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 20 degrees from vertical.

What is the car's speed?

Explanation / Answer

Distance from center of disk

R = ( 6.0 m /2 ) + 3.0 = 6.00 m

From vector diagram, horizontal force

F(h) = mg tan20

Here, F(h) provides the centripetal force mv²/R, therefore

mv²/R = mg tan20

Solve the equation for v

v = (Rg tan20)

v = (6.00 x 9.80 x tan20)

v = 4.626 m/s

If you rounded off the result to 3 significant digits

v = 4.63 m/s

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