Elastic Collision of Point Mass and Dumbell: Analyzing Kinetic Energy

[daveed]

Say we have a point mass $$M$$ traveling to the right at velocity $$V$$. It strikes a dumbell composed of two masses of $$M/2$$ separated by a massless rod of length $$L$$. The collision is elastic.

I am having some trouble thinking about this...

After the collision, the original mass is stationary because the dumbell has the same mass, so that ends up going at $$V$$ towards the right.

However, it also starts spinning, and has a certain kinetic energy. But if the dumbell is moving to the right at $$V$$, it would have the same translational kinetic energy as the original mass. So the rotational kinetic energy would be extra, and therefor something has gone horribly wrong in my analysis.

Is my assumption that the original mass stop moving incorrect? This holds true for regular, point masses colliding(ie. billiards balls), but I guess it wouldn't be for systems with rotational parts. Because to have an elastic collision means only to have kinetic energy conserved, I suppose that the original mass retains some of its momentum to the right, and gives the dumbell some, and I have to solve for the velocities/angular velocities such that the total energy in the system is conserved. Is this the right analysis of the system?

 

[arildno2]

Use lower case "t" in tex.

 

[Physics Monkey]

The result of the collision depends on where the incoming mass strikes the dumbell. If it were to hit the dumbell exactly in the middle then the incoming mass would come to rest just like in the point particle case. If it hits one of the balls of the dumbell then it won't come to rest. Solve the problem by applying conservation of momentum, angular momentum, and energy.