# Pulleys

## Pulleys, blocks and tackles

A 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)

### 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 a block or 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/s2, 32.17405 ft/s2) (when lifting a mass)

μ = mechanical efficiency of the system (equal to one for an ideal friction-less 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 load 100 kg can be calculated as

S = (100 kg) (9.81 m/s2) / ((1) (4))

= 245 N

## Related Topics

• Dynamics - Motion - velocity and acceleration, forces and torques
• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more

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