amount of energy lost to friction due to change in rotational inertia

1. The problem statement, all variables and given/known data

A 2.8-m-diameter merry-go-round with rotational inertia 140kg⋅m2 is spinning freely at 0.40rev/s . Four 25-kg children sit suddenly on the edge of the merry-go-round.

a) Find the new angular speed.

b) Determine the total energy lost to friction between the children and the merry-go-round.
3. The attempt at a solution

a) 0.17rev (verified)

b) The old mass is 17.85714286kg, old angular speed is 2.513274123 ms-1
The new mass is 117.85714286kg, new angular speed is 1.066237507ms-1

To find the change in energy:

0.5(117.85714286kg)(1.066237507ms-1)2 – 0.5(17.85714286kg)(2.513274123 ms-1)2

The answer is 260j but I’m not getting it.

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