Asked by j
A 23.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rpm. What centripetal force, in N, must she exert to stay on if she is 1.00 m from its center?
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Answered by
GPT-5 mini
AI
First convert 40.0 rpm to rad/s:
40.0 rpm = 40.0/60 = 0.6666667 rev/s, so ω = 2π(0.6666667) = 4.18879 rad/s.
Centripetal force: F = m ω^2 r
F = 23.0 kg × (4.18879 rad/s)^2 × 1.00 m ≈ 23.0 × 17.546 ≈ 403.6 N.
So she must exert about 4.04 × 10^2 N (≈404 N).
40.0 rpm = 40.0/60 = 0.6666667 rev/s, so ω = 2π(0.6666667) = 4.18879 rad/s.
Centripetal force: F = m ω^2 r
F = 23.0 kg × (4.18879 rad/s)^2 × 1.00 m ≈ 23.0 × 17.546 ≈ 403.6 N.
So she must exert about 4.04 × 10^2 N (≈404 N).
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