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)
Orders of Levers
First-order levers
- the fulcrum is positioned between the effort and the load
- the effort is smaller than the load
- the effort moves further than the load
- the lever can be considered as a force magnifier
Second-order Levers
- the effort and the load are postioned are positioned on the same size of the fulcrum but applied in oposite directions
- the load lies between the effort and the fulcrum
- the effort is smaller than the load
- the effort moves further than the load
- the lever can be considered as a force magnifier
Third-order Levers
- the effort lies between the load and the fulcrum
- the effort is greater than the load
- the load moves further than the effort
- the lever can be considered as a distance magnifier
Example - First-Class (Order) Lever - 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 (Order) 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 (Order) 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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