Finding final kinetic energy of a system

[stripes]

Homework Statement

A uniform solid sphere of mass M and radius R has a light, thin metal spike driven through it, so it is free to turn about this spike. So imagine a bowling ball on a stick that is free to rotate about this stick.

A bullet of mass m is fired at speed v into the ball at a distance 2R/3 from the center, and it comes to rest in the sphere. What is the final kinetic energy? Hint: angular momentum.

I recall my instructor saying it might or might not matter where the bullet ends up...but we never really concluded anything. If it does matter, let's say it ends up half way through the ball.

Homework Equations

The Attempt at a Solution

So we use angular momentum because it is conserved in this case, while linear momentum is not.

To be honest I'm not sure where to begin...I'm trying to put things together but I'm not sure where the distance 2R/3 comes into play, for example. If someone could help me out, I would really appreciate it.

 

[gneill]

A likely scenario is that the bullet strikes the bowling ball horizontally at a height of 2/3 R above the horizontal center line of the ball:

 

[tiny-tim]

hi stripes!

A uniform solid sphere of mass M and radius R has a light, thin metal spike driven through it, so it is free to turn about this spike. So imagine a bowling ball on a stick that is free to rotate about this stick.

A bullet of mass m is fired at speed v into the ball at a distance 2R/3 from the center, and it comes to rest in the sphere. What is the final kinetic energy?

i think this question is totally incomprehensible

does it mean 2/3R from the stick ?

and yes of course it matters how far in the bullet stops!

 

[stripes]

Hey guys. I have since solved the problem. Also, I copied it verbatim as per the assignment. If you ever check my other homework questions in physics, you will find that it's not uncommon for this instructor to word them poorly, like this. I just went to see him and clarify. Thanks anyways.

 

[haruspex]

A likely scenario is that the bullet strikes the bowling ball horizontally at a height of 2/3 R above the horizontal center line of the ball:

It will have to be a vertical axis, or there will be no 'final' KE; it will oscillate.

 

[gneill]

It will have to be a vertical axis, or there will be no 'final' KE; it will oscillate.

Ah. True. So the "spike" is vertical and the diagram I drew is looking down on the scene from above.