# Find the acceleration of 3 blocks and tensions

1. Feb 8, 2014

### avistein

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

In the figure shown.Find :
a)acceleration of 1 kg,2kg,and 3kg blocks and
b)tensions T1 and T2

3. The attempt at a solution
2T1=2T2=>T1=T2
T2=1*a ,where a is acceleration of mass 1kg
T2=a
Let ar be the acceleration of mass 2 kg and 3kg wrt to the 3rd pulley.then,
3g-T1=3ar
and T1-2g=2ar
solving ar=g/5
net acceleartion of 2 kg and 3kg is a-ar and a+ar
then what to do?

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2. Feb 8, 2014

### BvU

Complicated affair. My degree might not be enough, but who knows...
I think we need some relevant equations. Could you collect them for us ?
And then perhaps some given info too. This thing on earth or on the moon ?
Is T1=T2 a law of physics ?

Is T2 ending up in the middle of the pulley an accidental error? Or is that a spool of wire that is being held in place by the 1 kg weight.
Perhaps you want to introduce some more intermediary variables.

3. Feb 10, 2014

### BvU

How are you getting along with this one ?
I gather you succesfully completed the two-block exercise, this is a bit more challenging.

4. Feb 10, 2014

### avistein

Not done. I am still struggling with this.

5. Feb 10, 2014

### haruspex

No. The mass doesn't 'know' anything about the motion of the pulley. It feels two forces and it accelerates accordingly.

6. Feb 10, 2014

### BvU

We start with a simplification: the lower pulley only, static. later we let that part accelerate downwards, but first we have to discover something. We follow the advice in post #2: introduce T3 and T4. And we make a drawing.

#### Attached Files:

• ###### Pulley1.jpg
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7. Feb 10, 2014

### BvU

Wow, I see posts cross again. avi still awake ? Or at work / school?.

No matter, both helpers are useful to you. I continue with the simple case: the lower pulley only, static.

My questions are:
1. What other forces are there? So there is clearly no balance. And yet T1 = T3 (remember: pulleys only change force direction, not magnitude).
2. Can you calculate the acceleration ?
3. So what is T1?
4. Then: what is T4?

You can read up on this in links on Atwood's machine. The link even has a calculator, but you only want to use it to check things. Remember: you want to understand this. The numerical answer is only a side benefit, not a goal in itself.

Last edited: Feb 10, 2014