Merry-Go-Round. Two identical twins, Jena and Jackie, are playing one December on a large merry-go-round (a disk mounted parallel to the ground on a vertical axle through its center) in their school playground in northern Minnesota. Each twin has a mass of 29.0 kg. The icy coating on the merry-go-round surface makes it frictionless. The merry-go-round revolves at a constant rate as the twins ride on it. Jena, sitting a distance 1.71m from the center of the merry-go-round, must hold on to one of the metal posts attached to the merry-go-round with a horizontal force of 56.0 N to keep from sliding off. Jackie is sitting at the edge, a distance 3.58 m from the center. With what horizontal force must Jackie hold on to keep from falling off?

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nuuk nuuk · Answer 1 · 2019-10-11T09:43:47+02:00

Answer:245.44 N

Explanation:

Given

mass of each twins(m)=29 kg

Jena distance from center is 1.71 m

Horizontal force applied is 56 N

Jackie distance from center is 3.58

centripetal force is given by

[tex]F=m\omega ^2r[/tex]

In first case horizontal force is balanced by Centrifugal force

[tex]56=m\omega (1.71)^2[/tex]----1

[tex]F=m\omega (3.58)^2[/tex]----2

Divide 1 & 2 we get

[tex]\frac{56}{F}=\frac{1.71^2}{3.58^2}[/tex]

[tex]F=\left ( \frac{3.58}{1.71}\right )^2\times 56[/tex]

[tex]F=2.093^2\times 56=245.44 N[/tex]