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 8.00 s. Through how many revolutions does the tub turn while it is in motion

The tub of the washer does 37.5 revolutions while it is in motion.

Explanation:

At first we assume that the tub accelerates and decelerates uniformly. In this case, it is required to determine the number of revolutions done by the tub by means of the following equations of motion:

Acceleration

(Eq. 1)

Where:

- Angular acceleration experimented by the tub, measured in revolutions per square second.

, - Initial and final angular velocities of the tub, measured in revolutions per second.

- Acceleration time, measured in seconds.

(Eq. 2)

Where is the change in angular position of the tub during acceleration, measured in revolutions.

Deceleration

(Eq. 3)

Where:

- Angular acceleration experimented by the tub, measured in revolutions per square second.

, - Initial and final angular velocities of the tub, measured in revolutions per second.

- Deceleration time, measured in seconds.

(Eq. 4)

If we know that , , , and , then the amount of revolutions done by the tub during each phase is, respectively:

(Eq. 1)

(Eq. 3)

(Eq. 2)

(Eq. 4)

The total amount of revolutions done by the tub while it is in motion is:

The tub of the washer does 37.5 revolutions while it is in motion.

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