How do you calculate the effort force of the pulley?

To calculate the effort force of a pulley system, you need to consider the concept of mechanical advantage. The mechanical advantage of a pulley system tells us how much the force applied to the pulley can be amplified to move a load. In an idealized, frictionless pulley system, the mechanical advantage can be determined by counting the number of supporting ropes (or segments of rope) that support the load.

There are two types of pulleys to consider: fixed pulleys and movable pulleys.

Fixed Pulley:
In a fixed pulley, the pulley is attached to a stationary support, and the direction of the force is changed but not the magnitude. The mechanical advantage (MA) of a fixed pulley is always 1. This means the effort force (F_effort) required to lift the load is the same as the load force (F_load).
F_effort = F_load

Movable Pulley:
In a movable pulley, the pulley is attached to the load itself, and the direction of the force applied is the same as the direction of the load movement. The mechanical advantage (MA) of a movable pulley is equal to the number of supporting rope segments (n). Each supporting rope segment shares the load force, so the total effort force is reduced.
F_effort = F_load / n

For example, if you have a movable pulley system with three supporting rope segments, the effort force required would be one-third of the load force.

It's essential to note that real-world pulley systems may involve friction and other inefficiencies, which can affect the actual mechanical advantage and the effort force required. In those cases, additional factors need to be considered, such as the efficiency of the pulleys and the effects of friction.