Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Levers

Excerting forces with levers

Sponsored Links

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.

Levers - first-class

The moment action on both sides of the lever is equal and can be expressed as

Fe de = Fl dl                             (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)

The effort force can be calculated by modifying (1) to

Fe = Fl dl / de                                  (1b)

Lever Calculator

The calculator below can used to calculate the effort force for a lever:

Fl - load force (N, lb)

dl - distance form 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 positioned on the same side of the fulcrum but applied in opposite 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.

Levers - second-class

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.

Levers - third-class

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)

One or more forces acting on a lever

A lever with two acting load forces and one effort force is indicated in the sketch below:

Levers - with more than two forces

The generic equation for one effort force with one or more acting load forces can be expressed as

Fe = (FlA dlA +  FlB dlB + .. + FlN dlN ) / de                                                (2)

This equation is modified for three acting loads below.

Example - A Lever with three acting loads and one effort force

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)

Sponsored Links

Related Topics

Related Documents

Tag Search

  • en: levers mechanisms pound kg force moment equilibium
  • es: mecanismos de palancas libras kg vigor momento equilibium
  • de: Hebel Mechanismen Pfund kg Kraftmoment equilibium
Sponsored Links

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate this page to
About the Engineering ToolBox!

Citation

This page can be cited as

  • Engineering ToolBox, (2008). Levers. [online] Available at: https://www.engineeringtoolbox.com/levers-d_1304.html [Accessed Day Mo. Year].

Modify access date.

Customize Ads in the ToolBox

Make ads more useful in Google Ad Settings .

. .

close

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

4 20

Sponsored Links
.