Calculation
F1·l1 = F2·l2
In equilibrium, the moments of both lever arms about the pivot are equal; a shorter lever arm requires a greater force.
Momentengleichgewicht um den Drehpunkt ΣM = 0 (Dubbel Mechanik B 1.4.2, Kräftesystem in der Ebene): F1·l1 = F2·l2
Equilibrium of a two-sided lever
In equilibrium, the moments of both lever arms about the pivot are equal; a shorter lever arm requires a greater force.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Counter-force F2 — Force required at the second lever arm for the lever to be in equilibrium.
- Force F1 — Known force acting at the first lever arm.
- Lever arm l1 — Distance from F1's point of application to the pivot.
- Lever arm l2 — Distance from F2's point of application to the pivot.
Example
F1=100 N, l1=0.3 m and l2=0.1 m give F2=100·0.3/0.1=300 N.
Assumptions and limits
Rigid, massless lever, frictionless pivot and forces acting perpendicular to the lever arms; lever weight and angled force directions are excluded.
Understand Equilibrium of a two-sided lever
This calculator applies the classic law of the lever to a two-sided lever, determining the counter-force required for equilibrium.
What does this quantity describe?
For a two-sided lever in equilibrium, moments on both sides about the pivot are equal: F1·l1=F2·l2.
Formula and variables
F1·l1 = F2·l2
F1·l1 = F2·l2
| Symbol / input | Meaning |
|---|---|
| Counter-force F2 | Force required at the second lever arm for the lever to be in equilibrium. |
| Force F1 | Known force acting at the first lever arm. |
| Lever arm l1 | Distance from F1's point of application to the pivot. |
| Lever arm l2 | Distance from F2's point of application to the pivot. |
Choose the inputs correctly
F1 is the known force at the first lever arm, l1 and l2 the two lever arms measured from the pivot to each force's point of application.
How to use the calculator
Measure lever arms perpendicular to the respective force direction; for angled forces, first resolve the perpendicular component.
Worked example
F1=100 N, l1=0.3 m and l2=0.1 m give F2=100·0.3/0.1=300 N.
Understand the result and units
A shorter lever arm on the opposite side requires proportionally greater force; the law of the lever explains force amplification and ratio this way.
F1 is a force, l1 and l2 are lengths. F2 is output as a force.
Typical applications
Sizing scales, pry bars, seesaws, shears and other two-sided lever mechanisms in machine design and everyday use.
Assumptions, limits and common mistakes
Rigid, massless lever with a frictionless pivot and forces perpendicular to the lever arms; lever weight, friction and angled force directions are excluded.
Common mistake: Do not use distance along the lever instead of the perpendicular lever arm to the force's line of action when the force is not perpendicular to the lever.
Frequently asked questions
What is “Equilibrium of a two-sided lever” used for?
Sizing scales, pry bars, seesaws, shears and other two-sided lever mechanisms in machine design and everyday use.
Where do the input values come from?
F1 is the known force at the first lever arm, l1 and l2 the two lever arms measured from the pivot to each force's point of application.
What does the result not cover?
Rigid, massless lever with a frictionless pivot and forces perpendicular to the lever arms; lever weight, friction and angled force directions are excluded.