Question

23. 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? Compare each force with her weight.

Answer 1

Answer:

Explanation:

Given

mass of child=22 kg

weight of child $=mg=22\times 9.8=215.6 N$

$N=40 rev/min$

$\omega _1=\frac{2\pi 40}{60}=4.189 rad/s$

distance from, center $r_1=1.25 m$

Centripetal Force she exerts to stay on

$F_1=m(\omega _1)^2\times r_1$

$F_1=22\times (4.189)^2\times 1.25$

$F_1=482.56 N$

$F_1 is 2.23$ times of child weight

Now if

$N_2=3 rev/min$

$\omega _2=0.3142 rad/s$

$r_2=8 m$

$F_2=m(\omega _2)^2\times r_2$

$F_2=22\times (0.3142)^2\times 8=17.37 N$

$F_2\ is\ 0.08$ times of child weight