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Pulley

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 Sub Topics A pulley system is a lifting device which is useful for lifting loads through relatively larger distances than is possible with a screw jack. The pulleys used here are smaller in size than those used in a belt-drive system. A typical pulley is made of metal or wood and is grooved along the periphery to accommodate a coir rope, a wire rope or a chain. In the analysis of pulley systems two important assumptions are made: i) the weight of a pulley is small compared to the load lifted and ii) the friction between the pulley and the rope is negligibly small so that the tensions in the rope on either side of a pulley are the same.

Definition

A pulley is a machine in which a rope or cable passes back and forth over one or more grooved wheels. In a pulley system, one end of the rope is attached to the load and the other end is pulled in order to move or lift the load. A single pulley has only one wheel. The pulley makes the task of lifting a load more convenient since it is easier to pull a rope down than it is to lift a weight up.

Formula

Some of the important formulas related to pulley is given below:

Velocity Ratio (VR):

The number of times further the effort moves than the load is called the velocity ratio. It is also called the distance ratio.

VR = $\frac{Distance\ moved\ by\ the\ effort}{Distance\ the\ load\ is\ moved}$

It is the ratio between load force and effort.

MA = $\frac{L}{E}$

Efficiency, $\eta$ = $\frac{MA}{VR}$

Fixed Pulley

A fixed pulley is one with a fixed support which does not move with either the effort or the load. The pulley itself should turn on its axle as freely as possible for maximum efficiency. Given figure shows a single fixed pulley which is used to change the direction of the effort force E from a downward pull to an upward lift. The tension T in the string or rope applies the upward force of the load L.It is often easier to pull a rope downward than to lift a load upward. The velocity ratio of a fixed pulley must be exactly 1 as the load will rise by the same distance as the effort moves. The mechanical advantage is fixed pulley is almost 1, there being only a small amount of work wasted against friction on the pulley bearing and in lifting the weight of the rope.

Movable Pulley

A single moving pulley gives a velocity ratio of 2. This can be seen in the figure. For any distance The load is raised, there are two lengths of rope equal to that distance to be pulled upwards by the effort. So both the ropes supporting the load must be shortened by the distance the load is raised.

The mechanical advantage is found by measurement, but we can see that the upward lifting force is shared equally between two upward forces, the effort E and the tension T in the rope on the other side of the pulley. If the load is heavy compared with the pulley and frictional forces then the effort needed will be roughly half and the load and the mechanical advantage nearly 2. In other words, a single moving pulley can be used to magnify an effort force by almost 2.

A single moving pulley is often combined with a single fixed pulley to provide a simple machine with a downward effort and a velocity ratio of 2.

How a Block and Tackle Works?

The pulley is usually used in sets of two or more to gain a higher velocity ratio and mechanical advantage. Two sets of pulleys are used, one fixed and one moving. The pulleys are mounted, usually side by side, in a block or frame and the apparatus of pulleys and ropes is generally called the tackle. The whole system or machine is known as a block and tackle.

Many large machines use a block and tackle pulley systems, for example cranes and lift mechanisms. So that we can see more clearly where the ropes go, we usually draw the pulleys below each other in each block. The lower, moving pulley block is supported 4 ropes. To raise the load by 1m, will required 4m of rope to be pulled out of the machine by the effort and so the velocity ratio is exactly 4.

Pulley Problems

Let us discuss some problems related to the pulley.

Solved Examples

Question 1: A pulley system has a VR of 5. Calculate the load able to be lifted by a pulley system has an efficiency of 76%. An effort of 750N is again applied.

Solution:

Given that,
VR = 5, $\eta$ = 76% = 0.76, E = 750N
By using the formula for pulley,

Efficiency, $\eta$ = $\frac{MA}{VR}$

0.76 = $\frac{MA}{5}$

MA = 0.76$\times$5 = 3.80

Since, MA = $\frac{L}{E}$

3.80 = $\frac{L}{750}$

L = 3.80$\times$750 = 2850N or $\frac{2850}{9.8}$ = 290.81kg

Question 2: A simple rope and pulley system has a VR of 5. Find the effort required if the efficiency of the system is 45% and the load to be lifted is 2kN?

Solution:

Given parameters are,
VR = 5, $\eta$ = 45% = 0.45, L = 2kN = 2000N

Efficiency, $\eta$ = $\frac{MA}{VR}$

0.45 = $\frac{MA}{5}$

MA = 0.45$\times$5 = 2.25
We know that,

MA = $\frac{L}{E}$

2.25 = $\frac{2000}{E}$

E = $\frac{2000}{2.25}$ = 888.9N