How sure we know the distance is x?

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Homework Help Overview

The discussion revolves around a physics problem involving two masses connected by a pulley system, specifically focusing on the relationship between their accelerations and the constraints imposed by the inextensible string. The original poster expresses confusion regarding the assumptions made about the distance measurement and the nature of the string's configuration.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster questions the certainty of the distance measurement labeled as x, wondering if it could be different values. They also seek clarification on the assumption that the entire system operates with a single string.
  • Some participants clarify that the distance moved by mass m2 is the same as that of the pulley, emphasizing the concept of relative motion.
  • Others inquire about the mechanics of the system, particularly how the second string connected to the pulleys behaves when mass m1 moves.
  • One participant introduces the concept of constraint motion and discusses how the inextensibility of the string affects the movement of the masses.

Discussion Status

The discussion is active, with participants providing insights into the mechanics of the pulley system and addressing the original poster's concerns. There is an exploration of different interpretations regarding the string's configuration and the implications of constraint motion. No explicit consensus has been reached, but several productive lines of reasoning have been presented.

Contextual Notes

Participants note that the problem involves assumptions about the string's length and the relationship between the movements of the masses, which may not be clearly defined in the problem statement or diagram.

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Homework Statement



Please look at this pdf
http://iweb.tntech.edu/murdock/books/v1chap4.pdf

PDF pg. 18 - 22
Question# 14
14. Mass m1 on a frictionless horizontal table is connected to mass m2 through
a massless pulley P1 and a massless fixed pulley P2 as shown in Fig. 4.13. (a)
If a1 and a2 are the magnitudes of the accelerations of m1 and m2 respectively,
what is the relationship between these accelerations? Find expressions for (b)
the tensions in the strings and (c) the accelerations a1 and a2 in terms of m1, m2
and g.

Homework Equations



Fnet = ma
v = d/t
d^2 x / dt^2 = a
and so on

The Attempt at a Solution



I don't understand the solution he gives. Please turn to PDF page 20

The author says (first paragraph)
clearly the position of m2 is also measured by x. ` is the length of string from m1 to the pulley. xblock

Now I don't understand how sure we know it is x. Why can't it be X + 2, or X + 1500??

Later he says total length of the string is L, so it assumes that the entire system is actually running with one single string?? The given did not say that, and the diagram did not show that either.
In solving this problem, what do we have to think first? it seems very insightful that one sees the relationship in distance.
 
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The position of the mass m2 is also measured by x as the distance moved by the block m2 is same as the pulley.Of course the absolute distance differs but the change is the same.

And the length of the string is a constant. I don't see your point about running with a single string. They are clearly talking of the left string.
 
aim1732 said:
The position of the mass m2 is also measured by x as the distance moved by the block m2 is same as the pulley.Of course the absolute distance differs but the change is the same.

And the length of the string is a constant. I don't see your point about running with a single string. They are clearly talking of the left string.

How does this system works?
You see, with one single pulley, i know that m1 and m2 will travel the same distance, one moves forward and one moves downard

now, back to this problem. how does this system works? I see a second string connected from P1 to pulley P2.

So when m1 moves, what happen to the second string, how does it respond?
 
You may be aware that such problems are studied under Constraint motion. Here the only constraint is that the string is inextensible.
It is often possible to see the constraint from the diagram itself. Here the mass m2 moves x so p2 moves x. But you see the string is wrapped round the pulley o both sides so that its length would seem to increase by 2x. Since the string can not actually increase in length it will compensate by moving the block m1 by 2x.You see the wall to which p1 is attached can not move.

But these are elementary ways. A trained eye is a must for such questions. If you are familiar with rotational mechanics, this is an interesting application of Chasle's Theorem for general motion. The upper part of p1 in contact with the string is always at rest in same way as the bottom of a rolling ball is. Then velocity of the bottom point is 2v.You get the same result.
 

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