A problem of strings, pulleys and weights

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Homework Help Overview

The problem involves three unequal masses (m1, m2, m3) connected by frictionless, massless pulleys and strings. The objective is to find the relationship between the masses that allows m3 to remain stationary.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the masses, with some suggesting that equal masses would keep the system stationary. Others question whether the answer involves only masses or if acceleration is also a factor.

Discussion Status

Some participants have attempted to derive the relationship between the masses, while others express uncertainty about their approaches. A hint has been provided regarding the tension in the strings and its relation to the weights of the masses, indicating a potential direction for further exploration.

Contextual Notes

Participants note that the masses are unequal and discuss the implications of this on the system's behavior. There is also mention of neglecting gravitational forces between the masses, which may affect the analysis.

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Homework Statement


The fig has three masses m1 , m2 , m3 .. all of which are unequal.
Find relation between masses so that m3 remains stationary.

( pulleys , strings are frictionless and massless)

The Attempt at a Solution


I thought if mass on both side are equal then the system remains stationary.
So i said

m3 = m1 + m2

But the answers say a different story...

Please help!
 

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is the answer only in terms of masses? or is there any other quantity (such as acceleration)
 
The answer is only in masses (that is the relation between them)Please help!
 
anyone please ..atleast give me a hint?
 
I guess the concept of reduced mass is to be used here.
reduced mass of m1 and m2 is (m1 x m2)/(m1 + m2) which is equal to m3
Is this the correct answer?
Iam not sure of this.
 
No it isn't right.
The correct answer is


4/m3 = 1/m1 + 1/m2

I still don't konw how to get it. And i don't think this is a problem of reduced mass.(neglect gravitational force between the masses m1 m2 m3)
 
I still didnt get a hint(though I feel I have followed the rules right).
I still tried out the sum but reached nowhere!
 
I got the correct answer.
Please ignore my previous post as I did not think in detail before writing.
I will give you a hint.
As it is given the masses are unequal, the masses attached to the lower pulley (m2 and m1) won't be at rest. So, they have some common acceleration. You first calculate the tension in the string connecting these two masses. Use this equation to find the tension in the string connecting the mass m3.

Now, for m3 to remain at rest, this tension should balance its weight.
equate its weight and tension.
You will get the answer.

A.Q.
 
aha! Thanks A.q ! I got it!
 

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