A washing machine turns on and starts from rest. The spin cycle starts and the m

Question

A washing machine turns on and starts from rest. The spin cycle starts and the machine's angular speed increases at a constant rate for 10 a at which point it is turning at 5 rev/s. The lid is then opened. This shuts off the power to the machine and it now slows down at a constant rate so that it is completely stopped after 8 s. a. Through how many revolutions does the machine turn while it is in motion? b. Does a point at the edge of the washing machine, r = 0.5 m, experience a larger linear acceleration before or after the door is opened.

Explanation / Answer

(A) while accelerating,

wi = 0

wf = 5 rev/s = 10 pi rad/s

Applying wf = wi + alpha t

10pi = 0 + alpha(10)

alpha = pi rad/s

theta1 = wi t + alpha t^2 /2

= 0 + (pi)(10^2)/2

= 157.1 rad

while decelerating,

wi = 10 pi rad/s

wf = 0

0 = 10pi + alpha 8

alpha = - 1.25 pi

theta2 = (10pi x 8) + (-1.25pi x 8^2 /2 )

= 125.66 rad

total angle revolved = theta1 + thet2

= 282.76 rad

revolutions = 282.76 / 2pi = 45 rev

(b) linear acc. = alpah r

r = 0.5 m

alpha is greater after door is opened.

Ans: after door is opened

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