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SovXietday
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Homework Statement
This is a "DOE" (Design of Experiment) problem. Basically, the construction is fairly simple. 3 pulleys, 2 on either side, and a free pulley with a weight suspended on it in the middle. Picture is available (don't mind my crappy paint skills, rope lengths are all parallel).
I basically need to compare theoretical velocity of C after falling 5cm and after falling 85cm to my actual measured velocities. However, to be honest my experimental values are all sorts of messed up, and I'm simply not sure if my math is anywhere near right.
m1 = .270kg
m2 = .522kg
m3 = .300kg
Homework Equations
F(net) = ma
xf = 1/2at^2 + Vot + xi (dx/dt and dv/dt respectfully)
The Attempt at a Solution
First I set up my three equations.
m1g - T1 = m1a
T1 = m1g - m1a Eq1
2T2 - m2g = m2a
T2= 1/2(m2g + m2a) Eq2
m3g - T3 = m3a
T3 = m3g - m3a Eq3
So, Fnet = ma should be
T1 + T3 - T2 = ma (what is m? The mass sum of the system?)
Plug in.
m1g - m1a + m3g - m3a - 1/2m2g - 1/2m2a = ma
m1g + m3g - 1/2m2g = a(m + m1 + m3 + 1/2m2)
Isolate for a = (g[m1 + m3 - 1/2m2]) / (m + m1 + m3 + 1/2m2)
If I plug in what I *think* m is supposed to equal (1.092), I get a = 1.923m/s
Integrate a
Vf = 1.923t + Vo (Vo is 0)
Integrate vf
xf = .9615t^2 + xo (Xo is also 0)
Plug in .85m for Xf (furthest displacement of weight 3)
t = .94s
Vf = 1.923(.94)
Vf = 1.808 m/s at .85m
...not even close am I?