Question

Why does a knife have a sharp edge, and a needle has a sharp tip?

Answer 1

Pressure from a given force is inversely proportional to the contact area, so smaller areas produce higher pressure. Applying a force to a 1 mm² area results in 100 times more pressure than applying the same force to a 1 cm². Knife edges and needle tips have a narrow contact area. A sharp needle can puncture the skin with minimal force, while a finger cannot do so.