Question

23. (a) A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?

(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center?

(c) Compare each force with her weight.

(d) 23d) Suppose the merry-go-round rotates at 60rpm and the child's friction is just enough to prevent her from moving when she is at 1.25m from the center. What is the coefficient of static friction? Draw an FBD for this part.

Answer 1

a)

F = m r w^2 = 22* 1.25* (40* 2* 3.14 / 60) ^2

F = 482.02 N

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b)

F' = 22 * 8* (3* 2* 3.14 / 60)^2

F' = 17.353 N

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c)

comparison with F, F = 482 / 9.8 = 49.18 g

comparison with F', F' = 17.353 / 9.8 = 1.77 g

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d)

r w^2 = u g

1.25* (60* 2* 3.14 / 60)^2 = u * 9.8

u = 5.03

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