A 50.0 kg child stands at the rim of a merry-go-round of radius 2.10 m, rotating

Question

A 50.0 kg child stands at the rim of a merry-go-round of radius 2.10 m, rotating with an angular speed of 2.90 rad/s. What is the child's centripetal acceleration? What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? HINT: This question is really just asking you to use your result from (a) to find the magnitude of the centripetal force for the circular motion. What minimum coefficient of static friction is required? HINT: Draw the free body diagram for the child. What force provides the inward radial force? Write out the Sum of the Forces in the Radial direction = mv2/r, and the Sum of the Forces in the y-direction = may. Use the information in these two equations to solve for the coefficient of friction. This problem is nearly identical to the previous problem.

Explanation / Answer

a) a_c = w^2.r = 2.90^2 x 2.10 = 17.66 m/s2

b) F = m (a_c) = 50 x 17.66 =883 N

c) F = u.mg

883 = u.50g

u = 1.80

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