Pulleys

Pulleys are used in everyday life. They are used in factories for lifting loads, in hoisting flags, in drawing curtains in theatres, in lifts, in drawing water from well etc.

There are two types of pulley systems, i.e., fixed pulleys and movable pulleys.

Fixed Pulleys

We can think of a single fixed pulley as a lever of class I where the fulcrum is at the centre and the load and effort arm have the same length. (shown in the figure below)

Fixed Pulleys

If you pass a string over the pulley with one end carrying a weight and the other end attached to a spring balance you will get a measure of the effort you are exerting to pull up the weight.

If the weight is 10 N, you will notice that the effort is also almost 10 N. There is no mechanical advantage in using a single pulley. When you pull the rope down, the weight goes up. This way by standing on the ground you are able to raise a flag to the top of a flag pole with the help of a fixed pulley.

A fixed pulley is used to change the direction of force. Pulling down is easier as gravity helps and one can use one's own weight also.

The diagram shows fixed pulley being used by a bag to lift a load of 400N through a vertical height of 5 m in 10 s. The effort applied is 480 N (i) What is the V.R of the pulley? (ii) Calculate the M.A and efficiency (iii) Why is the efficiency of the pulley not 100% (iv) Calculate the energy gained by the load. (v) How much power was developed by the bag? The justification for using the pulley?

(i) V.R = 1 because if effort comes down by a distance of d m, load is raised by the distance as it is clear from the diagram

(ii)

Efficiency

(iii) A fraction of the force applied is used in overcoming the weight of the pulley and rope and friction.

(iv) d = 5 m

Energy gained by load = L x d = 400 x 5 = 2000 J

Movable Pulleys

Figure (a) below shows a pulley which can move up or down with a load. Here you will notice that the effort is required to lift the load as shown by the spring balance in the diagram.

Though there is a M.A. of 2 by using a movable pulley it is not convenient to pull the load upwards. For this purpose a combination of a fixed and a movable pulley as shown in figure (b) below has to be used. This arrangement will have some

Movable Pulleys

mechanical advantage and it will also be convenient to lift the load.

You will notice that in this type of arrangement if you pull the rope through 2 m, each of the two strings sharing the load will be shortened by 1 m. Hence, the load rises only by 1 m. (Shown in figure (c) above)

Thus, the velocity ratio of the system shown in the figure above is 2.

Block and Tackle

Instead of using separate pulleys a more practical way is to use a number of pulleys and to pass a continuous rope around them. This is a pulley system in which each block contains one or more pulleys mounted on the same axle as shown in figure (a) below.

T = E. Both the ropes share the load equally, hence

We can also have a system with the lower block having one pulley less than the upper block as shown in figure (b) below. The upper block of pulleys is fixed while the pulleys of the lower block are movable.

E = T tension in the rope. T is the same on each rope.

Load is supported by all the ropes equally. Hence L = nT where 'n' is the number of ropes supporting the load.

….for (b)

Each block containing one or more pulleys

Figure (c) above shows a system of four pulleys while figure (d) shows a system of five pulleys.

…..for (c)

….for (d)

The load to be raised is attached to hook on the frame of the lower block and the effort E is applied to the end of the rope passing round the top most pulley.

Suppose the rope is pulled down with a vertical force of 1000 N, then the tension on each rope will be 1000 N (frictional forces are neglected).

Total upward pull is 4 x 1000 or 4000 N with an effort of 1000 N [Figure (c) above]

In practice owing to the weight of the lower block and the friction between the pulley and the rope, the effort E needed to raise a load of 4000 N is more than 1000 N, say 1200 N.

Figure shown below illustrates what happens when the load W is raised to a distance x.

Each of the lever pulleys then releases a length of rope 2x. Thus, the effort E moves through a total distance 4x.

Usually V.R. = Total number of pulleys in the system

Mechanical advantage is 5 in figure (d) above, which is equal to the number of strings which support the movable block.

M.A. = Number of strings which support the movable block.

Load W raised to distance x

The velocity ratio is independent of friction while the mechanical advantage depends upon friction. In the absence of friction and with a weightless movable pulley the efficiency would be 100 per cent. This efficiency can never be achieved.