Force-amplifying effectiveness of a simple machine (lever, wedge, wheel and axle, pulley, or screw). The theoretical mechanical advantage of a system is the ratio of the force that performs the useful work to the force applied, assuming there is no friction in the system. In practice, the actual mechanical advantage will be less than the theoretical value by an amount determined by the amount of friction.
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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 fixed 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:
Generally, the mechanical advantage is calculated as follows:
Additionally, the Force exerted IN to the machine × the distance moved IN will always be equal to the force exerted OUT of the machine × 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 load 1 foot.
This requires an ideal simple machine, meaning that there are no losses due to friction or elasticity. If friction or elasticity exist in the system efficiency will be lower; Workin will be greater than Workout.
The IMA of a machine can be found with the following formula:
The AMA of a machine is calculated with the following formula:
The vertical vector force "V" is transmitted through the bars (with a vector force "F") of which one is anchored on the right side and the other pushes away a block on the left against a vector force "H". The angle α should be relatively small, say less than 5 degrees, for best performance. The ratio "H/V" equals the mechanical advantage MA.
In the equations the friction on the block on the left (illustrated by normal vector force "N") is ignored, as is friction in the hinges. The friction in the hinges will have less influence on the mechanical advantage with a large 'bar length'/'hinge pin diameter' ratio. However, in that case one has to be increasingly aware of material deformation.
Calculation: for angle α=0.5 degree the MA=57.3; α=1 > MA=28.6; α=2 > MA=14.3; α=3 > MA=9.5; α=5 > MA=5.7