# Two masses and a pully

1. Dec 2, 2009

### joemama69

1. The problem statement, all variables and given/known data

An unknown mass, m1, hangs from a massless string and descends with an acceleration g/2. The other end is attached to a mass m2 which slides on a frictionless horizontal table. The string goes over a uniform cylinder of mass m2/2 and radius R. The cylinder rotates about a horizontal axis without friction and the string does not slip on the cylinder. Express your answers in parts b, c, and d in terms of g, m2 and R.

a) Draw free-body diagrams for the cylinder and the two masses.

b) What is the tension in the horizontal section of the string?

c) What is the tension in the vertical section of the string?

d) What is the value of the unknown mass m1?

2. Relevant equations

3. The attempt at a solution

part b)

T1/SUB] = m2/SUB]a
T2/SUB] -m1/SUB]g = -m1/SUB]a
T2/SUB]R - T1/SUB]R = MR2/SUP]$$\alpha$$...T2/SUB] - T1/SUB] = Ma

T1/SUB] = T2/SUB] - Ma = m1/SUB]g - .5m1/SUB]g - .25m2/SUB]g = g(.5m1/SUB] - .25m2/SUB])

part c)

T2/SUB] = T1/SUB] + Ma = .5m2/SUB]g + .25m[SUB]2/SUB]g = .75m[SUB]2/SUB]g

part d) it keeps canceling out,, is something wrong above
[b]1. The problem statement, all variables and given/known data[/b]

[b]2. Relevant equations[/b]

[b]3. The attempt at a solution[/b][/SUB][/SUB]

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