SIMPLE MACHINES / INCLINED PLANE

Can a longer ramp make the same lift easier?

Raise a load to the same height using a longer frictionless path.

ORIGINAL IDEAL EXAMPLE

200 N load
50 N effort

At constant speed without friction, work in equals work out. Effort times ramp length equals load times vertical rise.

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

inclined-plane.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Ramp selected · related inputs are marked.

pulling force50.00 N✓ passes

BASELINE INPUTS

load200 N

CALCULATED

angle14.478 deg

effort50 N

mechanicalAdvantage4

centerX484.12 mm

centerZ125 mm

blockZ160 mm

negativeAngle-14.478 deg

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Inclined plane: use a longer path to reach the same height
# Scope: Quasistatic frictionless ramp; length is measured along the ramp, force parallel to it.
load = 200 N
length = 1000 mm in 500..2000
height = 250 mm in 100..400
angle := asin(height / length) [deg]
effort := load * height / length [N]
mechanicalAdvantage := length / height
centerX := sqrt(length^2 - height^2) / 2 [mm]
centerZ := height / 2 [mm]
blockZ := centerZ + 35 mm [mm]
negativeAngle := -angle [deg]
part ramp "Ramp": box length, 100 mm, 10 mm at centerX, 0 mm, centerZ rot 0 deg, negativeAngle, 0 deg
part block "Load": box 60 mm, 80 mm, 60 mm at centerX, 0 mm, blockZ
check pulling force: effort <= 60 N
scenario longer ramp: length = 1500 mm

Calculated from your source · not saved

Baseline · Baseline

pulling force50.00 N ✓ passes

longer ramp · longer ramp

pulling force33.33 N ✓ passes

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

How the model works

At constant speed without friction, work in equals work out. Effort times ramp length equals load times vertical rise.

effort = load × height / length

Try the alternative

Lengthening the ramp reduces force while increasing travel. Ramp length is the sloped distance, not its horizontal footprint.

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

Assumptions and limits

This assumes quasistatic motion and no friction. It omits traction, stability, rolling resistance and ramp strength.