e Gravitron is an amusement park ride in which riders stand against the inner wa

Question

e Gravitron is an amusement park ride in which riders stand against the inner wall of a large spinning steel cylinder. At some point, the floor of the Graviton drops out, instilling the fear in riders that they will fall a great height. However, the spinning motion of the Gravitron allows them to remairn safely inside the ride. Most Gravitrons feature vertical walls, but the example shown in the figure has tapered walls of According to knowledgeable sources, the coefficient of static friction between typical human clothing and steel ranges between 0.210 to 0.390. In the figure, the center of mass of a 54.6 kg rider resides 3.00 m from the axis of rotation. As a safety expert inspecting the safety of rides at a county fair, you want to reduce the chances of injury. What minimum rotational speed (expressed in rev/s) is needed to keep the occupants from sliding down the wall during the ride? Number revis What is the maximum rotational speed at which the riders will not slide up the walls of the ride? Number rev/ s

Explanation / Answer

normal force perpendicular to incline N = m*g*cos(90-theta)

frictional force f = u*N up the incline

gravitational force Fg = m*g*sin(90-theta)

net force Fnet = Fg - f

Fnet = m*r*w^2

Fg - f = m*r*w^2

m*g*sin(90-theta) - u*m*g*cos(90-theta) = m*r*w^2

for u = 0.39

9.8*sin(90-23.3) - 0.39*9.8*cos(90-23.3) = 3*w^2

w = 1.58 rad/s = 1.58/(2pi) rev/s = 0.251 rev/s   <<------ANSWER

for u = 0.21

9.8*sin(90-23.3) - 0.21*9.8*cos(90-23.3) = 3*w^2

w = 1.65 rad/s = 1.65/(2pi) rev/s = 0.263 rev/s <<------ANSWER

DONE please check the answer. any doubts post in comment box

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