Pulleys and belts

Pulleys

Pulleys use mechanical advantage, similar to levers, to lift up loads. Pulleys are wheel shaped with a groove that allows a cord to sit inside the groove. They can be used by hand or attached to a motorised winch to increase the amount of weight that can be lifted.

Pulleys are a simple and manoeuvrable way to move large objects. They are easy to transport to where they are needed and set up, but they do require somewhere stable to hang.

A single pulley changes the direction of force, making pulling down easier than lifting up. Single pulley systems are demonstrated in cranes, lifting a bucket from a well, raising a flag or adjusting window blinds. Even though there is no actual mechanical advantage with one pulley, it is referred to as having a mechanical advantage of one.

Showing a rope over a single pulley system and an arrow to show the downward direction of effort to pull a load.A single fixed pulley has a mechanical advantage of one

One pulley doesn’t make a mechanical advantage, as the same amount of force is needed. However, if additional pulleys are added, a mechanical advantage is created. Using two pulleys together means you need half the force to lift. This is called a block and tackle, and is used to lift large, difficult-shaped objects, such as furniture. Adding more wheels to the block and tackle increases the load it can lift.

Showing a rope over a two pulley system and an arrow to show the downward direction of effort to pull a load.A block and tackle
curriculum-key-fact
The mechanical advantage is equal to the number of sections of rope pulling up on the object.
Showing a rope under a moveable pulley system and fulcrum with an arrow to show the upward direction of effort to pull a load.The mechanical advantage of a movable pulley (one where the pulley can move freely along the rope) is two

Example

The 10 N load below would still require 10 N of force to lift as the extra pulley is not taking any additional strain in weight - the weight is still taken by only one section of rope.

Showing a load supporting rope under a fixed pulley holding a 10 N load.  A redirecting rope from a second fixed pulley shows the downward effort to pull the load.

The 10 N load below would require half of the force to lift. There are two sections of rope taking the strain, so 5 N of force would be needed to lift it. The mechanical advantage would be 2.

Showing a load supporting rope under a pulley holding a 10 N load.  A second pulley with a redirecting rope over shows the downward effort to pull the load has a mechanical advantage of two.
Question

The pulley system below features 300 N of load and 3 pulleys:

Three pulleys with three supporting ropes to lift a 300 N load. Shows downward direction of effort to lift the load.

What weight is needed to pull the load?

Three sections of rope are taking the strain of the load.

Weight = 300 ÷ 3

= 100 N

Belts

Belt drives transfer movement from one rotating pulley to another, each held on a shaft. Shafts and pulley wheels can be made out of any material, whereas pulley belts are generally made from a soft, flexible material such as rubber. Grooves on the pulleys and belts help them to grip and turn.

A close-up image of a car belt inside of a car engine.
Grooves on pulley and belt help this grip

Winches, treadmills and washing machines are examples of belt-driven mechanisms.

A washing machine with an open enclosure showing all of its parts.
Washing machine belt drive

Belts can be attached around different-sized pulleys to drive shafts to change speed. As with gears, the bigger the wheel, the slower the speed. The velocity ratio between two pulleys can be calculated.

curriculum-key-fact
Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley

This can then be used to calculate the output speed:

curriculum-key-fact
Output speed = input speed ÷ velocity ratio

Example

A driven pulley has a diameter of 120 mm and a driver pulley has a diameter of 40 mm.

A driver pulley with a diameter or 40 mm and an input speed of 100 rpm driving a driven pulley with a diameter of 120 mm through a belt.

Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley

= 120 ÷ 40 = 3 or 3:1

The smaller driver pulley turns three times to make the driven pulley turn once.

The output speed of the larger driven pulley can then be calculated using the information available - the input speed is 100 revolutions per minute (rpm) and the velocity ratio has been calculated as 3.

Output speed = input speed ÷ velocity ratio

= 100 ÷ 3 = 33 rpm

Question

Calculate the velocity ratio and the output speed of the driven pulley on this lawnmower belt and pulley:

Viewing the underside of a lawnmower and its driver pulley (diameter 150 mm) and driven pulley (15 mm).

Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley

= 15 ÷ 150 = 0.1 or 1:10

The smaller driver pulley turns ten times for every one turn of the driven pulley.

Output speed = input speed ÷ velocity ratio

= 300 ÷ 0.1 = 3,000 rpm

The smaller driven pulley will turn at 3,000 rpm. This is the speed that the lawnmower blade will spin at on the lawnmower, ten times faster than the speed of the motor.

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