Why are sharper knives more effective at cutting?
When talking about a sharp knife, we generally think about a thinner blade. The thing that really matters is the edge of the knife. The thinner the edge, the sharper the blade. So the question is why does a thinner blade cut more effectively? Let’s imagine we’re cutting a piece of cheese. And let’s, for the sake of argument, say it’s about two centimetres thick. It should seem quite natural that the thinner the edge, the higher the pressure for the same force and the easier the cut will be.
Let’s say our cutting force is 10 newtons. That’s about what you’d expect for a one-kilogram mass. And let’s think about our three knife blades. We have A, where the edge is one-millimetre thick; B, where it’s 0.5 millimetres’ thick; and C, where it’s 0.25 millimetres’ thick. So I’ve just picked some numbers, so that B is sharper than A and C is sharper than B. We apply the same force for each knife on a new bit of cheese. But the area gets smaller for the sharper knives.
The numbers for the areas don’t actually matter that much. But you can check my calculations by thinking about how you would turn the thickness of the knife, one millimetre, into centimetres. And then you’d multiply that by the length of the cheese. The last thing we have to find is the pressure which is calculated by taking the force and dividing it by the area. This gives us 50 newtons per square centimetre for the thickest blade, 100 newtons per square centimetre for the medium blade, and 200 newtons per square centimetre for our thinnest and sharpest blade. So with a sharper knife, if we exert the same force we’ll achieve a much higher pressure, making it easier to cut things.
But what if we want to use the same pressure? What happens to the force? Well, the force is equal to the pressure multiplied by the area. So we use 10 newtons for the thickest blade, five newtons for the medium blade, and only 2.5 newtons for the sharpest one. So to achieve the same cutting pressure, we can use less force if we use a sharper knife. So why are sharper knives more effective at cutting? It’s because sharp knives have smaller contact areas. So with the same force, this translates into a greater pressure.