The spin cycles of a washing machine have two angular speeds, 440rev/min and 612

Question

The spin cycles of a washing machine have two angular speeds, 440rev/min and 612rev/min . The internal diameter of the drum is 0.600m .

A) What is the ratio of the maximum radial force on the laundry for the higher angular speed to that for the lower speed? ( flower/fhigher = ____ )

B) What is the ratio of the maximum tangential speed of the laundry for the higher angular speed to that for the lower speed? ( vlower/vhigher = ____ )

C) Find the laundry's maximum tangential speed .  ( vtan = ___ m/s )

D) Find the laundry's maximum radial acceleration, in terms of g ( arad = ___ g )

Explanation / Answer

Wlower=440*(2pi/60) =46.08 rad/s

Whigher=612*(2pi/60)=64.09 rad/s

a)

Maximum Radial force

F=mW2r

=>Flower/Fhigher=(Wlower/Whigher)2=(46.08/64.09)2

Flower/Fhigher=0.517

b)

Tangential speed

V=Wr

=>Vlower/Vhigher=Wlower/Whigher =46.08/64.09

Vlower/Vhigher=0.719

c)

r=d/2=0.3 m

Maximum Tangential speed

Vtan=Whigherr=64.09*0.3=19.23 m/s

d)

Maximum Radial accelertion

amax=Whigher2R =(64.09)2*0.3 =1232.26 m/s2

in terms of g

amax=1232.26g/9.8 =125.74g

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