Roundup is an amusement ride. Riders enter a 18 m diameter rotary cage which is

Question

Roundup is an amusement ride. Riders enter a 18 m diameter rotary cage which is accelerated in a horizontal plane to a sufficient constant speed and raised to nearly vertical position as shown below.

Express answers in 2 significant digits

a. So that the riders remain pressed against the walls in the vertical position, the linear speed it needs to be moving is more than ______ m/s.

b. The angular velocity is _______ rad/s.

c. The cage makes one rotation every ______ s/

d. A rider will feel _______ g's acceleration at the bottom of the vertical spin. (1 g = 9.8 m/s2 ).

Consider the possibility that in the horizontal position, the floor of the cage is lowered after the cage reaches the necessary speed.

e. When the cage reaches the necessary minimum speed in the initial horizontal position, the centripetal force is ______ N on a 60 kg rider.

Explanation / Answer

Given that

Diameter (d) =18m then Radius (r) =d/2 =9m

The linear speed is given by

F =mv2/r ===>a =v2/r===>v=Sqrt(rg) =Sqrt(9*9.81) =9.396m/s

Now the angular velocity is given by

v =wr ====>w =v/r =9.396/9 =1.044rad/sec

We know that w =2pi/T then T =2pi/w =6.28/1.044 =6.015s

Now centripetal force acting is F =mv2/r =60*(9.396)2/9 =588.56N

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