Question

A 27.0 kg child is riding a playground merry-go-round that is rotating at 25.0 rev/min. What centripetal force (in N) is exerted if he is 1.25 m from its center? (Enter the magnitude.) N (b) What centripetal force (in N) is exerted if the merry-go-round rotates at 1.5 rev/min and he is 8.00 m from its center? (Enter the magnitude.) N (c) Compare each force with his weight. (Enter the ratios of the magnitudes.) F(a) w = F(b) w =

Answer 1

231.318853151 N

5.32958637659 N

`F_1=0.873329758565w` and
`F_2=0.0201215176373w`

Step-by-step explanation:

m = Mass of child = 27 kg

r = Distance from center

`\omega` = Angular velocity

Centripetal force is given by

`F_1=m\omega^2 r\\\Rightarrow F_1=27* \left((25* 2\pi)/(60)\right)^2* 1.25\\\Rightarrow F_2=231.318853151\ N`

The centripetal force is 231.318853151 N

At r = 8 m and
`\omega=1.5\ rev/min`

`F_2=m\omega^2 r\\\Rightarrow F_2=27* \left((1.5* 2\pi)/(60)\right)^2* 8\\\Rightarrow F_2=5.32958637659\ N`

The centripetal force is 5.32958637659 N

Comparing

`(F_1)/(w)=(231.318853151)/(27* 9.81)=0.873329758565\\\Rightarrow F_1=0.873329758565w`

`(F_2)/(w)=(5.32958637659)/(27* 9.81)=0.0201215176373\\\Rightarrow F_2=0.0201215176373w`

`F_1=0.873329758565w` and
`F_2=0.0201215176373w`