In a home laundry dryer, a cylindrical tub containing wet clothes is rotated ste

Question

In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis as shown in the figure below. So that the clothes will dry uniformly, they are made to tumble. The rate of rotation of the smooth-walled tub is chosen so that a small piece of cloth will lose contact with the tub when the cloth is at an angle of = 69.5° above the horizontal. If the radius of the tub is r = 0.335 m, what rate of revolution is needed?
ANSWER: 51.47 rev/min
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rev/min

My answer is close but not correct. If someone could help me out that would be great!

Explanation / Answer

Using newton's second law of motion

Fnet = m*a

N + mg = m*v^2/r

but m*v^2/r is balanced by the component of gravity

m*v^2/r = m*g*sin(theta)

v^2/r = g*sin(theta)

v = sqrt(r*g*sin(theta))

v = sqrt(0.335*9.81*sin(69.5)) = 1.75 m/sec

Using v = r*w

1.75 = 0.335*w

w = 5.22 rad/sec

w = 5.22*(60/(2*3.142))

w = 49.84 rev/min

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