Levers
Forces with levers
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A lever is a mechanism that can be used to exert a large force over a small distance at one end of the lever by exerting a small force over a greater distance at the other end of the lever.
In general the effort force can be expressed as
Fe = Fl dl / de (1)
where
Fe = effort force (N, lb)
Fl = load force (N, lb) (note that weight is a force)
dl = distance from load force to fulcrum (m, ft)
de = distance from effort force to fulcrum (m, ft)
Example - A force (weight) of 1 pound is exerted at the end of a lever at distance 1 ft from the fulcrum
The effort force at a distance of 2 ft from the fulcrum can be calculated as
Fe = (1 lb) (1 ft) / (2 ft)
= 0.5 (lb)
The formula (1) can be modified to express required load if you know the effort, or required distance from fulcrum if load and effort forces are known and so on.
The level above where the fulcrum located between the load and effort force is often characterized as a first-class level mechanism.
A level where the load and effort force are located on the same side of the fulcrum is often characterized as a second-class level mechanism.
Example - Second-Class Lever
A force (weight) of 1 pound is exerted at a distance of 1 ft from the fulcrum.
The effort force at a distance of 2 ft from the fulcrum can be calculated as
Fe = (1 lb) (1 ft) / (2 ft)
= 0.5 (lb)
Example - Lever calculation with SI-units - weight of 1 kg mass acting 1 m from the fulcrum
The effort force at a distance of 2 m from the fulcrum can be calculated as
Fe = (1 kg) (9.81 m/s2) (1 m) / (2 m)
= 4.9 N
A lever mechanism where the input effort is higher than than the output load is often characterized as a third-class lever mechanism.
Example - Third-Class Lever
A force (weight) of 1 pound is exerted at a distance of 2 ft from the fulcrum.
The effort force at a distance of 1 ft from the fulcrum can be calculated as
Fe = Fl dl / de
= (1 lb) (2 ft) / (1 ft)
= 2 (lb)
With more than two forces acting on the lever
With more than two forces acting a lever formula (1) must be modified to
Fe = (FlA dlA + FlB dlB + .. + FlN dlN ) / de (2)
Example - Three weights acting on a lever
A weight A of 1 pound is exerted at a distance of 1 ft from the fulcrum. A weight B of 2 pound is exerted at a distance of 2 ft from the fulcrum, and a weight C of 3 pound is exerted at a distance of 3 ft from the fulcrum.
The effort force at a distance of 2 ft from the fulcrum can be calculated as
Fe = (FlA dlA + FlB dlB + FlC dlC ) / de
= ((1 lb) (1 ft) + (2 lb) (2 ft) + (3 lb) (3 ft)) / (2 ft)
= 7 (lb)
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