Question

In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 1.3-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.19?

Answer 1

8.2 m/s

Step-by-step explanation:

radius (r) = 1.3 m

coefficient of friction (u) = 0.19

acceleration due to gravity (g) = 9.8 m/s^{2}

for the passengers to remain stuck on the wall, the normal force must be equal to the centripetal force (while considering the coefficient of friction).

normal force = centripetal force x coefficient of friction

mg =
`(mv^(2) )/(r)` x u

g =
`(v^(2) )/(r)` x u

v =
`\sqrt{(gXr)/(u) }`

v =
`\sqrt{(9.8x1.3)/(0.19) }`

v = 8.2 m/s

the minimum speed the passengers can have to stick to the wall = 8.2 m/s