You\'ve taken your neighbor\'s young child to the carnival to ride the rides. Sh

Question

You've taken your neighbor's young child to the carnival to ride the rides. She wants to ride The Rocket. Eight rocket-shaped cars hang by chains from the outside edge of a large steel disk. A vertical axle through the center of the ride turns the disk, causing the cars to revolve in a circle. You've just finished taking physics, so you decide to figure out the speed of the cars while you wait. You estimate that the disk is 6 m in diameter and the chains are 6 m long. The ride takes 10 s to reach full speed, then the cars swing out until the chains are 25 from vertical.

What is the car's speed?

Explanation / Answer

from Newton's 2nd law for the net centripetal forces and the vertical forces on a single rocket car. The net centripetal force are :

F(c) = ma(c) = Tcos----->equation (1)

Where T is the tension in the chain. The net vertical forces are :

F = 0 = Tsin - mg
mg = Tsin------>equation (2)

Dividing (2) by (1), you get :

g / a(c) = tan
a(c) = g / tan

Centripetal acceleration, a(c) is equal to v² / r,

so :

v² / r = g / tan
v = [gr / tan]^0.5
= [(9.8m/s² x 5.0m) / tan25]^0.5
= 10.25m/s

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