Pulleys

A pulley is a simple machine that consists of a wheel with a groove, through which a rope/cable passes over.

The pulley’s main purpose is to change the direction of force, but they can also be used in systems to achieve mechanical advantage to lift heavy loads.

Pulleys can be either fixed (to a wall or ceiling), or movable (usually attached to the load). Pulley systems are many pulleys working at the same time.

MA & VR §

Formula §

$$M{A}_{Pulley}=\frac{F_{Load}}{F_{Effort}}=No.ofsupportingropes=VR$$

Deriving the formula §

Take a single pulley system, with the pulley fixed to the ceiling:

In such a system, the tension from the rope transfers the force to the effort (the person pulling). As such, to keep the pulley system in equilibrium, the same force is required from the effort (red arrow) as the gravitational force acting on the load (blue arrow). As such the MA of a single, fixed pulley systems is simply 1.

Now take a double pulley system, with one fixed and one movable pulley. Since the movable pulley is attached to the load, we can assume it also carries all of the load force (assume that the actual pulleys are weightless). Then, the rope going through it ‘splits’ the force equally, and thus the effort needs to only lift half the load. MA is equal to 2

TLDR: Count the number of ropes that support the load force. No. of supporting ropes = MA.