eli5 what is the logical explanation that the smaller the surface the higher the pressure?

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I mean I know that it’s a fact but why?

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Pressure is just a way of measuring how widely distributed a force is. If the total amount of force stays the same but the area the force is applied to shrinks, the force-to-area ratio (a.k.a. pressure) increases.

Imagine carrying a bag of sand. It’s heavy, isn’t it?

Imagine two people carrying a bag of sand. Not as heavy, is it?

Imagine four people splitting the sand. Each person’s carrying a lot less weight, right?

Pressure happens when you apply force across a surface. If the surface is big, the force is spread out and “shared” by everything the surface touches, so the pressure is lower. If the surface is small, the force is NOT spread out as much thus the pressure is higher. The smaller the surface, the higher the pressure.

Pressure is just force by a surface area : p = F / S

When keeping the same force, if S gets smaller, p increases (because S is in the denominator).

The pressure is simply the force over a specific area.

If I have two legs holding weight, each leg only needs to hold half the weight.

If two square inches of floor are experiencing a force, each one only gets half of that force.

So by reducing the area of contact, we concentrate the force down and so the pressure on that smaller area is higher.

you can place a 10lbs block on your hand and nothing happens. you’re just holding it. place that 10lbs on a needle and now you are bleeding.

Pressure is how much force you put on a given area. Let’s assume we use square centimeters.

If I put a dice (let’s assume the dice is perfectly one centimeter per side) on the floor and I step on it, my 75 kg of weight will give a pressure of 75kg/square centimeter, on that dice.

If I put more dices, let’s say 5rows of dices, 2 dices wide, and step on it, my weight will go on all the 10 dices, each dice will receive 7,5 kg of my weight, therefore it will receive a pressure of 7.5 kg/square cm.

You can “try at home”. Stepping on a singe dice is painful, because all the weight is concentrated in a little spot therefore that part of your foot gets a lot of pressure. And pressure is what hurts you in that case.

Extreme opposite example, you can lay down on a carpet of nails, uninjured, because you distribute the weight. the more you distribute, the less force for each nail, therefore less pressure each nail can do to hurt you. (Don’t try at home as nails are quite expensive, you need some thousand and it takes hours to build).

Pressure is a measure of how much force IS FOCUSED onto a given spot.