the tub of a clothes washer goes into its spin-dry cycle starting from rest and reaches an angular speed of 6.50 rev/s in 7.85 seconds. at this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. the tub then slows to a stop in 15.07 seconds. Assuming a constant angular acceleration, while the tub is starting and stopping, how many revolutions does the tub turn during this 22.92 second interval?
oh god, could someone PLEASE help me with this question? please just don't tell me the answer, set me up with something comprehendable? any help is appreciated!!
6.50/2, times by 22.92.
Add the number of revolutions turned starting up to the number turned while slowing down. The easiest way do do this is to use the average spin rate, 3.25 rev/s (both while speeding up and while slowing down).
Total number of spins = 3.25 spins/s * (7.85 + 22.92)
Of course, I'd be happy to help you understand how to solve this problem step by step! Let's break it down into smaller parts.
To find the number of revolutions the tub turns during the given time interval, we need to determine the angular displacement during each phase (starting and stopping) separately and then add them.
1. Starting phase:
The tub starts from rest and reaches an angular speed of 6.50 rev/s in 7.85 seconds. We can use the following formula to find the angular displacement during this phase:
θ = ω0t + (1/2)αt^2
where:
θ is the angular displacement,
ω0 is the initial angular velocity (0 in this case),
t is the time (7.85 seconds in this case),
α is the angular acceleration (which we need to find).
Since we are solving for α, we can rearrange the equation:
α = (2θ) / t^2
Substituting the given values:
α = (2 * 6.50 rev/s) / (7.85 s)^2
2. Stopping phase:
The tub slows down from an angular speed of 6.50 rev/s to rest in 15.07 seconds. We can use the same formula to find the angular displacement during this phase. However, the final angular velocity is zero:
θ = ω0t + (1/2)αt^2
Since θ is the angular displacement and ω0 is the initial angular velocity (6.50 rev/s):
θ = (1/2)αt^2
Substituting the given values:
(1/2)α(15.07 s)^2
3. Total angular displacement:
Now that we have the angular displacement during both phases, we can add them together to find the total angular displacement during the 22.92-second interval:
Total angular displacement = angular displacement during starting phase + angular displacement during stopping phase
4. Calculating the number of revolutions:
Since one revolution is equal to 2π radians, we can convert the total angular displacement from radians to revolutions:
Total revolutions = Total angular displacement / (2π)
By following these steps and plugging in the given values, you should be able to find the number of revolutions the tub turns during the given time interval.