How can i approach this problem?

[Shahroze]

Can u tell me if i am going right if i say that the tension in the string is 20N and that 20N is cancelled by the other 20N force i.e F so the acceleration will be zero.

[Ghideon]

Hi Shahroze.

I'll try to give some guidance; 

What numerical value of the gravitational constant g is used in the calculation?

I suppose the lower left pulley connected to [math]m_{1}[/math] can be moved up and down and the upper right pulley is stationary, correct?

 

 

[studiot]

1 hour ago, Shahroze said:

Can u tell me if i am going right if i say that the tension in the string is 20N and that 20N is cancelled by the other 20N force i.e F so the acceleration will be zero.

What is your justification for saying this?

Hint think very carefully about the question. Why would it mention friction if nothing moves?

[Shahroze]

Ok so my second approach is that the mass m2 will give a tension of 20N and the mass m1 will give a tension of 5N because it is supported by two strings. So is the overall tension in the string 25N. Now if i am correct then the net force will be 5N. Now am i correct?? Can i proceed further? I am really confused

43 minutes ago, studiot said:

What is your justification for saying this?

Hint think very carefully about the question. Why would it mention friction if nothing moves?

Ok so my second approach is that the mass m2 will give a tension of 20N and the mass m1 will give a tension of 5N because it is supported by two strings. So is the overall tension in the string 25N. Now if i am correct then the net force will be 5N. Now am i correct?? Can i proceed further? I am really confused

 

[studiot]

Are you thinking that the tension in the string has to be the same at all points?

 

If so why?

1 hour ago, Shahroze said:

Ok so my second approach is that the mass m2 will give a tension of 20N and the mass m1 will give a tension of 5N because it is supported by two strings. So is the overall tension in the string 25N. Now if i am correct then the net force will be 5N. Now am i correct?? Can i proceed further? I am really confused

 

Are you thinking of this as a statics problem or a dynamics problem?

You seem to want to introduce equilibrium which would make it a statics problem.

But it is not a statics (equilibrium)  it is a dynamics problem
So if m2 is moving down m1 is moving up ie the string is taught.

If m1 is moving up why should the net force on it be 10N ?

As a dynamics problem do you know the law of conservation of momentum?

Can you see how to apply it here?

[Ghideon]

As studiot said;

9 hours ago, studiot said:

it is not a statics (equilibrium)  it is a dynamics problem

Sometimes it helps to draw an alternative picture of the problem and an approximation may be good enough. 
As a hint I tried an alternative below. The first image is a zoomed in version of the left part of the setup in the OP, intended to act as comparison for the second image. The second image is an approximation of the first one. The layout is different but the impact on the rest of the system, not displayed, is intended to be similar. Does this help to show that the system is not at equilibrium? And then apply studiot's comments?

Edited September 15, 2018 by Ghideon

[studiot]

48 minutes ago, Ghideon said:

As studiot said;

Sometimes it helps to draw an alternative picture of the problem and an approximation may be good enough. 
As a hint I tried an alternative below. The first image is a zoomed in version of the left part of the setup in the OP, intended to act as comparison for the second image. The second image is an approximation of the first one. The layout is different but the impact on the rest of the system, not displayed, is intended to be similar. Does this help to show that the system is not at equilibrium? And then apply studiot's comments?

Good advice and good pics +1

 

 

 

13 hours ago, Ghideon said:

I suppose the lower left pulley connected to m1 can be moved up and down and the upper right pulley is stationary, correct?

 

There is a condition that m₁ does not move either up or down and the string just slips through.

However this set of values does not meet that condition which is

4m₂m₃ = m₁(m₂ + m₃)

[Ghideon]

 

On 2018-09-15 at 10:57 PM, studiot said:

There is a condition that m₁ does not move either up or down and the string just slips through.

Thanks! I did not see that possibility and therefore I should have worded my question clearer. I wanted to make sure that this was not a trick question where all pulleys are attached to some rigid frame and none of them are allowed to move relative to the others.

On 2018-09-15 at 10:57 PM, studiot said:

However this set of values does not meet that condition which is

4m₂m₃ = m₁(m₂ + m₃)

+1 for showing me condition and the math.

Maybe OT but I'm curious: without giving away too much information to the OP, did you find the condition by calculating or by experience / intuition? It's been a long time since I solved these kind of problems so I feel rusty, to say the least. Verifying the condition will be a good exercise for me. 

[studiot]

2 hours ago, Ghideon said:

 

Thanks! I did not see that possibility and therefore I should have worded my question clearer. I wanted to make sure that this was not a trick question where all pulleys are attached to some rigid frame and none of them are allowed to move relative to the others.

+1 for showing me condition and the math.

Maybe OT but I'm curious: without giving away too much information to the OP, did you find the condition by calculating or by experience / intuition? It's been a long time since I solved these kind of problems so I feel rusty, to say the least. Verifying the condition will be a good exercise for me. 

Thanks, pulley problems were once very popular in high school applied maths.

Since you are interested here is a slightly more complicated one fully worked.

[Ghideon]

21 hours ago, studiot said:

Since you are interested here is a slightly more complicated one fully worked.

Thanks! I'll go through the details, it may take a while. I think I'll post any follow-ups in a new topic, where homework help rules don't apply.

 

( This is probably the first time I respond in a homework section only to get a homework myself, nice  )