# Pulleys: One mass hanging between two other masses

• geralt
In summary, the problem involves three masses connected by a continuous pulley system. The question asks to find the acceleration of the hanging block and the tension in the string. The acceleration of the hanging block is the average of the acceleration of the other two blocks. To find the tension, we need to use the equation F=ma with three different masses. This will allow us to eliminate the tension and solve for the accelerations.
geralt

## Homework Statement

Explanation: There are three masses in this problem. Two masses are sitting on two opposite surfaces. These surfaces have a space in between them, where a third mass is hanging down. These masses are connected by a continuous pulley system.

μ = 0.

The question asks us to find the acceleration of the hanging block, and the tension in the string. We are given the following hint: You will need to find a relationship between a1 (acceleration), a2, and a3. If m1 moves distance d1, and m3 moves a distance d3, how far does m2 move?

I've already determined that the acceleration of the hanging block is the average of the acceleration of the other two blocks, but I don't know where to go from there. Any help would be greatly appreciated!

## The Attempt at a Solution

The only force would be the hanging mass pulling down on the other two blocks via the pulley. So the force would be m2g, m2 being the hanging mass. The mass would be the total masses of the three blocks. Then using f=ma, I get the equation a=m2g/(total mass). I have no idea for tension...

oy geralt! welcome to pf!
geralt said:
The only force would be the hanging mass pulling down on the other two blocks via the pulley. So the force would be m2g, m2 being the hanging mass. The mass would be the total masses of the three blocks. Then using f=ma, I get the equation a=m2g/(total mass). I have no idea for tension...

call the tension "T" (the string is continuous, and the pulleys are presumably massless and frictionless, so it'll be the same all the way along)

you need to do F = ma three times, once for each mass

that should give you enough equations to eliminate T and find the accelerations!

show us what you get

## 1. How does a pulley system with one mass hanging between two other masses work?

A pulley system with one mass hanging between two other masses works by using a combination of fixed and movable pulleys to distribute the weight of the hanging mass. The fixed pulleys change the direction of the force, while the movable pulleys decrease the amount of force required to lift the hanging mass.

## 2. What are the advantages of using a pulley system with one mass hanging between two other masses?

The main advantage of using a pulley system with one mass hanging between two other masses is that it allows for the lifting of heavy objects with less effort. This makes it useful in various industries, such as construction and manufacturing, where heavy objects need to be lifted and moved.

## 3. What is the mechanical advantage of a pulley system with one mass hanging between two other masses?

The mechanical advantage of a pulley system with one mass hanging between two other masses is equal to the number of supporting ropes or strands. In this case, there are two supporting ropes, so the mechanical advantage is 2. This means that the force needed to lift the hanging mass is half of the weight of the mass.

## 4. How does the mass of the hanging object affect the operation of a pulley system with one mass hanging between two other masses?

The mass of the hanging object affects the operation of a pulley system with one mass hanging between two other masses in terms of the effort required to lift the object. The heavier the hanging mass, the more effort is needed to lift it. However, the mechanical advantage of the pulley system remains the same regardless of the mass of the hanging object.

## 5. Can a pulley system with one mass hanging between two other masses be used to lift objects vertically and horizontally?

Yes, a pulley system with one mass hanging between two other masses can be used to lift objects both vertically and horizontally. The direction of the force applied to the hanging mass can be changed by adjusting the position of the pulleys, allowing for movement in different directions.

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