Merry-Go-Round. Two identical twins, Jena and Jackie, are playing one December o
ID: 2190558 • Letter: M
Question
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?Explanation / Answer
From the centripetal force equation .. F = mr?² .. (m) and (?²) are constants .. so F depends on the radius .. Let F be the force for Jackie F/ 59N = 3.52m / 1.78m .. .. F = 3.52 x 59 / 1.78 .. .. ?F = 116.70 N The tangential (horizontal) velocity for Jackie is obtained from .. F = mv²/r (alternative to mr?²) v² = Fr / m v² = 116.7 x 3.52 / 30.1kg .. .. v² = 13.65 .. .. ?v = v13.65 = 3.70 m/s