Find the acceleration of 3 blocks and tensions

[avistein]

Homework Statement

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

The Attempt at a Solution

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

 

[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.

 

[BvU]

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

 

[avistein]

Not done. I am still struggling with this.

 

[haruspex]

Let a_r be the acceleration of mass 2 kg and 3kg wrt to the 3rd pulley.then,
3g-T1=3a_r

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

 

[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.

 

[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.