Two identical twins, Jene and Jackie, are playing one December on a large merry-

Question

Two identical twins, Jene 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 30.7 kg. The icy coating on the merry-go-round surface makes it frictionless. The merry-go-round revolves at a constanttt rate as the twins ride on it/Jena, sitting a distance 1.77 m 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 57.0 N to keep from sliding off. Jackie is sitting at the edge, a distance 3.70 m from the center. Part A With what horizontal force must jackie hold on to keep from falling off? Part B If Jackie falls off, what will be her horizontal velocity when she becomes airborne?

Explanation / Answer

From the centripetal force equation .. F = mr² ..
(m) is mass of boy and (²) is angular velocity
Let F be the force for Jackie , equate centripetal force equation for jackie and jene
F/ 57N = 3.7m / 1.77m

F = 119.15 N

B.)

The tangential (horizontal) velocity for Jackie is obtained from .. F = mv²/r (alternative to mr²)
v² = Fr / m
v² = 119.15 x 3.7 / 30.7 kg

v² = 14.36

v = 3.78 m/s

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