SIMPLE MACHINES / WEDGE

Why does a shallow wedge need less pushing force?

Use horizontal travel to lift a vertical load by a smaller distance.

ORIGINAL IDEAL EXAMPLE

500 N load
100 N effort

For the ideal single wedge, horizontal input work equals vertical output work. A shallow working face trades travel for force.

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

wedge.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Wedge working face selected · related inputs are marked.

pushing force100.00 N✓ passes

BASELINE INPUTS

load500 N

CALCULATED

angle11.31 deg

effort100 N

mechanicalAdvantage5

faceLength101.98 mm

centerX50 mm

centerZ10 mm

negativeAngle-11.31 deg

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Wedge: convert horizontal motion into a small lift
# Scope: Single frictionless wedge lifting a vertical load quasistatically. The working face is shown as a thin inclined plate, not a solid wedge CAD feature.
load = 500 N
length = 100 mm in 80..200
rise = 20 mm in 10..50
angle := atan(rise / length) [deg]
effort := load * rise / length [N]
mechanicalAdvantage := length / rise
faceLength := sqrt(length^2 + rise^2) [mm]
centerX := length / 2 [mm]
centerZ := rise / 2 [mm]
negativeAngle := -angle [deg]
part face "Wedge working face": box faceLength, 50 mm, 3 mm at centerX, 0 mm, centerZ rot 0 deg, negativeAngle, 0 deg
check pushing force: effort <= 120 N
scenario steeper wedge: rise = 40 mm

Calculated from your source · not saved

Baseline · Baseline

pushing force100.00 N ✓ passes

steeper wedge · steeper wedge

pushing force200.00 N × fails

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

How the model works

For the ideal single wedge, horizontal input work equals vertical output work. A shallow working face trades travel for force.

effort = load × rise / length

Try the alternative

A steeper wedge increases lift per push but requires more force. This example is a lifting wedge, not a cutting or fracture model.

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

Assumptions and limits

Friction, self-locking, contact stresses and material fracture are omitted. The geometric model shows the inclined working face rather than a solid wedge feature.