Solving Linear Momentum in Boxcar A and Flatcar B Collision

[bungie77]

Homework Statement

A 40-tonne boxcar A is moving with a velocity of 7.2 km/h when it strikes, and is automatically coupled with, a 12-tonne flatcar B which carries a 20-tonne trailer truck C. Both the flat car and trailer truck are at rest with their brakes released. What is the velocity of the boxcar immediately after the end of the flatcar hits the trailer truck? Neglect friction and assume the impact of the flatcar and trailer truck to be perfectly plastic (e = 0).

Homework Equations

Conservation of linear momentum.

The Attempt at a Solution

Able to calculate the velocity of the coupled pair immediately after impact using conservation of linear momentum. So velocity will be constant until the trailer truck hits the end of the flatcar at which point the velocity of the boxcar changes. Unsure where to go from this point!

 

[hotcommodity]

You said yourself that linear momentum is conserved in this collision. That means that the total momentum of the system initially will equal the total momentum of the system after the collision. Can you show me how you would set up that equation?

 

[bungie77]

ok so perhaps I could set it up like this:

m*v(of coupled pair) = m*v(of boxcar) + m*v(of new coupled pair flatcar and trailer truck)

But I have two unknowns being the two velocities of the boxcar and the new coupled pair.

 

[andrei.suba]

use the conservation of kinetic energy as well as conservation of momentum.

 

[hotcommodity]

You can't use the conservation of kinetic energy when you have an inelastic collision.

You know the initial velocity of the boxcar, and the initial velocity of the trailer truck (which is zero). They "stick" to each other after the collision, so you'll have one final velocity. Does that make sense?

 

[bungie77]

Yeah I can calculate that. Perhaps I didn't phrase the question well (although I just copied it from the sheet). There is a trailer truck sitting on top of the flat car. The boxcar runs into the flat car and they form a couple. I can calculate the velocity immediately after, but what the question is asking is what is the velocity of the boxcar when the truck hits the end of the flat car. I will get a diagram if you wish :)

 

[hotcommodity]

Certainly, let's take a look at the diagram :)

 

[bungie77]

Here is a diagram of the question.

 

[hotcommodity]

Ok, I have a better visual now, thanks. The thing is, we're not given distances and times, so we have to assume everything occurs instantaneously. I'm not sure what the problem means by "perfectly plastic," I've never heard that term. The problem tells you to neglect friction, so that tells us that we should use a conservation law. Of course we're going to use the conservation of linear momentum. The boxcar is coupled with the flatcar instantaneously. It doesn't matter that there's a truck on top of the flatcar, we simply add its mass into the equation. It can move around on the flat car in any fashion, but in the end, linear momentum must be conserved. When I worked out the problem, using mass one as the box car, and mass two as the flatcar and truck combined, I arrived at one of the multiple choices listed. Let me know if you have any questions.