One push, turned sideways
Why Does a Sharp Edge Cut So Easily?
A wedge takes the push you give it and redirects it sideways, and the thinner the wedge, the bigger that sideways push becomes.
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Step 1 of 5
A wedge changes a push's direction.
The sloping faces cannot move sideways out of the way, so anything they meet is shoved outward instead. Your push goes in downward and comes out sideways.
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Step 2 of 5
Thinner means a bigger sideways push.
A shallow wedge travels a long way to open a small gap, and that trade — lots of travel for a little movement — is exactly what multiplies the force.
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Step 3 of 5
Sharpness is really about area.
The same push spread over a wide dull edge is a gentle nudge everywhere. Squeezed onto an edge a few atoms wide it becomes a pressure nothing resists.
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Step 4 of 5
Nails, axes and teeth are the same machine.
A nail is a wedge that pushes wood fibres aside. An axe splits along the grain. Your front teeth are wedges too, and your back teeth are not.
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Step 5 of 5
Blunt tools squash instead of splitting.
Once the edge is rounded, the sideways push arrives too weak to part anything, so the material crushes and tears. Sharpening simply rebuilds the angle.
A sharpened kitchen knife has an edge around 0.5 micrometres across — about a hundredth the width of a human hair.
The short version
A sharp edge cuts because a wedge turns your push sideways and concentrates it onto almost no area at all.
Try it yourself
Press the flat of a butter knife into a block of cheese, then the edge. Same hand, same push, completely different result.
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