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# Pulley

The simple machines can be divided with its six main components that are: pulleys, levers, screws, wheels and axles, inclined planes, and wedges. The inclined planes Wedges and screws come in category of inclined plane while pulleys and wheels are a type of lever. Here we discuss all about the pulley. This is wheel shaped containing grooved rim. It is mainly used for reduction of force and its direction. If we want to hoist up a heavy load then we will have to exert force on the down side of the rope. So, it is easy to move down a load rather than take it on the upside with use of rope which needs a greater force than the former condition.

In all these processes, the movable pulley is used which is attached to load and reduce the level of required force to do the work. The combination of pulley is used to alter the amount of required force and direction of work. Thus it is useful for moving, pulling, and lifting loads and makes our heavy work easier. Let’s discuss the working process of pulley and its complete description in detail.

## What is a Pulley?

A pulley is a wooden or metallic wheel with a grooved rim which can take a string. Small plastic pulleys are also available in the market to carry small loads. The pulley can rotate freely about an axis passing through its centre. The end of the axle of the pulley are supported on a frame known as block.

The block of the pulley either fixed or free to move. According to this the pulley can be classified into two
1. Fixed pulley
2. Movable pulley
When the block is fixed, it is said to work as a fixed pulley and when the block is free to move with load, then the same pulley is said to work as a movable pulley.

## Fixed Pulley

In this arrangement, the block of pulley is fixed on high platform. An extensible string passes over the groove. One end of the string is attached to the body to be lifted while the other end is free.

A single fixed pulley dose not provide mechanical advantage, yet it is very useful in our daily life. The main advantage of the pulley is to be able to reverse the direction of the applied force so that a given job may be done conveniently.

People use fixed pulleys to gather fresh water from wells. A bucket hangs from the pilley to carry water up from deep under the ground.

## Movable Pulley

In this arrangement, the block is not fixed but carries the load. An inextensible string is wound round the groove and its one end is fixed to a fixed support while other end kept free to apply the effort. When the effort is applied, the block together with the load moves upwards.

## Pulley Formula

The velocity ratio (V.R) :
V.R of the pulley system can be found by comparing the distance moved by load and effort.

Velocity Ratio (V.R) = $\frac{Distance\ moved\ by\ the\ effort}{Distance\ moved\ by\ the\ load}$

Mechanical Advantage (M.A) :
Mechanical Advantage of a Pulley is given by the ratio of the power and load arms. Let E be the force i.e., effort applied at the free end. And L is the load which applied at the another end. Hence,
Mechanical Advantage (M.A) = $\frac{L}{E}$

The efficiency $\eta$ of a machine is related to the mechanical advantage and velocity ratio as given below
$\eta$ = $\frac{M.A}{V.R}$

Pulleys are used to change the direction of a force and to gain a mechanical advantage greater than 1.

## Parts of a Pulley

A pulley is a wheel with groove that holds a rope or a chain. The groove in the wheel keeps the rope or chain in place. Pulleys help lift loads. A person pulls one end of the rope. This force will lift the load on the other end.

## Pulley Problems

The following are the pulley problems.

### Solved Examples

Question 1: A machine has a velocity ratio of 10, it is used to raise a load of 2000 N. Find 1) The work obtained from the machine. 2) M.A and 3) efficiency of the machine.
Solution:

1) Work obtained from the machine = Load $\times$ distance moved
= $2000 \times 5$
= $10000 J$

2) Mechanical Advantage (M.A) = $\frac{Load}{Effort}$
= $\frac{2000}{250}$
=$8$

3) Efficiency = $\frac{M.A}{V.R}\times 100$
= $\frac{8}{10} \times 100$
= $80%$

Question 2: A block and tackle of $pulleys in each block has an efficiency of 80%. It is used to lift a load of 320 N. Calculate the following 1. V.R 2. M.A 3. Effort Solution: 1) V.R = The total number of pulleys in the system =$8$2) Efficiency =$\frac{M.A}{V.R}M.A$=$Efficiency \times V.R$=$\frac{80}{100} \times 8$=$6.4$3)$\frac{Load}{Effort}$=$M.A$or$Effort$=$\frac{Load}{M.A}$=$\frac{320}{6.4}$=$50 N\$

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