A neighbor\'s child wants to go to a neighborhood carnibal to experience the wil

Question

A neighbor's child wants to go to a neighborhood carnibal to experience the wild rides. The neighbors is worried about the safety because one of the rides looks dangerous. She knows that you have been taken physics and so asks your advice. The ride in question has a 10-lb chair which hangs freely from a 30-ft long chain attached to a pivot on the top of a tall tower. When a child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed. It rotates about the tower once every 3 seconds. When you ask the operator, he says that the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds and he weighs 200 lbs. Has the operator shown that this ride safe for a 50-lb child?

Explanation / Answer

here

w = 2 * pie * f

w = 2 * pie / t

m * g = W

g = 32 m/s^2

then

m * w^2 * L * sin(theta) = T * sin(theta)

T = m * 4 * pie^2 * L / t^2

T =( (50 + 10) / 32 ) * 4 * 3.14 * 3.14 * 30 / 3^2

T = 250 lbs > 200 lbs

so this ride is not safe for 50lb child

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