Merry Go Round Kid Jumps on find the work

[SteveoFitz]

Hey I'm new here I have a question that is bothering me, so here it is:
Q: A playground merry-go-round of radius R = 2.15 m has a moment of inertia of I = 214 kg·m2 and is rotating at 13.4 rev/min about a frictionless vertical axle. Facing the axle, a 20.4 kg child hops onto the merry-go-round and manages to sit down on its edge. Find the work done by the child.

A: Now the first part of this question was also to find the final anguar speed of the merry go round which i found to be 9.30 rev/min, or 0.974 rad/s which is the right answer. Now at first I thought this was going to be easy enough and that the work done would equal the change in Kinetic energy of the system since that is the only thing slowing it down. However i seem to be mistaken as I just keep getting this question wrong.

Any help would be appreciated, this is for a quiz due in a couple days. Thanks!

 

[Doc Al]

Originally posted by SteveoFitz
Now at first I thought this was going to be easy enough and that the work done would equal the change in Kinetic energy of the system since that is the only thing slowing it down.

Did you find the change in KE of the merry-go-round alone? (Not including the child.)

 

[SteveoFitz]

Hmm...ya I tried that I end up coming out with about 109 J lost from the kid jumping on, still to no avail :)

 

[Doc Al]

Originally posted by SteveoFitz
Hmm...ya I tried that I end up coming out with about 109 J lost from the kid jumping on, still to no avail :)

What's the problem with that answer?

 

[SteveoFitz]

Darn I don't understand what you mean still...

Wf = final angular velocity of the wheel
Wi = initial angular velocity of the wheel
I = moment of inertia of the wheel

I just did Work = change in KE = 1/2IWf^2 - 1/2IWi^2

 

[Doc Al]

Originally posted by SteveoFitz
Darn I don't understand what you mean still...

Wf = final angular velocity of the wheel
Wi = initial angular velocity of the wheel
I = moment of inertia of the wheel

I just did Work = change in KE = 1/2IWf^2 - 1/2IWi^2

Sounds good to me. What makes you think it's wrong?

I don't like this question, since the interaction of the child/merry-go-round is quite complex. You really can't simply find the real work; all you can calculate is the ΔKE which is better called pseudo-work. But I assume that's what you were asked to calculate? The bigger question is why calculate that?

You can understand much about this problem by using 1) conservation of angular momentum (which you used), along with 2) the energy equation (or first law of thermo). The energy equation says ΔE = W + Q. If you choose as your system the child + merry-go-round, you can ignore those messy forces between them: the external work and heat flow is zero. You have to realize that there are two forms of energy you must keep track of (in this problem): KE and thermal energy. So, the energy equation gives: ΔE = ΔKE + ΔE_thermal = 0; which means that the lost KE goes into increasing the thermal energy of the system.

Does this help at all?

 

[SteveoFitz]

Our school uses something called CAPA which is basically an online physics assignment. I put that answer that I got in and it said it was incorrect that's how I know I'm wrong, I have 2 more trys at it before I just lose the marks.

Your idea about using the thermal energy would be good, but we haven't studied that yet so I'm assuming there's another way to do it.

Thanks for the quick replies.

 

[Doc Al]

Just for laughs, why not enter the total ΔKE for the child+merry-go-round.