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)[2 pt(s) ]When the floor drops out from under them, what keeps the riders from falling to their doom? (b)[4 pt(s) ]What is the speed (not angular velocity) of a rider against the wall when the floor drops out? (c)[12 pt(s) ]What is the minimum coefficient of static friction allowed for this ride? (d)[2 pt(s) ]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)[3 pt(s) ]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.

Answer 1

a) when the floor drops the centripetal force and frictional force keeps the from falling

b) time period = 3 secs

angular speed= w = 2.09 rad /s

now velocity = w* r = 2.09 rad /s * 4 = 8.37 m/s

c) centripetal acceleration = V²/r = 17.54 m/s2 ( this provides the normal force N = m*a_c)

now, now , the frictional force on the wall will be mu* N

= mu* m* a_c

now, this frictional force should balance the weight mg

so, mu* m* a_c = mg

=> mu* a_c= g

=> mu = g/17.54

=>mu = 0.558

d) yes less static friction would mean that the frictional force wont be able to counter the weight mg .

e) yes , as frm the force equation we can see that mass cancel outs, so a less mass person would have the same frictional force as a heavier one.and hence can be allowed in the ride.