Question

A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min.

What centripetal force must she exert to stay on if she is 1.25 m from its center?

What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center?

Answer 1

a) 482.5N

b) 17.4N

Step-by-step explanation:

40 rev/min = 40 * 2π / 60 = 4.2 rad/s

3 rev/min = 3 * 2π / 60 = 0.314 rad/s

The centripetal acceleration that the child is subjected to

`a = \omega^2r`

And their centripetal force is

`f = ma = m\omega^2r`

From here we can plug the number in

(a)
`f_1 = m\omega_1^2r_1 = 22*4.2^2*1.25 = 482.5N`

(b)
`f_2 = m\omega_2^2r_2 = 22*0.314^2*8 = 17.4N`