SIMPLE MACHINES / LEVER

Can a longer handle lift the same load with less effort?

Move the effort farther from the fulcrum and compare the hand force.

ORIGINAL IDEAL EXAMPLE

100 N load
25 N effort

Balance moments about the fulcrum. The load force times its arm equals the effort force times its arm.

Conceptual schematic; use the model below for parameter-linked geometry.

lever.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Lever selected · related inputs are marked.

hand force25.00 N✓ passes

BASELINE INPUTS

load100 N

CALCULATED

beamSpan250 mm

beamCenter75 mm

effort25 N

mechanicalAdvantage4

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Lever: trade handle travel for lifting force
# Scope: Ideal weightless first-class lever; forces perpendicular to the arms.
load = 100 N
loadArm = 50 mm in 25..100
effortArm = 200 mm in 100..600
beamSpan := loadArm + effortArm [mm]
beamCenter := (effortArm - loadArm) / 2 [mm]
effort := load * loadArm / effortArm [N]
mechanicalAdvantage := effortArm / loadArm
part beam "Lever": box beamSpan, 8 mm, 12 mm at beamCenter, 0 mm, 20 mm
part fulcrum "Fulcrum": box 20 mm, 30 mm, 20 mm
check hand force: effort <= 40 N
scenario longer handle: effortArm = 400 mm

Calculated from your source · not saved

Baseline · Baseline

hand force25.00 N ✓ passes

longer handle · longer handle

hand force12.50 N ✓ passes

Calculated from the same .napkin source. Edits preview a temporary study and are not saved.

How the model works

Balance moments about the fulcrum. The load force times its arm equals the effort force times its arm.

effort = load × loadArm / effortArm

Try the alternative

A longer handle lowers the required hand force. Your hand must move farther for the same load movement.

Choose a scenario, change an input, then inspect the equations and force check in Source.

Assumptions and limits

The model neglects the lever’s weight, pivot friction, bending and material strength. The force check is an example hand-force budget.