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

Answer:

231.318853151 N

5.32958637659 N

$F_1=0.873329758565w$ and $F_2=0.0201215176373w$

Explanation:

m = Mass of child = 27 kg

r = Distance from center

$\omega$ = Angular velocity

Centripetal force is given by

$F_1=m\omega^2 r\\\Rightarrow F_1=27\times \left(\dfrac{25\times 2\pi}{60}\right)^2\times 1.25\\\Rightarrow F_2=231.318853151\ N$

The centripetal force is 231.318853151 N

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

$F_2=m\omega^2 r\\\Rightarrow F_2=27\times \left(\dfrac{1.5\times 2\pi}{60}\right)^2\times 8\\\Rightarrow F_2=5.32958637659\ N$

The centripetal force is 5.32958637659 N

Comparing

$\dfrac{F_1}{w}=\dfrac{231.318853151}{27\times 9.81}=0.873329758565\\\Rightarrow F_1=0.873329758565w$

$\dfrac{F_2}{w}=\dfrac{5.32958637659}{27\times 9.81}=0.0201215176373\\\Rightarrow F_2=0.0201215176373w$

$F_1=0.873329758565w$ and $F_2=0.0201215176373w$