A 27.1 kg child is riding a playground merry-go-round that is rotating at 31.6 rev/min. What centripetal force (in N) must she exert to stay on if she is 1.75 m from its center

Question

Physics

Elena Carey

16 January, 00:33

A 27.1 kg child is riding a playground merry-go-round that is rotating at 31.6 rev/min. What centripetal force (in N) must she exert to stay on if she is 1.75 m from its center

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Answers (1)

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Jaden Brock · Answer 1

F_c = 519.32 N

Explanation:

We are given;

Mass of child; m = 27.1 kg

Angular velocity; ω = 31.6 rev/min

Radius; r = 1.75m

Since we want to find the force in Newton's, let's convert the angular velocity to Linear Velocity. The formula is:

v = r * RPM * 0.10472

v = 1.75 * 31.6 * 0.10472

v = 5.791 m/s

Formula for centripetal force is;

F_c = mv²/r

F_c = (27.1 * 5.791²) / 1.75

F_c = 519.32 N