Rotational Kinetic Energy of a rod

AI Thread Summary
The discussion revolves around calculating the fraction of kinetic energy converted into internal energy during a collision involving a wooden block and a bullet. The initial kinetic energy is given by Ki = (1/2)mv^2, while the final kinetic energy after the bullet embeds in the block is corrected to Kf = (1/2)(m + M)v^2. A participant initially miscalculated the final kinetic energy and received feedback on the correct formula, emphasizing the importance of using the moment of inertia. To find the fraction of energy converted into internal energy, the correct approach involves determining the difference between initial and final kinetic energies, then dividing by the initial kinetic energy. The conversation highlights the need for clarity in understanding kinetic energy equations in rotational dynamics.
klopez
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1.A wooden block of mass M resting on a frictionless, horizontal surface is attached to a rigid rod of length and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and becomes embedded in it.

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What fraction of the original kinetic energy is converted into internal energy in the collision?



Here is my attempt:

Ki = (1/2)mv^2

kf = (m+M) L^2

Now I'm a bit confused what they mean by fraction, so I initial thought I had to divide Kf/Ki , which is:

2(m + M)L^2 / (mv^2)

but WebAssign marked it wrong. I have one more try and I want to try the other way, Ki/Kf but I don't want to get it wrong.

Can anyone help me and tell me if I'm doing this right or not. Thanks

Kevin
 
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Your final kinetic energy equation is wrong. First off, it doesn't have the right units. It looks like you just used I. The final energy should be 1/2 I w^2, where the equation v = Lw holds.
 
Oh okay I see how I got the final kinetic energy wrong. I did only use I. I fixed it, and now its:

Kf = (1/2)(m + M)v^2

Can anyone confirm this?

And if that's correct, how do I find the fraction?
 
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