The Wall of Death in an amusement park is comprised of a vertical cylinder that

Question

The Wall of Death in an amusement park is comprised of a vertical cylinder that can spin around the vertical axis. Riders stand against the wall of the spinning cylinder and the floor falls away leaving the riders held up by friction. The radius of the cylinder is 3.95 m. The coefficent of static friction between the rider and the wall is 0.260, and the coefficient of kinetic friction is 0.186. Find the tangential velocity of the spinning wall necessary so that the riders do not slip down the wall. The Wall of Death in an amusement park is comprised of a vertical cylinder that can spin around the vertical axis. Riders stand against the wall of the spinning cylinder and the floor falls away leaving the riders held up by friction. The radius of the cylinder is 3.95 m. The coefficent of static friction between the rider and the wall is 0.260, and the coefficient of kinetic friction is 0.186. Find the tangential velocity of the spinning wall necessary so that the riders do not slip down the wall.

Explanation / Answer

Let:
R be the reaction of the wall on the riders,
m be the mass of a rider,
g be the acceleration due to gravity,
w be the angular velocity of the wall,
r be the radius of the wall,
u be the coefficient of static friction.

For vertical equilibrium:
mg = uR

Ensuring the riders stay against the wall requires:
R >= mrw^2

Eliminating R:
mg >= umrw^2
w^2 < g / ur

w < sqrt(9.81 / (0.260 * 3.95) rad/s.
= (60 / 2pi)sqrt(9.81 / (0.3 * 3.5) rev/min.
= 29.52 rev/min.

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