# Pulley system, calculate acceleration

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#### dodo lee 1. The problem statement, all variables and given/known data
this is a pulley system,
each masses are moving with acceleration with a1,a2,a3..
question)
1) How can i calculate the ratio a1:a2:a3 ?
2) How can i calculate the T(tenstion)?

2. Relevant equations

a1,a2,a3: acceleration of each masses.
g=10m/s2
weight of all pulleys : 0
The mass 5kg does not spin.

3. The attempt at a solution

i think this is atwood system , but not simple, very complex.
help me...

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#### chopnhack

As drawn, the right side is going to jamb the pulley and then act as a single mass. Are you sure its drawn correctly?

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#### dodo lee

As drawn, the right side is going to jamb the pulley and then act as a single mass. Are you sure its drawn correctly?
I missed the condition " the mass 5kg does not spin'
Others, all correctly drawn.im sure....

#### chopnhack

Then wouldn't you treat this as 2kg vs 6kg?

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#### dodo lee

Then wouldn't you treat this as 2kg vs 6kg?
Then a1, a2, a3 would be same...?
If i treat this as 2kg vs 6kg, all the a=5m/s2,
I would be happy if The answer is so simple./o\

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#### dodo lee

Then wouldn't you treat this as 2kg vs 6kg?
Anyway thank you very much for your replies.

#### haruspex

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As drawn, the right side is going to jamb the pulley and then act as a single mass.
I don't think so. Imagine P2 position as fixed. P3 can move up x while a2 moves down x and a3 moves up 2x.

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#### dodo lee

I don't think so. Imagine P2 position as fixed. P3 can move up x while a2 moves down x and a3 moves up 2x.
you are right. if P3 is fixed, M3 moves up 2x, m2 moving down 1x, but P3 is also moving up, by 1x.the M2 is drawing with 2T tension. so net of M3 is 3x.the not fixed P3 makes this problem complicated.

#### haruspex

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the not fixed P3 makes this problem complicated
So work in terms of relative accelerations. What equation can you write relating the acceleration of the 5kg relative to P2 to the acceleration of the 1kg relative to P2?

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#### dodo lee #### haruspex

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You seem to have written 2x in one place and 3x in another. Which is it?

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#### dodo lee

You seem to have written 2x in one place and 3x in another. Which is it?
while 1kg, moves up 2x to p3, p3 moves up 1x, so 1kg will move 3x to p2.

whe

#### haruspex

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while 1kg, moves up 2x to p3, p3 moves up 1x, so 1kg will move 3x to p2.

whe
Very good.
So, what equation does that give you for the accelerations?

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#### dodo lee Very good.
So, what equation does that give you for the accelerations?

#### haruspex

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Don't worry about masses and forces yet, just think about the relationships that must apply to the accelerations because of the string lengths remaining constant.
In terms of a1, a2 and a3:
- what is the acceleration of P2?
- what is the acceleration of the 5kg mass relative to P2?
- what is the acceleration of the 1kg mass relative to P2?
- according to what you found in post #12, what equation connects those?

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#### dodo lee

Don't worry about masses and forces yet, just think about the relationships that must apply to the accelerations because of the string lengths remaining constant.
In terms of a1, a2 and a3:
- what is the acceleration of P2?
- what is the acceleration of the 5kg mass relative to P2?
- what is the acceleration of the 1kg mass relative to P2?
- according to what you found in post #12, what equation connects those?
good morning sir,
i can calculate a1 a2 a3 to pulleys
but about equation of motion, im very confused because of existance of 5kg.

5kg is connected to p3 and also tp p2.
T= 1*a3 + 1*g'---p3 equation
3T-5*a2=5g'
then, what?
i m not sure the motion equation to each pulley, p1,p2,p3.

#### haruspex

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i can calculate a1 a2 a3 to pulleys
I don't know what you mean by that. Please answer my questions in post #15.

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