Question

The cylindrical tub of a dryer in a laundromat rotates counterclockwise about a horizontal axis at 41.5 rev/min as it dries the clothes. If the diameter of the cylinder is 0.692 m, at what angle will a piece of cloth lose contact with the wall of the cylinder and fall down

Answer 1

The angle that the piece of cloth will lose contact with the wall would be
`37.31^(o)`

Step-by-step explanation:

for a body moving in a circular path The net force is equal to the centripetal force and can be calculated thus;

mgsin θ = m
`w^(2)`r

isolating sine θ

sin θ =
`w^(2)`r/ g

where w is the angular velocity = 41.5 rev/min = 41.5 rev/min x 2π/60 secs = 4.34587 rad/s

r is the radius = = d/2 = 0.692/2 = 0.3145 m

g is the acceleration due to gravity = 9.8 m/
`s^(2)`

sin θ = (
`4.34587^(2)` x 0.3145)/ 9.8

sin θ = 0.6061

θ =
`sin^(-1)`0.6061

θ =
`37.31^(o)`

Therefore the angle that the piece of cloth will lose contact with the wall would be
`37.31^(o)`