Final answer:
The relationship between the input force and the output force in a pulley system is that the output force is approximately an integral multiple of the input force, depending on the number of cables pulling directly upward. This is due to the mechanical advantage of the pulley system.
Step-by-step explanation:
For a pulley, the relationship between the input force and the output force depends on the number of cables pulling directly upward on the system. If the pulleys are friction-free, then the force output is approximately an integral multiple of the tension in the cable. The mechanical advantage (MA) of the pulley system is equal to the number of cables pulling directly upward. Since each attachment applies an external force in approximately the same direction as the others, they add up, producing a total force that is nearly an integral multiple of the input force, resulting in a larger output force.
Fixed Pulley: In a fixed pulley system, the pulley is attached to a fixed point, and only the direction of the force is changed. The input force is equal to the output force, but the direction is altered. No mechanical advantage is gained in terms of force.
Movable Pulley: In a movable pulley system, the pulley is attached to the object being lifted. The input force is exerted downwards, and the output force is the weight of the object. The mechanical advantage in this case is equal to 2, meaning the output force is twice the input force.
Block and Tackle (Combination of Pulleys): By combining multiple pulleys, a block and tackle system can be created. The mechanical advantage in this case is determined by the number of ropes supporting the load. More ropes result in a higher mechanical advantage, reducing the input force needed to lift the load.