Four trains coupling - find speed of resulting train

[dsptl]

Three identical train cars, coupled together, are rolling east at 4 m/s. A fourth car traveling east at 6 m/s catches up with the three and couples to make a four-car train. What is the speed of the four-car train?

I have no idea what to do. Please Help...thanks in advance :)

 

[Topher925]

Start by assuming a perfectly elastic collision(no energy loss in the collision). Since the collision is elastic you can assume conservation of momentum before and after the collision. What is the momentum before and after the collision?

 

[baba89]

To find the speed of the resulting four-car train, we can use the concept of conservation of momentum. This principle states that in a closed system, the total momentum before an event is equal to the total momentum after the event. In this case, the coupling of the fourth car to the three-car train is the event.

First, we need to determine the total momentum before the coupling. The three identical train cars have a mass of m and are traveling at 4 m/s, so their total momentum is 3m * 4 m/s = 12m. The fourth car has a mass of m and is traveling at 6 m/s, so its momentum is m * 6 m/s = 6m.

Next, we need to determine the total momentum after the coupling. Since the four cars are now coupled together, they will have the same speed. We can represent this speed as v. Therefore, the total momentum after the coupling is (3m + m) * v = 4m * v.

Now, we can set up an equation using the principle of conservation of momentum:

Total momentum before = Total momentum after
12m + 6m = 4m * v

Solving for v, we get v = (12m + 6m) / 4m = 4.5 m/s.

Therefore, the speed of the resulting four-car train is 4.5 m/s.

I hope this helps! If you have any further questions or need clarification, please let me know.