Question

A 23.0-kg child is riding a playground merry-go-round that is rotating at 30.0 rpm.

(a)What centripetal force must she exert to stay on if she is 1.00 m from its centre?

(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 8.30 m from its centre? N

(c) Compare each force with her weight. force from part (a) weight = force from part (b) weight =

Answer 1

(a) mass of child (m) = 23 kg
rotational speed (N) = 30 rpm
we know that the angular velocity is given by (w) = 2N/60
= 2*30/60 = 3.142 rad/s
Distance of the child from center (R) = 1 m
Centripetal force is given by (F) = mRw² = 23*1*(3.142)² = 227 N
(b) Now the rotational speed (N) = 3 rpm
Angular velocity (w) = 2N/60 = 0.3142 rad/s
Distance of the child from the center (R) = 8.3 m
Centripetal force is given by (F) = mRw² = 23*8.3*(0.3142)² =18.841 N
(c) We know that the weight = mass*acceleration due to gravity= mg
First we compare for the first part
Force from part a /Weight = 227/mg = 227/(23*9.81) = 1.006
Now for second case
Force from part b /Weight = 18.841/mg = 18.841/(23*9.81) =0.084