22.0-kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force is exerted if he is 1.25 m from its center? (b) What centripetal force is exerted if the merry-go-round rotates at 3.00 rev/min and he is 8.00 m from its center? (c) Compare each force with his weight.

a) Centripetal force is 482.79 N towards center.

b) Centripetal force is 17.37 N towards center.

c) First centripetal force is 482.79 N which is greater than weight of 215.82 N

First centripetal force is 17.37 N which is less than weight of 215.82 N

Explanation:

Centripetal force is given by the expression, F = mrω², m is the mass, r is the radius and ω is the angular velocity,

a) Mass, m = 22 kg

Radius, r = 1.25 m

Angular speed, ω = 40 rev / min = 4.19 rad/s

Substituting

F = mrω²

F = 22 x 1.25 x 4.19² = 482.79 N

Centripetal force is 482.79 N towards center.

b) Mass, m = 22 kg

Radius, r = 8 m

Angular speed, ω = 3 rev / min = 0.314 rad/s

Substituting

F = mrω²

F = 22 x 8 x 0.314² = 17.37 N

Centripetal force is 17.37 N towards center.

c) Weight = mg = 22 x 9.81 = 215.82 N

First centripetal force is 482.79 N which is greater than weight of 215.82 N

First centripetal force is 17.37 N which is less than weight of 215.82 N