3 a A 150 kg child is riding a playground merrygoround that

3. (a) A 15.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rpm. What centripetal force must she exert to stay on if she is 1.50 m from its center?
_____________N
(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 5.00 m from its center?
______________N
(c) Compare each force with her weight.
___________________(force from part (a) / weight)
___________________ (force from part (b) / weight)

Solution

here,

mass of child , m= 15 kg

angular speed, w =40 rpm

w = 4.19 rad/s

distance from the centre , d = 1.5 m

a)

the centripital force , F = m*w^2 *d

F = 15 * 4.19^2 * 1.5

F = 394.38 N

b)

when angular speed , w = 3 rpm

w = 0.314 rad/s

distance from the centre , d = 5 m

the centripital force , F\' = m*w^2 *d

F = 15 * 0.314^2 * 5

F = 7.39 N

C)

ratio a = force from a /weight

ratio a = F /mg

ratio a = 394.38 /( 15 * 9.8)

ratio a = 2.68

ratio b =force from part b /weight

ratio b = F\' /mg

ratio b = 7.39 /( 15 * 9.8)

ratio b = 0.05