or more simply:
The first equation shows that the force exerted IN to the machine multiplied by the distance moved IN will always be equal to the force exerted OUT of the machine multiplied by the distance moved OUT. For example, using a block and tackle with 6 ropes, and a 600 pound load, the operator would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the 600 pound load 1 foot.
The second equation is a simplified formula based just on the forces in and out. Using the example above, 100 pounds of force IN results in 600 pounds of force OUT, an MA of 6. Both of these equations calculate only the ideal mechanical advantage (IMA) and ignore any losses due to friction. The actual mechanical advantage (AMA) includes those frictional losses. The difference between the two is the mechanical efficiency of the system.
There are two types of mechanical advantage: ideal mechanical advantage (IMA) and actual mechanical advantage (AMA).
The ideal mechanical advantage (IMA), or theoretical mechanical advantage, is the mechanical advantage of an ideal machine. It is usually calculated using physics principles because there is no ideal machine.
The IMA of a machine can be found with the following formula:
The actual mechanical advantage (AMA) is the mechanical advantage of a real machine. Actual mechanical advantage takes into consideration real world factors such as energy lost in friction.
The AMA of a machine is calculated with the following formula:
The following simple machines exhibit a mechanical advantage:
Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single pulley. It has an MA = 1 (assuming frictionless bearings in the pulley), meaning no mechanical advantage (or disadvantage) however advantageous the change in direction may be.
A single movable pulley has an MA of 2 (assuming frictionless bearings in the pulley). Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not increased.
By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may stand on the ground and pull down, we still have a mechanical advantage of four.
Here are examples where the fixed point is not obvious:
The theoretical mechanical advantage for a screw can be calculated using the following equation:
Note that the actual mechanical advantage of a screw system is greater, as a screwdriver or other screw driving system has a mechanical advantage as well.