Analyzing Pulley System: Acceleration and Masses

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Homework Help Overview

The discussion revolves around a pulley system where participants analyze the relationships between the accelerations of different masses and the implications of the conservation of string length. The original poster seeks validation of their equations and understanding of how to determine which mass has an acceleration greater than gravitational acceleration without solving the equations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of equations relating the accelerations of the masses, question the implications of tension in the system, and explore the principle of string length conservation. There are attempts to clarify the definitions of variables used to describe the system.

Discussion Status

The conversation is ongoing, with participants providing insights and asking for clarifications on the principles involved. Some guidance has been offered regarding the relationship between the lengths of the string and the accelerations, but no consensus has been reached on the specific equations or interpretations.

Contextual Notes

Participants express uncertainty regarding the measurements of the masses' positions and the implications of unknown variables in the context of the problem.

asi123
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Homework Statement



Hey guys.
look at this pulley system.
I drew all the forces, and also, the pulleys have no mass and so as the rope.
What do you say about the equations I wrote, are they right?
And BTW the first part of the question is to figure which mass has acceleration bigger then g and they say you can figure it out without solving the equations, any idea?

Homework Equations


The Attempt at a Solution

 

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asi123 said:
What do you say about the equations I wrote, are they right?

Hi asi123! :smile:

If the last equation is a3 = 2a2 = 2a1, then it's wrong.
And BTW the first part of the question is to figure which mass has acceleration bigger then g and they say you can figure it out without solving the equations, any idea?

erm … T > 0, so isn't it obvious? :wink:
 
tiny-tim said:
Hi asi123! :smile:

If the last equation is a3 = 2a2 = 2a1, then it's wrong.


erm … T > 0, so isn't it obvious? :wink:

I meant the size of the accelerations, not direction, isn't that right?
Maybe it's a3 = a2 = 2a1 ?
 
asi123 said:
I meant the size of the accelerations, not direction, isn't that right?
Maybe it's a3 = a2 = 2a1 ?

No, you should be getting one equation, not two …

you only have one principle to help you … the conservation of the length of the string! :wink:
 
tiny-tim said:
erm … T > 0, so isn't it obvious? :wink:

Yeah, you right, it's pretty obvious, by the equations we can see than m2 accelerate faster then g.

I don't quite understand the principle of the length of the rope, can you please help me with it?
I mean, what is the connection between the length of the rope and the acceleration?

Thanks.
 
asi123 said:
I don't quite understand the principle of the length of the rope, can you please help me with it?
I mean, what is the connection between the length of the rope and the acceleration?

The rope starts at m2, and finishes at m3.

Call the positions x1 x2 and x3. What is the length of the rope in terms of x1 x2 and x3?

Then differentiate twice. :biggrin:
 
tiny-tim said:
The rope starts at m2, and finishes at m3.

Call the positions x1 x2 and x3. What is the length of the rope in terms of x1 x2 and x3?

Then differentiate twice. :biggrin:

I'm sorry, I don't understand what you mean by x1, x2 and x3.
Do you mean for example that x1 is the length between m1 and m2 or something like that?
 
asi123 said:
I'm sorry, I don't understand what you mean by x1, x2 and x3.
Do you mean for example that x1 is the length between m1 and m2 or something like that?

Any three parameters will do.

Personally, I'd choose the height from the ceiling, but your suggestion will work also. :smile:
 
Ok, one second, am I right to say a3 = 2a1 ?
 
  • #10
asi123 said:
… a3 = 2a1 ?

only if a2 = 0 … which it isn't! :smile:

(you're trying to oversimplify! :wink:)
 
  • #11
tiny-tim said:
Any three parameters will do.

Personally, I'd choose the height from the ceiling, but your suggestion will work also. :smile:

What do you mean you choose the height from the ceiling? something like I drew in the pic?
 

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  • #12
asi123 said:
What do you mean you choose the height from the ceiling?

(i can't see the pic yet)

I mean the height of each mass below the ceiling.
 
  • #13
tiny-tim said:
(i can't see the pic yet)

I mean the height of each mass below the ceiling.

Well, how can you obviously know that? it's not like they are telling you "this mass is 30 cm beneath and the other on is 60 cm...":smile:, I mean, how can you measure that?

Thanks by the way :smile:
 
  • #14
asi123 said:
Well, how can you obviously know that? it's not like they are telling you "this mass is 30 cm beneath and the other on is 60 cm...":smile:, I mean, how can you measure that?

Thanks by the way :smile:

You're welcome! :smile:

"how can you obviously know that?"… you don't know … that's why they're called unknowns!
 
  • #15
tiny-tim said:
You're welcome! :smile:

"how can you obviously know that?"… you don't know … that's why they're called unknowns!

Well, if you don't know, than how can you find the connection between the accelerations of the masses?
Do you see the pic I posted by the way?
 
  • #16
asi123 said:
Well, if you don't know, than how can you find the connection between the accelerations of the masses?

(still no pic)

Because there is an equation for the lengths of the string, between the masses, in terms of x1 x2 and x3.
 
  • #17
tiny-tim said:
(still no pic)

Because there is an equation for the lengths of the string, between the masses, in terms of x1 x2 and x3.

Ok, I didn't quite get it, but thanks anyway.
 

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