• Pixel-art sticker of Rampa, personifying Inclined Plane, with the caption “Gentle Slope, Lighter Push.”

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Rampa

Inclined Plane Physics

\[F = mg\sin\theta\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Rampa, who takes the long way up: a ramp trades distance for force, and holding a load on a frictionless slope takes F = mg sin θ. On a 30° slope you need only sin 30°, half the weight, to push the load up. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Rampa, a ramp who trades extra distance for a smaller push.

On a slope, gravity's pull mg can be split into two parts: one pressing into the surface, mg cos θ, and one pulling the load down the slope, mg sin θ. With no friction, holding the load or pushing it up slowly needs a force of only mg sin θ along the slope.

On a 30° slope, sin 30° = 0.5, so you need half the load's weight. Raising a 20 kg box by 1 m means pushing with about 98 newtons over 2 m of slope, instead of lifting 196 N straight up 1 m. The work is the same, 196 joules, either way. The ramp only lets you use a smaller force over a longer distance.

Wheelchair ramps, loading ramps, roads up mountains and screw threads (a ramp wrapped around a cylinder) all use this idea. It is one of the classical simple machines.

Real ramps have friction, which adds to the push needed going up. Steeper slopes need more force, and above some angle loads slide down by themselves.

Equations

\[F = mg\sin\theta\]
Symbols
SymbolMeaningUnit
\(F\) force along the slope needed to hold the load (no friction) \(\mathrm{N}\)
\(m\) mass of the load \(\mathrm{kg}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(\theta\) angle of the slope \(\mathrm{rad}\)