# Pulleys

A pulley consists of a wheel with a grooved rim and a block which holds it. A rope runs in the groove around the wheel and one end will usually be attached to either: a weight, a fixed object like the ceiling or to another pulley. Pulleys are often used to lift things. For example, a pulley could be attached to an overhead beam and a rope could be run up and over the pulley to an object on the floor. This would enable a force applied downwards to lift the object off the floor. A simple single pulley like this is usually used to change the direction of a force.

There are several common reasons why this is done. If the force is being applied by a person, then the pulley enables them to apply force in a way that takes advantage of their biomechanics plus gravity. It is much easier to apply a downward force using your bodyweight than it is to apply the same force by pulling something upwards. In addition, it’s often both easier and safer to move a load at a distance than when standing right next to it because the load itself does not get in the way and does not represent a crushing risk. When the power is being supplied by a mechanical winch, it is usually much easier to move a pulley then it is to move the winch itself.

A single fixed pulley helps you alter the direction of the force, but it does not offer any mechanical advantage. If you want to lift something that weighs 10kg, you have to pull down with a force equivalent to 10kg. Similarly, if you want to raise the weight 1m into the air, you have to pull the loose end of the rope a total distance of 1m.

This pulley is suspended rather than fixed. This means that the rope on the left and right of the pulley are both lifting the 10kg load. They each lift half its weight, so the load is effectively split into two. If the load is lifted 1 metre, the rope on the right hand side must be shortened by one metre and this also applies to the rope on the left hand side.

The Velocity Ratio (sometimes called movement ratio) is defined as the ratio of the distance moved by the effort to the distance moved by the load. In this case, where the loose end of the rope must move a total distance of 2m in order to lift the weight 1m, the velocity ratio is 2:1.

Single pulley systems are straightforward. If the pulley is fixed, then the force required is equal to the weight. If the pulley moves with the weight then the force is equal to half of the weight. Another way of thinking about this is to divide the weight by the number of sections of rope supporting it to obtain the force needed to lift it. In the first example there is only one section of rope supporting the weight, so 10/1 = 10 Kg required to lift the weight. In the second example there are two sections of rope supporting the weight, so 10/2 = 5 Kg required to lift it.

A pulley system with the effort applied from above is very difficult to use. The most practical way to use a single moving pulley is combine it with a fixed pulley, as this allows the effort to be applied downwards. As one of the pulleys is a fixed pulley, the mechanical advantage is calculated as if only the moving pulley exists.

In this example, the weight is The weight is 300 Kg and there are 6 sections of rope supporting it. To get the force required simply divide 300 by 6, which equals 50 Kg. Remember, in all cases, just divide the weight by the number of sections of rope supporting it to get the force needed to lift the weight. The Velocity Ratio (defined as the ratio of the distance moved by the effort to the distance moved by the load) is 6:1 in this case. In other words, the loose end of the rope must move a total distance of 6m in order to lift the weight 1m.

If you look at the example above, you can see that it does not represent a very realistic way of using pulleys as it requires three ceiling attachments and three attachments to the weight itself. There are two ways around this problem. The first is to stack the pulleys vertically as shown.

This arrangement is much simpler to implement as it only requires one attachment point at each end. However it does require specially made pulleys of decreasing diameter in order to prevent the rope from fouling. This means that there is a practical limit to the number of pulley wheels in each stack.

In this example the 200kg weight is hanging from four sections of rope, remember to ignore the loose end of the rope where the effort is applied. That means each section of rope is supporting a quarter of the total weight, and to raise the weight into the air, you have to pull with only a quarter of the force. To get the force required simply divide 200 by 4, which equals 50 Kg. The Velocity Ratio (defined as the ratio of the distance moved by the effort to the distance moved by the load) is 4:1 in this case. In other words, the loose end of the rope must move a total distance of 4m in order to lift the weight 1m.

Block and Tackle

Another option is to mount the pulley wheels independently on the same axle form a block.  Two blocks with a rope attached to one of the blocks and threaded through the two sets of pulleys form a block and tackle. A block and tackle is assembled so one block is attached to fixed mounting point and the other is attached to the moving load. The ideal mechanical advantage of the block and tackle is equal to the number of parts of the rope that support the moving block.

#### Key Points

• A pulley is a wheel on an axle or shaft that is designed to change the direction of a cable supporting a load.
• Pulleys are used to transmit power and may be used in combination to provide mechanical advantage.
• Two pulleys with a rope attached to one of them and threaded through both form a block and tackle.
• A block and tackle is assembled so one block is attached to fixed mounting point and the other is attached to the moving load.
• The mechanical advantage is equal to the number of parts of the rope that support the moving block.