# Series of masses and pulleys

• Amir80om
In summary, the conversation discusses a system of masses and pulleys, where one mass is removed and added to another. The goal is to prove that all masses except the two that have had the mass added to them have a downward acceleration, and that the heavier mass has a downward acceleration while the lighter mass has an upward acceleration. It is also required to prove that all accelerations are relevant to the mass squared. The conversation includes attempts at solutions, as well as a request for a diagram or explanation in Spanish or French. However, it is against forum guidelines to post solutions in languages other than English.

## Homework Statement

There is serie of mass and pulleys. We Know we have more than two masses. System is balanced.We take m(m<<1) from on of the masses and add to another one.
a) prove all the masses except these two have downward accleration
b) prove mass with heavier has accleration downward and mass with lighter has accleration upward
c) prove that all acclerations are relevant to m^2

## The Attempt at a Solution

a) First System is balanced and when we take m out of one mass there will be accleration => speed of center of mass will increase => potential energy of center of mass will reduce => center of mass has downward accleration => T is Force that connects pulleys to wall and M is sum of all masses T<MG I don't Know how to prove this for all the masses individually.
b) since all the mass except two masses have downward acclerations and length of rope is constant one of two masses or both of them must have acclerations upward. Heavier mass is going down relevant to lighter mass but I don't know how to prove (b)

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Can we assume that a single string runs through the system? If so, consider what happens to its tension and how that affects the balance on each of the unchanged masses.

Amir80om said:

## Homework Statement

There is serie of mass and pulleys. We Know we have more than two masses. System is balanced.We take m(m<<1) from on of the masses and add to another one.
a) prove all the masses except these two have downward accleration
b) prove mass with heavier has accleration downward and mass with lighter has accleration upward
c) prove that all acclerations are relevant to m^2

## The Attempt at a Solution

a) First System is balanced and when we take m out of one mass there will be accleration => speed of center of mass will increase => potential energy of center of mass will reduce => center of mass has downward accleration => T is Force that connects pulleys to wall and M is sum of all masses T<MG I don't Know how to prove this for all the masses individually.
b) since all the mass except two masses have downward acclerations and length of rope is constant one of two masses or both of them must have acclerations upward. Heavier mass is going down relevant to lighter mass but I don't know how to prove (b)
Is there a diagram of this thing, or are we supposed to have ESP?

It would be useful if you could upload a diagram or a sketch of the system, as it is difficult to visualize the masses that should be hanging.

PD: If your native language is Spanish or French I could post the answer with it.

Chestermiller said:
Is there a diagram of this thing, or are we supposed to have ESP?
My impression is that there is no specific set-up. One is supposed to demonstrate these as general results.
I think I see how to do it if we can assume that it is a single string running through the system.

CharlieCW said:
I could post the answer with it.

haruspex said:

I mean I could offer the tips and/or explanations required in the native language of the OP so it's easier for them to read. I don't see how that is against the guidelines.

CharlieCW said:
I mean I could offer the tips and/or explanations required in the native language of the OP so it's easier for them to read. I don't see how that is against the guidelines.

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CharlieCW said:
I mean I could offer the tips and/or explanations required in the native language of the OP so it's easier for them to read. I don't see how that is against the guidelines.
The forum rules state that the language used for posting must be English.

CharlieCW and Chestermiller
gneill said:

haruspex said:
And that I'd put down to language/translation issues
I try to be a little flexible when it appears that the poster's first language is not English.

## 1. What is a series of masses and pulleys?

A series of masses and pulleys is a system of connected pulleys and masses that work together to move objects or transfer force.

## 2. How does a series of masses and pulleys work?

In a series of masses and pulleys, a rope or belt is wrapped around a series of pulleys and attached to a series of masses. When one mass is pulled, the rest of the masses will also move in the same direction due to the tension in the rope or belt.

## 3. What are the advantages of using a series of masses and pulleys?

A series of masses and pulleys can multiply force, change the direction of force, and distribute weight evenly. It can also make lifting heavy objects easier by reducing the amount of force needed.

## 4. What are some real-world applications of a series of masses and pulleys?

A series of masses and pulleys is commonly used in elevators, cranes, and construction equipment. It is also used in exercise machines, such as weightlifting machines, to provide resistance.

## 5. How can the mechanical advantage of a series of masses and pulleys be calculated?

The mechanical advantage of a series of masses and pulleys can be calculated by counting the number of ropes or belts supporting the mass being lifted. Each supporting rope or belt adds to the mechanical advantage by reducing the amount of force needed to lift the mass.