Pressure: Definition
We are notoriously casual about the distinction between pressure and force. This is partly because they are in fact related but at the same time distinctly different. A reasonable illustration of the difference between the concepts can be explored with a sharp pencil. If you take the eraser end and push on your fingertip what you experience is both a force and a pressure. If you reverse the pencil and push wiht the same 'effort' on your fingertip with the sharp end you experience the same force but a very different pressure.
Pressure = Force/Area
The core idea is that the same force in different settings can produce dramatically different pressures.
We can also see why it is easy to confuse the ideas of pressure and force. Because of the way pressure is defined increasing the force usually leads to increasing the pressure. The effect of the area on the pressure is more hidden in our experience.
When you go to cut a slice of some vegetable the edge of a sharp knife has less area which increases the pressure and cuts the vegetable. A dull knife has a 'wider' edge and therefore less pressure unless you press harder (more force)to get a similar effect.
Martial artists require a significant force to stop themselves when they are thrown on the mat. By organizing their bodies to increase the area that contacts the floor they reduce the pressure on their bodies and minimize injuries.
Social pressure is not formally part of physics but it operates much the same way. 5 people suggesting I should do something for the good of the group feels like a fair bit of social pressure. Me suggesting that a group of 5 people do something does not feel like so much social pressure. I'll leave it to you to consider what is the force and what is the area in this analogy.
