Pressure Distribution on Split Block: Does Total Pressure Change on Ground?

[nilic1]

Homework Statement

A block exerts a pressure on the ground. If the block is split vertically into two halves does the total pressure on the ground increase, decrease or remain the same?

Homework Equations

Pressure = Force/Area

The Attempt at a Solution

I think that it doubles but I am not sure. I am confused because the total area of contact remains the same and the total weight remains the same. Can you work out the total pressure using total pressure = total force/total area once they are split up or do you have to work them out individually?

 

[Orodruin]

If you just analyse one of the halves, what happens to the weight? What happens to the area? As a consequence, what happens to the pressure? (Force/area)

 

[nilic1]

Each half will have half the weight, so half the force and half the area and so the pressure is equal to that of the whole block. So I think I am right to say that by splitting it up vertically even though they might lie side by side touching each other, the overall pressure on the ground still doubles compared to when the block was whole. In short once split you have to work them separately and not continue treating them as one whole object.

 

[Faiq]

But having a practical look at the problem defies the abovementioned logic. Take something in your hand. Feel the pressure it exerts. Now cut it in half the pressure will remain same

 

[Orodruin]

So I think I am right to say that by splitting it up vertically even though they might lie side by side touching each other, the overall pressure on the ground still doubles compared to when the block was whole. In short once split you have to work them separately and not continue treating them as one whole object.

No, this is wrong. Pressure is not a property you add up from different parts. It is a quantity you compute for each part of a surface.

 

[haruspex]

the overall pressure on the ground still doubles

You just proved the pressure stays the same. It seems to me that you are sometimes confusing pressure with force, e.g. thinking that two lots of the same pressure means double the pressure. The confusion may come partly from the use of the expression "total pressure" in the question. That suggests adding pressures, but you can only add pressures exerted on the same patch of surface. Two blocks placed side by side cannot be said to exert a total pressure. An average pressure, perhaps.

Take something in your hand. Feel the pressure it exerts.

That's not so easy. You would be too aware of the total weight to be able to judge in terms of pressures.

 

[CWatters]

Consider cutting the block into 1,000,000 bits. Do you think the pressure will be 1,000,000 times greater?

 

[nilic1]

So should the answer be ... total pressure acting remains the same?

 

[haruspex]

So should the answer be ... total pressure acting remains the same?

I would say the pressure remains the same. As I wrote, I don't think "total pressure" means anything in this context. It would be meaningful if we were discussing adding pressures onto the same region.