posted by Anonymous .
A playground merry-go-round has a radius of R= 2 m and has a moment of inertia Icm= 9×103kg⋅m2 about a vertical axis passing through the center of mass. There is negligible friction about this axis. Two children each of mass m= 20kg are standing on opposite sides at a distance ro= 1.2m from the central axis. The merry-go-round is initially at rest. A person on the ground applies a constant tangential force of F= 2.0×102N at the rim of the merry-go-round for a time Δt= 18s . For your calculations, assume the children to be point masses.
(a) What is the angular acceleration α of the merry-go-round? (in rad/s2)
(b) What is the angular velocity ωfinal of the merry-go-round when the person stopped applying the force? (in rad/s)
(c) What average power Pavg does the person put out while pushing the merry-go-round? (in Watts)
(d) What is the rotational kinetic energy R.K.Efinal of the merry-go-round when the person stopped applying the force? (in kg⋅m2/s2)
R=2 m, Ic=9000 kg•m², r₀=1.2 m, m=20 kg, F=200 N, Δt=18 s.
I=Ic+2I₀=Ic+2m r₀² =
α=M/I=FR/I =200•2/9057.6 = 0.044 rad/s²
ω=α•Δt =0.044•18=0.792=0.8 rad/s
P=Fv=P ωR = 200•0.8•2 = 320 W.
KE=Iω²/2 = 9057.6•0.8²/2 = 2898.4 J.
The power is wrong
KE=Iù²/2 = 9000•0.8²/2 = 2880 J.
(Whitout the children)