Question

The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 9.00 s, at which time it is turning at 6.00 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 13.0 s. Through how many revolutions does the tub turn while it is in motion?

Answer 1

`n_(tot) = 66\,rev`

Step-by-step explanation:

The total of revolutions during the whole process is:

`n_(tot) = n_(1) + n_(2)`

The acceleration of each stage is determined below:

Acceleration:

`\ddot n_(1) = (\dot n_(1))/(t_(1))`

`\ddot n_(1) = (6\,(rev)/(s) )/(9\,s)`

`\ddot n_(1) = (2)/(3)\,(rev)/(s^(2))`

Deceleration:

`\ddot n_(2) = -(\dot n_(1))/(t_(2))`

`\ddot n_(2) = -(6\,(rev)/(s) )/(13\,s)`

`\ddot n_(2) = - (6)/(13)\,(rev)/(s^(2))`

The total of revolutions during the process is:

`n_(tot) = (1)/(2)\cdot \ddot n_(1)\cdot t_(1)^(2) + \dot n_(1)\cdot t_(2)+(1)/(2)\cdot \ddot n_(2)\cdot t_(2)^(2)`

`n_(tot) = (1)/(2)\cdot \left((2)/(3)\,(rev)/(s^(2)) \right)\cdot (9\,s)^(2) + \left(6\,(rev)/(s)\right)\cdot (13\,s) + (1)/(2)\cdot \left(-(6)/(13)\,(rev)/(s^(2)) \right) \cdot (13\,s)^(2)`

`n_(tot) = 66\,rev`

Answer 2

da = 66 rev

The tub turn 66 revolutions while it is in motion

Question:

The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 9.00 s, at which time it is turning at 6.00 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 13.0 s. Through how many revolutions does the tub turn while it is in motion?

Step-by-step explanation:

Given:

Acceleration Time t1 = 9.00s

Deceleration Time t2 = 13.00s

Maximum angular velocity w2= 6.00rev/s

Initial and final angular speed w1= 0rev/s

Calculating the average angular velocity wa;

wa = (w1+w2)/2

wa = (6+0)/2

wa = 3 rev/s

Angular distance covered da= average angular velocity × time

da = wat1 + wat2

da = 3×9 + 3×13

da = 27+39

da = 66 rev

The tub turn 66 revolutions while it is in motion