Mechanical energy lost when child jumps onto merry-go-round

[jybe]

Homework Statement

I have a basic problem where a child jumps tangentially onto the outer edge of a stationary merry-go-round, and you have to use conservation of momentum to find the final angular speed of the merry-go-round.

But the next part of the question asks "how much mechanical energy was lost to friction as the child jumped onto the merry-go-round?"

I tried using change in kinetic energy -- 1/2(m*r(omega)) - 1/2(mv²) = 0 but didn't get the right answer. I really can't think of how else I would find this, because the only thing that's changing is the kinetic energy. I would really appreciate it if somebody could help me out with this

 

[TSny]

You have the right idea. Make sure you include all the final kinetic energy.

 

[jybe]

You have the right idea. Make sure you include all the final kinetic energy.

1/2 * (mass of child + mass of merry-go-round) * (r*omega)² - 1/2mv² = 0

Does this look better? I'm still not getting the right answer but it's much closer...maybe I messed up the calculation or the answer is wrong...but is this correct?

 

[TSny]

1/2 * (mass of child + mass of merry-go-round) * (r*omega)² - 1/2mv² = 0

Does this look better? I'm still not getting the right answer but it's much closer...maybe I messed up the calculation or the answer is wrong...but is this correct?

You are not using the correct expression for the rotational KE of the merry-go-round. It will involve the concept of "moment of inertia" (sometimes called "rotational inertia").