(a) The tub of a washing machine goes into its spin cycle, starting from rest an

Question

(a) The tub of a washing machine goes into its spin cycle, starting from rest and steadily gaining angular speed for 10 seconds, upon which it reaches the final angular speed of 20 rev/s. Find: (1) the angular acceleration, (2) the total number of revolutions that the tub has turned before reaching the final speed, and (3) the final power output of the washing machine motor. The tub is 6 kg with a radius of 18 cm. It can be approximated as a thin cylinder shell. (b) If a person opens the lid at this point, the safety switch of the washing machine will turn it off. Assuming the tub can slow down at the maximal deceleration of 5 rad/s2 , how long does it take for the tub to come to a stop? How many revolutions does the tub turn till the stop? 2

Explanation / Answer

Since the speeding up and slowing down is uniform, we can say:-

Average angular speed during spin up = (0 + 20)/2 = 10 rev/s

Average speed during slowdown = (20 + 0)/2 = 10 rev/s

In fact, during the whole action, the average speed w = 10 rev/s

1) Angular acceleration = angular speed/time = 10/10 = 1 rev/s2

2) No. of revolutions = angular speed x time

= 10rev/s x 10s = 100 rev

3) Power P = T x w

where T = torque = I x angular acceleration

I = mr^2/2 = (6*0.18^2)/2 = 0.0972 kg-m2

so, T = 0.0972*(1 *2pi rad/s2) = 0.6107 N-m

Finally:   

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