Chapter 8, Problem 63A

A railroad diesel engine weighs four times as much as a freight car. If the diesel engine coasts at 5 km/h into a freight car that is at rest, how fast do the two coast after they couple?

To determine

To Calculate: The final velocity after coupling.

Answer to Problem 63A

  $4\text{km/h}$

Explanation of Solution

Given info:

Mass of the engine is 4 times the mass of freight car.

$M_e=4M_f$

Initial velocity of engine, $u_e=5\text{km/h}$

Initial velocity of freight car, $u_f=0$

Formula used:

According to law of conservation of momentum,

Initial momentum = Final momentum

Initial momentum of diesel engine + Initial momentum of freight car = combined momentum

Calculation:

  $\begin{array}{l}{M}_e{u}_e+M_f{u}_f=\left(M_e+M_f\right)v\\ 4M_f\left(\text{5}\text{km/h}\right)=5M_{f}v\\ v=4\text{km/h}\end{array}$

Conclusion:

Thus, the final velocity after coupling is $4\text{km/h}$ .