At the fair there is a ride called Mr. Roto. Mr. Roto consists of a steel cylind
ID: 1346651 • Letter: A
Question
At the fair there is a ride called Mr. Roto. Mr. Roto consists of a steel cylindrical drum of radius 4.0m. Riders enter the drum and stand with their backs to the inside wall of the drum. (The inside wall is covered with a rubber pad that will provide friction between the riders and the wall). Then the drum begins to spin. Once the spinning motion has reached a maximum speed, the floor of the ride drops out and the riders are left “suspended” in air. A typical rider has a mass of 80kg. The period of the rotational motion of the ride is T = 3.0s when it has achieved the speed at which the floor drops out.
(a) ]When the floor drops out from under them, what keeps the riders from falling to their doom?
(b)What is the speed (not angular velocity) of a rider against the wall when the floor drops out?
(c)What is the minimum coefficient of static friction allowed for this ride?
(d)The coefficient of static friction for silk on rubber is about µs = 0.4. Would a person wearing a silk dress be in any danger on this ride? Why?
(e)While on the ride you notice another rider whose mass is exactly half of yours. Should they be allowed to ride the ride? Justify your answer.
Explanation / Answer
given,
mass = 80 kg
time period = 3 s
radius = 4 m
frictional force between the wall and the rider will keep the riders from falling to their doom
speed = distance / time
speed = 2 * pi * 4 / 3
the speed of a rider against the wall when the floor drops out = 8.377 m/s
mg = k * mv^2 / r
g = k * v^2 / r
k = 8.3777^2 / (4 * 9.8)
minimum coefficient of static friction allowed for this ride = 1.79
yes, a person wearing a silk dress be in any danger on this ride because µs = 0.4 which is less than the minimum coefficient of friction allowed, so rider will sip fromthe drum
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