Question

The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 7.00 s, at which time it is turning at 5.00 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 14.0 s. Through how many revolutions does the tub turn while it is in motion?

Answer 1

The no. of revolutions does the tub turn while it is in motion is = 52.51 revolutions

Step-by-step explanation:

Given data

`\omega_1` = 0

`\omega_2` = 5
`(rev)/(sec)`

Time taken = 7 sec

(1). The angular acceleration is given by

`\alpha = (d \omega)/(dt)`

`\alpha = (5)/(7)`

`\alpha = 0.714 (rev)/(s^(2) )`

We know that from the equation of motion

`\omega_2^(2) = \omega_1^(2) + 2 \alpha \theta_1`

`5^(2) = 0 + 2 (0.714) \theta_1`

`\theta_1 = 17.5 \ rev` -------- (1)

(2). The angular acceleration is given by

`\alpha = (d \omega)/(dt)`

`\alpha = - (5)/(14)`

`\alpha =` - 0.357
`(rev)/(s^(2) )`

We know that from the equation of motion

`\omega_2^(2) = \omega_1^(2) + 2 \alpha \theta_2`

`0^(2) = 5^(2) + 2 (-0.357) \theta_2`

`\theta_2` = 35.01 rev ------- (2)

Total no of revolution made by the machine is

`\theta = \theta_1 + \theta_2`

`\theta =` 17.5 + 35.01

`\theta =` 52.51 rev

Therefore the no. of revolutions does the tub turn while it is in motion is = 52.51 rev