(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

F(net) = ma

xf = 1/2at^2 + Vot + xi (dx/dt and dv/dt respectfully)

3. The attempt at a solution

First I set up my three equations.

m1g - T1 = m1a

T1 = m1g - m1aEq1

2T2 - m2g = m2a

T2= 1/2(m2g + m2a)Eq2

m3g - T3 = m3a

T3 = m3g - m3aEq3

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?

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# Homework Help: Finding tension and acceleration in a 3 weight, 3 pulley system

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