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Simple Machines · Question 14 of 20

Inclined planes

The ramp is the only simple machine that just lies there — and it moved every block of every pyramid.

Plate XVI — The ramp discount push = mg·sinθ · path × 1/sinθ
Flatten the slope and watch the push arrow shrink — then check the path price.
1.6 m up24°50 kgweightsame climb, gentler slope → smaller push, longer walk
FIG. XVI — THE RAMP DISCOUNT
Slope angle 24°
Flatten the ramp and watch the push arrow shrink.
Push needed
20kg-force
Straight lift
50kg-force
Path vs climb
2.5× longer
Lifting the crate straight up costs its full 50 kg of push. Rolling it up this slope costs only 20 kg — but look at the path: it's 2.5× longer than the climb. The ramp never erases the bill; it lets you pay in small change.
The short answer

A ramp lets you raise something by pushing it up a gentle slope instead of lifting it straight up — easier, but you travel farther.

What's actually happening

Lifting a 100 kg crate one metre straight up means supplying its full weight of force over that metre. Slide it up a five-metre ramp to the same height and you only fight the fraction of gravity that points along the slope — about a fifth of the weight (ignoring friction). The ramp converts one brutal lift into a long gentle push.

The exchange rate is the slope itself: force needed ≈ weight × height ÷ ramp length. Five times the path, one-fifth the force. The work — force times distance — comes out identical either way, plus a friction surcharge. That surcharge is real but it buys something too: friction is often what keeps the crate from sliding back down while you catch your breath.

The inclined plane's best disguise is the screw: wrap a long thin ramp around a cylinder and every turn of the screwdriver pushes the thread a tiny distance along a very long slope — enormous force multiplication in a pocket-sized package. A car jack lifting a tonne with one lazy arm, a vice crushing wood, a jar lid sealing tight: all ramps, coiled up. Mountain switchback roads are the same idea drawn on a landscape — nobody builds a road straight up a hill.

Try it at home Measure the ramp discount
  1. 1Make a ramp from a plank or stiff book onto a chair seat. Tie a rubber band to a filled water bottle.
  2. 2Lift the bottle straight up by the band and measure how far the band stretches — that is the full-weight price.
  3. 3Now drag it slowly up the ramp by the same band. The stretch is visibly shorter. Tilt the ramp steeper and watch the stretch grow back toward the full price.