# What Is a Block & Tackle Pulley?

UC Irvine

A block and tackle pulley system uses multiple pulleys to gain mechanical advantage in lifting. It reduces the force required to lift heavy objects, though at the expense of having to pull a greater distance than the weight is lifted. It is often seen in ports, where transfer of cargo between water and land transportation requires heavy lifting.

## Definition

Block and tackle can be defined as a combination of one or more pulley blocks and the associated tackle necessary to give a mechanical advantage.

"Block and tackle" actually refers to an apparatus consisting of multiple pulley blocks and the tackle (rope, chain) that runs along each of the pulleys. A pulley block can contain more than one pulley in a single unit, to allow the tackle to run through multiple times.

Block and tackle pulleys go by many names. For example, gun tackle, watch tackle, and double tackle are two-pulley systems in order of increasing mechanical advantage; the double tackle provides a 2:1 mechanical advantage.

Mechanical advantage can be defined as the ratio of the force exerted by a machine to the force applied to it.

It is calculated by dividing the force output by the force input. So, for example, if 25 Newtons is needed to lift a 100 Newton weight, the mechanical advantage is 4:1.

Note that to lift a load in the diagram, each line must be shortened the same distance (except for the lead line marked as an arrow). If a mass is to be lifted a distance x, the bottom pulley must become a distance x closer to the top pulley. Therefore, all lines between the pulleys must shorten a distance x. Therefore, the distance the lead line must be pulled to lift the mass a distance x is calculated as x --- (# of lines between both pulleys).

The mechanical advantage, at least for the two-block set-up illustrated here, is the ratio (number of lines between both pulleys) : 1.

To be able to lift so much with so little effort has a trade-off. Force may not be conserved in a block and tackle arrangement, but energy is. One has to put the same amount of energy in to lift a load as if there were no mechanical advantage at all.

To understand where the trade-off lies, recall that mechanical work (the movement of a load using force) is a measure of energy, and that work = force --- distance, where "distance" is the distance over which the force is applied.

In terms of work, the law of conservation of energy can be restated as follows: the force exerted into a machine multiplied by the distance over which the force is applied will always equal the force exerted by the machine multiplied by the distance over which it exerts a force. In other words, for constant work, as force goes down, distance must go up.

Therefore, the trade-off is the longer distance one must pull in order to make a load travel just a short distance.

## A Common Error

Tension Error (Courtesy: U. of Mich. Dept of Physics)

Pulleys are overlapped within pulley blocks for more than just the practicality of compactness. It also avoids lateral forces.

An occasional error is to represent a pulley system with lateral displacement of the pulleys. This is an inefficient system, however, and not useful in practice, because it introduces lateral forces into the tension of the tackle.

For example, suppose a person hangs from two ends of a rope looped over a single pulley. If the person weighs 100 N, each rope end pulls up with a tension of 50 N. But if the person hangs from a near-horizontal clothesline, the tension in the line is much greater because the tension it exerts to hold up the person is oblique to the downward direction of the person's weight. The downward component of the tension is less than the total tension, so the tension must be greater than 50 N.

Therefore, the numbers in the image here are incorrect. The tensions marked should be higher than 50 and 25, because the tension has been increased by lateral pulley displacement. These numbers would only be correct if all the lines are vertical.