- #1
mmoe
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Homework Statement
I still don't got the hang on Atwood Machines, and i don't know if I am wrong here or just overthinking it. But i got this one exercise where i am kind of stuck in two of the sub-exercises. So I am hoping there is someone here who could guide me in the right direction.Atwood Machine ( http://imgur.com/Dzvt4HR ), with massless strings and pulleys and no friction.
Let the acceleration of the top mass be a1 and the acceleration for the bottom two a2 and a3. Let the movable pulleys have the acceleration atr.
a) Show that atr = (a2 + a3)/2
b) find the masses' acceleration
Homework Equations
F=ma
The Attempt at a Solution
a) I can see that if i move the top mass a distance y, conservation of string tells me that the movable pulleys will move 1/2y.
ym1 = 1/2*ym2
ym1 = 1/2*y2m
ym2 = y2m
Hence ym1 = (ym2 + y2m)/2
Two time derivatives gives a1 = (a2 + a3)/2 = atr
It gives the right answer, but i got a feeling that I've done something that should be quite obvious wrong. b) I find the F=ma for each mass
T-mg = ma1 (1)
T-mg = ma2 (2)
t-2mg = ma3 (3)
i also got these equations from the conservation of string:
a1=1/2a2 (4) && a1=1/2a3 (5) && a2=a3 (6)
Combining (4) and (5) with equations (1),(2) & (3), should give me a1,a2,a3 and T.
The thing is, i really don't know where to start here. Since a2 = a3, you only have to solve for a1 and a2 (correct me if I am wrong). But how would i go forward solving (1) and (2) with (4). I don't know if I am overthinking this way to much or if i have done something wrong, so i come to you kindly asking for directions.
Thanks :)