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

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) = mRw^{2} =
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) = mRw^{2} =
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

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