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.

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nuuk nuuk · Answer 1 · 2019-11-05T05:34:36+01:00

Answer:

Explanation:

Given

mass of child=22 kg

weight of child [tex]=mg=22\times 9.8=215.6 N[/tex]

[tex]N=40 rev/min[/tex]

[tex]\omega _1=\frac{2\pi 40}{60}=4.189 rad/s[/tex]

distance from, center [tex]r_1=1.25 m[/tex]

Centripetal Force she exerts to stay on

[tex]F_1=m(\omega _1)^2\times r_1[/tex]

[tex]F_1=22\times (4.189)^2\times 1.25[/tex]

[tex]F_1=482.56 N[/tex]

[tex]F_1 is 2.23[/tex] times of child weight

Now if

[tex]N_2=3 rev/min[/tex]

[tex]\omega _2=0.3142 rad/s[/tex]

[tex]r_2=8 m[/tex]

[tex]F_2=m(\omega _2)^2\times r_2[/tex]

[tex]F_2=22\times (0.3142)^2\times 8=17.37 N[/tex]

[tex]F_2\ is\ 0.08[/tex] times of child weight