Question

The tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 10.0 s, at which time it is turning at 6.00 rev/s. At this point, the lid of the washing machine is opened, and a safety switch turns it off. The tub then smoothly slows to rest in 13.0 s. Through how many revolutions does the tub rotate while it is in motion?

Answer 1

Answer:

69 revolutions

Explanation:

given,

initial angular velocity = 0

final angular velocity = 6 rev/s

when safety switch turned off

tub smoothly slows to rest in (t)= 13 s

total revolution of tub = ?

angular acceleration = $\dfrac{\omega_f-\omega_0}{t}$

angular acceleration = $\dfrac{6-0}{10}$

                                   = 0.6 rev/s²

now,

$\theta = \omega_i t +\dfrac{1}{2}\alpha t^2$

$\theta = 0+\dfrac{1}{2}\times 0.6 \times 10^2$

                 = 30 revolution

now,

when safety switch turn off

angular acceleration = $\dfrac{\omega_f-\omega_0}{t}$

angular acceleration = $\dfrac{0-6}{13}$

                                   = -0.462 rev/s²

now,

$\theta = \omega_i t +\dfrac{1}{2}\alpha t^2$

$\theta = 6 \times 13 -\dfrac{1}{2}\times 0.462 \times 13^2$

                 = 39 revolution

total revolution = 30 + 39 = 69 revolutions.

tub will rotate 69 revolutions