m/s4.0m/s) 5 - 2.0 m/s