A problem of strings, pulleys and weights

In summary, the answer is that the masses attached to the lower pulley (m2 and m1) won't be at rest and 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 and you will get the answer.
  • #1
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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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  • #2
is the answer only in terms of masses? or is there any other quantity (such as acceleration)
 
  • #3
The answer is only in masses (that is the relation between them)Please help!
 
  • #4
anyone please ..atleast give me a hint?
 
  • #5
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.
 
  • #6
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)
 
  • #7
I still didnt get a hint(though I feel I have followed the rules right).
I still tried out the sum but reached nowhere!
 
  • #8
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.
 
  • #9
aha! Thanks A.q ! I got it!
 

1. What is a problem of strings, pulleys, and weights?

A problem of strings, pulleys, and weights is a physics problem that involves analyzing the forces and motions of a system of strings, pulleys, and weights. It typically requires knowledge of topics such as Newton's laws of motion, forces, and mechanical advantage.

2. How do you solve a problem of strings, pulleys, and weights?

To solve a problem of strings, pulleys, and weights, you first need to identify all the forces acting on the system and their directions. Then, you can use Newton's laws of motion, along with the concept of mechanical advantage, to determine the acceleration and tension in the strings. Finally, you can apply these values to calculate the motion of the system.

3. What is the principle of mechanical advantage in a problem of strings, pulleys, and weights?

The principle of mechanical advantage states that using a system of pulleys and strings can reduce the amount of force needed to lift a weight. The more pulleys there are in the system, the greater the mechanical advantage and the less force is needed to lift the weight.

4. What are some real-life applications of problems involving strings, pulleys, and weights?

Real-life applications of problems involving strings, pulleys, and weights can be found in many everyday objects and systems, such as elevators, cranes, and weightlifting machines. These systems use pulleys and strings to efficiently lift and move heavy objects.

5. What are some common mistakes when solving a problem of strings, pulleys, and weights?

Some common mistakes when solving a problem of strings, pulleys, and weights include forgetting to account for all the forces acting on the system, not correctly identifying the direction of the forces, and not using the correct equations for calculating tension and acceleration. It is also important to double-check your calculations and units to ensure an accurate solution.

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