A fairgrounds ride spins its occupants inside a flying saucer-shaped container.

Question

A fairgrounds ride spins its occupants inside a flying saucer-shaped container.  

a. If the horizontal circular path the riders follow has a 6.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 2.5 times that due to gravity?

b. If the saucer has portholes along the circumference and one of the riders drops the teddy bear she won at the shooting gallery through one, with what speed will the teddy bear fly away from the ride at the moment it is let go.

c. If the bear weighs .25 kg and the coefficient of sliding friction between the bear and the ground is .7, how far will it slide after hitting the ground before stopping?

Explanation / Answer

W = mg
Fc = mV²/R
Fc = 2.5(mg)
mV²/R = 2.5mg
V²/R = 2.5g
V² = 2.5Rg
V = 2.5(6)(9.81) = 12.13054 m/s
wR = V
w = V/R = 12.13054/6 = 2.02 rad/s
2.02(60) = 121.3054 rad/min
121.3054/2 = 19.306 rev/min

b) v = 12.13 m/s

c) a = 0.7*9.81 = 6.867 m/s^2

s = 12.13^2 / 2*6.867 = 10.71 m

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