Automatic Clothes Dryer

Classical Mechanics Level 3

In an automatic clothes dryer, a hollow cylinder moves the clothes on a vertical circle of diameter 0.72 m. The appliance is designed so that when a piece of clothing reaches an angle of 60° above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. What is the frequency of the rotating cylinder in order for the clothes to lose contact with the wall as such?

1.26 Hz 1.46 Hz 0.89 Hz 0.45 Hz

Wee Xian Bin by Wee Xian Bin , 25, Singapore

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1 solution

Wee Xian Bin
Jul 5, 2016

Consider the following right-angled triangle representing the free body diagram with the clothes' centripetal acceleration r ω 2 rω^2 and the clothes' gravitational acceleration g g . Since g g will provide for the vertical component of r ω 2 rω^2 , sin ⁡ ⁡ ( 60 ° ) = g r ω 2 \sin⁡(60°)=\frac{g}{rω^2} . Thus ω = 9.81 ( 0.72 2 ) ( 3 2 ) = 5.609 rad s − 1 ω=\sqrt{\frac{9.81}{(\frac{0.72}{2})(\frac{\sqrt3}{2})}}=5.609\mbox{ rad }s^{-1} , therefore f = ω 2 π = 0.8928 Hz f=\frac{ω}{2\pi}=0.8928\mbox{ Hz} .

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