Answer to Question #241364 in Mechanics | Relativity for Anas

Question

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. (a) What is the child's centripetal acceleration? (b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

Answer 1

m=50 kg, r=2.0m, ω=3.00 rad/s

(a)

a = ω²r

a = (3.00 rad/s)²(2.00 m)

a = 18m/s²

(b)

F = ma

F = (50.0 kg)(18 m/s²)

F = 900 N

(c)

net force = force due to friction

ma = μmg

a = μg

18 m/s² = μ(9.81 m/s²)

μ = 1.83