Question

(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 45.0 rev/min. What centripetal force (in N) must she exert to stay on if she is 3.00 m from its center? N

(b) What centripetal force (in N) does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 5.00 m from its center? N
(c) Compare each force with her weight. force from (a) weight = ________? force from (b) weight = _________?

Answer 1

(a) 1264.49 N

(B) 9.36 N

(C) For part a
`(F)/(mg)=(1264.49)/(19* 9.8)=6.791`

For part b
`(F)/(mg)=(9.36)/(19* 9.8)=0.05`

Step-by-step explanation:

We have given mass of the child m = 19 kg

Angular speed
`\omega =45rpm=(2* \pi * 45)/(60)=4.71rad/sec`

Distance from the center r = 3 m

So centripetal force
`F=m\omega ^2r=19* 4.71^2* 3=1264.49N`

(b) Angular speed

Distance from the center r = 5 m

So centripetal force
`F=m\omega ^2r=19* 0.314^2* 5=9.36N`

(C) Now comparison with weight

For part a
`(F)/(mg)=(1264.49)/(19* 9.8)=6.791`

For part b
`(F)/(mg)=(9.36)/(19* 9.8)=0.05`