# Pulleys

## Pulleys, blocks and tackles

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Pulley is a device that can increase the magnitude of an effort force.

### Without Pulley

With no pulley - the effort force is similar to the load - in opposite direction.

S = F (1)

where

S = effort force (N, lb)

F = load (N, lb)

### Single Pulley

#### Fixed Pulley

With a single fixed pulley the effort force is similar (or more due to efficiency loss) to the load.

S = F (2)

The advantage with the single fixed pulley is that the direction of force is changed - it is possible to pull down instead of lifting up.

#### Movable Pulley

With a single moveable pulley the effort force is half (or more due to efficiency loss) of the load.

S = 1/2 F (3)

### Combined Pulleys

With a combined moveable pulley as above - the effort force is half (or more due to efficiency loss) of the load.

S = 1/2 F (4)

With two pulleys and the ropes as above - the effort force is 1/3 (or more due to efficiency) of the load.

S = 1/3 F (5)

### General Equation for Blocks and Tackles

The general effort force equation for block and tackle to raise or pull a load can be expressed as

*S = F / (μ n) *

* = (m g) / (μ n) (6)*

*where *

*S = effort force (N, lb)*

*F = load, often weight (N, lb)*

*m = mass (kg, slugs) (when lifting a mass)*

*g = constant of gravitation (9.81 m/s^{2}, 32.17405 ft/s^{2}) (when lifting a mass)*

*μ = mechanical efficiency of the system (equal to one for an ideal frictionless system, a fraction less than one for real-world systems with energy losses due to friction)*

*n = number of ropes between the sets of pulleys*

### Example - Pulley and Effort Force

The effort force for a pulley with *4 ropes*, no friction loss (*μ = 1*) and a load *100 kg* can be calculated as

*S = (100 kg) (9.81 m/s ^{2}) / ((1) (4))*

* = 245 N *

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