# Pully with three masses

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1. Jul 16, 2016

### IhasSwag

1. The problem statement, all variables and given/known data
Find the relation between the mass of block 1 and the mass of block 2. Assume that the pullies are massless and frictionless and that the rope is inelastic. All masses are unknown.

mblock2 > mblock1
mblock2 < mblock1

The system below is at rest.

2. Relevant equations
F = mg = T

3. The attempt at a solution
I'm quite clueless on how to approach this problem, but this is how far I came.
m1*g - T1 = m1*a
m2*g - 0.5*T2 = m2*a

∑F = m1*a + m2*a = m1*g - T1 +m2*g - 0.5*T2

I'm not sure how to go any further.

Thanks in advance for the help!

2. Jul 16, 2016

### Delta²

Focus on Pulley with block 2. Since the pulley is at rest, the sum of forces on that pulley equals zero.

3. Jul 16, 2016

### IhasSwag

So T1 + T3 - m2*g = 0 ?
m1*g + m3*g = m2*g
m1 + m3 = m2 ?
Am I approaching this problem the right way now?

I found out that I made a mistake in the possible answers. It should be:
mblock2 = 2*mblock1
mblock2 > 2*mblock1
mblock2 < 2*mblock1

4. Jul 16, 2016

### TSny

The rope has the same tension throughout.

5. Jul 16, 2016

### Delta²

Yes correct. Now notice that the tension should be the same so $T_1=T_3$.

6. Jul 16, 2016

### IhasSwag

If T1 = T3 then m1 = m3
This means that m2 = 2*m1 ?

But now I face another problem because according to my teacher, the answer should have been: m2 < 2*m1

7. Jul 16, 2016

### Delta²

Is the rope considered to be massless?

8. Jul 16, 2016

### IhasSwag

It doesn't state that the rope is massless, so I guess not.

9. Jul 16, 2016

### IhasSwag

I meant to say that the rope has mass

10. Jul 16, 2016

### Delta²

If the rope is massless then what we did here is correct and your teach is wrong.

However, if the rope is NOT massless, then the tension forces $T_1+T_3$ have to lift the weight of the segment of rope that is attached to pulley 2, so it will be $T_1+T_3=m_2g+m_rg$ where m_r the mass of the rope along the circumference of pulley 2.

11. Jul 16, 2016

### IhasSwag

The rope is indeed not massless.
Thank you very much for your help.