Pulleys

Pulleys are simple machines used basically to lift a body vertically by applying forces to ropes or wires. They are widely used in civil construction to lift materials between different levels.

Depending on how they are attached, pulleys can reduce the human effort required to lift very heavy objects. For this reason, this instrument represented an evolution mainly for the development of commerce , optimizing the work of loading and unloading ships.

fixed pulley

The following image shows a person lifting an object by means of a single pulley attached to the ceiling, called a fixed pulley.

The force exerted has a direction opposite to the direction of motion of the object and is exactly equal to the force that would have been exerted if the object were lifted directly with the hands. Fixed pulleys do not decrease the applied force. The benefit is the ease of positioning an object in the desired location.

movable pulley

Fix the figure below. The number 1 pulley is fixed and only changes the direction of force application, but does not generate a decrease in the effort required to lift the object.

Pulley 2 is attached to the lifted object and there is no direct contact between it and the ceiling, so it is called a movable pulley. From the application of force F, both the object and the pulley assume higher positions, but the applied force is not equal to the object’s real weight.

Each moving pulley halves the force needed to lift an object. The greater the number of moving pulleys, the less force applied to the system to change the vertical position of the object.

The force F required to lift an object of weight P is defined from the number of moving pulleys (n) by setting the following equation:

F =    P 
      2 ^N

Pulleys 2, 3 and 4 of the following system are movable.

Applying the previous equation shows that the force required to lift the object attached to pulley 4 is equal to one-eighth of the object’s actual weight.

F =    P      ⇒ F =    P       ⇒ F =    P 
      2 ^N                    2 ^{3                    8} 

This means that if the object has, for example, a weight of 640 N, which corresponds to a body of mass 64 kg, it will be lifted by eight times less force. The force required for this case corresponds to 80 N, that is, as if the object had only 8 kg of mass.