sirfederation
Nov28-03, 04:20 AM
The Tub of a washer goes into a spin cycle, starting from rest and gaining angular speed steadily for 8 s, when it is turning at 5 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 12s. Through how many revolutions does the Tub turn while it is in motion?
Ok, I am going to do this problem in 2 stages: One for Wi =0 and Wf=5 rev/s and the second for Wi=5rev/s and Wf=0
First stage:
Known
Wi=0
Wf=5 rev/s
T=0
T=8s
Oi=0
Unknown
A=?
Of=?
Wf= (5 rev/s)(2(pi)rad/rev)
Wf= 10(pi) rad or 31.4 rad
A = (Wf-Wi)/T
A = 31.4/8
A = 3.9 rad/(s^2)
Of=Oi+(Wi(T)+.5(A)(T)^2
Of= 0 + (10)(pi)(8) + .5(3.9)(8)^2
Of= 80(pi) + 40(pi)
Of= 377 rad (I am going to leave it in this form because I am going to have to plug it into stage two.
Stage two:
Known
Wf= 0
Wi= 5 rev/s or 10(pi) rad/s
Oi= 377 rad (found in stage one)
T=12 s
Unkown
A=?
Of=?
A = (Wf-Wi)/T
A = (0-31.4)/12
A = -2.6 rad/s^2
Of=Oi+(Wi)(T)+.5(A)(T)^2
Of= 377 + 31.4(12) + .5(-2.6)(12)^2
Of= 377 + 376.8 - 187.2
Of=566.8 rad
Now we need to convert to revolutions:
566.8 rad(57.3/rad)= 32477.64 degrees
32477.64/(360/rev) = 90. 2 rev
Ok here is what I do not get.
My revolutions for the washer when its acceleration is increasing in stage one is slower than the revolutions when the acceleration is decreasing in stage two. I think I am correct but it doesn't make sense.
Ok, I am going to do this problem in 2 stages: One for Wi =0 and Wf=5 rev/s and the second for Wi=5rev/s and Wf=0
First stage:
Known
Wi=0
Wf=5 rev/s
T=0
T=8s
Oi=0
Unknown
A=?
Of=?
Wf= (5 rev/s)(2(pi)rad/rev)
Wf= 10(pi) rad or 31.4 rad
A = (Wf-Wi)/T
A = 31.4/8
A = 3.9 rad/(s^2)
Of=Oi+(Wi(T)+.5(A)(T)^2
Of= 0 + (10)(pi)(8) + .5(3.9)(8)^2
Of= 80(pi) + 40(pi)
Of= 377 rad (I am going to leave it in this form because I am going to have to plug it into stage two.
Stage two:
Known
Wf= 0
Wi= 5 rev/s or 10(pi) rad/s
Oi= 377 rad (found in stage one)
T=12 s
Unkown
A=?
Of=?
A = (Wf-Wi)/T
A = (0-31.4)/12
A = -2.6 rad/s^2
Of=Oi+(Wi)(T)+.5(A)(T)^2
Of= 377 + 31.4(12) + .5(-2.6)(12)^2
Of= 377 + 376.8 - 187.2
Of=566.8 rad
Now we need to convert to revolutions:
566.8 rad(57.3/rad)= 32477.64 degrees
32477.64/(360/rev) = 90. 2 rev
Ok here is what I do not get.
My revolutions for the washer when its acceleration is increasing in stage one is slower than the revolutions when the acceleration is decreasing in stage two. I think I am correct but it doesn't make sense.