The tub of a washer goes into its spin cycle, starting from rest and gainiing angular speed steadily for 8.0 s when it is turning at 5.0 rev/s. At this time the person doing the laundry opens the lid and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn whil it is in motion.

Question

Mathematics

Gerald Wolfe

6 February, 00:59

The tub of a washer goes into its spin cycle, starting from rest and gainiing angular speed steadily for 8.0 s when it is turning at 5.0 rev/s. At this time the person doing the laundry opens the lid and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn whil it is in motion.

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Answers (1)

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Kameron Steele · Answer 1

Angular acceleration is change of angular velocity over time:

α = 5 / 8 = 0.625 rev / s²

Number of revolutions of the 1st part:

α · t² / 2 = 0.625 * 8² / 2 = 20 rev.

The 2nd part:

α = 5/12 = 0.41667 rev/s²

5 * 12 - (0.41667 * 12² / 2) = 60 - 30 = 30 rev.

In total: 20 + 30 = 50 revolutions