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

Answer:

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

Explanation:

Given data

$\omega_1$ = 0

$\omega_2$ = 5 $\frac{rev}{sec}$

Time taken = 7 sec

(1). The angular acceleration is given by

$\alpha = \frac{d \omega}{dt}$

$\alpha = \frac{5}{7}$

$\alpha = 0.714 \frac{rev}{s^{2} }$

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

$\alpha = \frac{d \omega}{dt}$

$\alpha = - \frac{5}{14}$

$\alpha =$ - 0.357 $\frac{rev}{s^{2} }$

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