# How a movable pulley increases mechanical advantage?

• eagermind
In summary, the conversation discusses the concept of mechanical advantage in relation to a movable pulley. The mechanical advantage of roughly 2 means that by pulling 2 feet of rope, the object is raised 1 foot, requiring an input force equivalent to half the weight of the object. This can be visualized through a series of diagrams and a free body diagram. The tension on one end of the rope is equal to the other, so an object with a weight of P would require a parallel force of P/2 to be raised.
eagermind
Firstly, I'm sorry for posting this here it seems like the best place possible, but I'm not quite so sure I didn't see a section for civil engineering. So I don't understand why a movable pulley increases the mechanical advantage. This occurs in a situation when one end of the string is fixed and the input force is on the other end of the string, through the pulley. From the pulley hangs the mass. I just simply don't understand why there is a mechanical advantage of roughly 2. Please help me wrap my mind around why this occurs?

a mechanical advantage of 2 means that you pull 2 ft of rope and the object raises 1 ft so that then implies you used a force equivalent to half the weight of the object to raise the object.

It works the same way as a lever ... but you'll have to draw a series of diagrams to see this. If the mechanical advantage is 2x then you also have to pull the rope twice as far to raise the block the same height.

Without the pulley - if you pull the rope 1m, the rope holding the weight gets shorter by 1m, and the weight goes up 1m, and you do mg in work. If you loop the rope around a pulley on the weight, then if you pull the rope 1m, the rope gets shorter by 0.5 m on each side of the pulley, and so the weight goes up 0.5m and you have done mg/2 in work, moving the same distance ... so the force must be half.

You could also draw a free body diagram about the floating pulley...

It should have two force vectors upwards for the rope and 1 down for the weight of the object. The tension on one end of the rope is equal to the other. So an object of weight P, requires you to tug perfectly parallel with force P/2.

A movable pulley increases mechanical advantage by reducing the amount of effort or force needed to lift an object. This is because the pulley system allows the weight of the object to be distributed between multiple strands of the rope or cable, reducing the overall force required to lift the object. As a result, the mechanical advantage of a movable pulley is roughly 2, meaning that the force needed to lift the object is two times less than the weight of the object.

To understand this concept more clearly, let's consider a simple example. Imagine you want to lift a 10kg weight using a single fixed pulley. In this case, you would need to apply an upward force of 10kg to lift the weight. However, if you use a movable pulley, the weight of the object is distributed between two strands of the rope. This means that only half of the weight (5kg) is acting on each strand, so you only need to apply a force of 5kg to lift the weight. This results in a mechanical advantage of 2.

In summary, a movable pulley increases mechanical advantage by reducing the amount of force needed to lift an object. This is achieved by distributing the weight of the object between multiple strands of the rope, resulting in a reduced force required to lift the object. I hope this helps clarify the concept for you.

## 1. How does a movable pulley increase mechanical advantage?

A movable pulley increases mechanical advantage by reducing the amount of force needed to lift an object. When a rope is threaded through a movable pulley, it allows the weight of the object to be distributed between the rope and the pulley, making it easier to lift the object.

## 2. How is mechanical advantage calculated for a movable pulley?

Mechanical advantage for a movable pulley is calculated by dividing the weight of the object being lifted by the force applied to the rope. For example, if an object weighs 100 pounds and a force of 50 pounds is applied to the rope, the mechanical advantage would be 2.

## 3. What is the difference between a movable pulley and a fixed pulley?

The main difference between a movable pulley and a fixed pulley is that a movable pulley has a rope that can move through the pulley, while a fixed pulley is stationary and only changes the direction of the force. A movable pulley is able to provide a mechanical advantage, while a fixed pulley does not.

## 4. Can a movable pulley increase mechanical advantage indefinitely?

No, a movable pulley cannot increase mechanical advantage indefinitely. The mechanical advantage is limited by the number of movable pulleys used. Each additional pulley increases the mechanical advantage by 1, but there is a limit to how many pulleys can be used effectively.

## 5. What are some common examples of movable pulleys in everyday life?

Movable pulleys are commonly used in elevators, cranes, and sailboats. They can also be found in exercise machines, construction equipment, and window blinds. Movable pulleys are often used in systems that require lifting or moving heavy objects with less force.

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