Why does an increase in surface area lead to a reduction in pressure?

[Kaushik]

From what I read on the internet I found that increase in surface area that is in contact is offset by the reduction in pressure. What exactly does it mean?
This is what I understood from the it (but my understanding might be absurd ): does reduction in pressure mean that the "hills" or "irregularities" that are in contact become more pointy? As there is less pressure they don't feel pressed so that there is no reason for them to flatten?
If not please explain it in the molecular scale if possible.
Please and Thank You!

 

[jackwhirl]

Are you familiar with the relationship between pressure and area?

 

[Kaushik]

Are you familiar with the relationship between pressure and area?

Yes! Pressure is inversely proportional to area.
$P = F/A$

 

[jackwhirl]

Right, so picture an object, say a hardcover book resting on a surface, like a table.

The book has an amount of mass, and gravity causes the book to press against the table with a force proportional to that mass. That force, divided by the area of the book in contact with the table gives pressure according to the equation you've just given.

Now, if you want to move the book across the table, you've got to press on it with enough force to overcome the static friction holding the book in place. This amount of force depends on the mass of the book and the materials of the book and table. It does not depend on the surface area of the book in contact with the table. So, for example, the force required to move the book should be the same whether it is open or closed, provided both front and back book covers are made of the same material.

Opening the book doubles the surface area in contact with the table, but does not change the mass of the book. The normal force remains the same, and the pressure is halved, now being spread over double the area.

Does that all make sense?

 

[Kaushik]

Right, so picture an object, say a hardcover book resting on a surface, like a table.

The book has an amount of mass, and gravity causes the book to press against the table with a force proportional to that mass. That force, divided by the area of the book in contact with the table gives pressure according to the equation you've just given.

Now, if you want to move the book across the table, you've got to press on it with enough force to overcome the static friction holding the book in place. This amount of force depends on the mass of the book and the materials of the book and table. It does not depend on the surface area of the book in contact with the table. So, for example, the force required to move the book should be the same whether it is open or closed, provided both front and back book covers are made of the same material.

Opening the book doubles the surface area in contact with the table, but does not change the mass of the book. The normal force remains the same, and the pressure is halved, now being spread over double the area.

Does that all make sense?

But when the surface area in contact increases there are more irregularities kind of interlocked. So more force would require to overcome it.

You say that the pressure is halved, but how does it offset the increase in area?

Let me consider the same book you mentioned about. When I open the pages, more surface area is in contact. So when I try pushing it, due to more surface area in contact, there are more number of irregularities that opposes the force applied by me and hence prevents the book from moving (upto a certain limit). When I try moving the same book when it is closed, the surface area in contact is relatively less. Hence, there are less interlockings between the book and the surface, due to which the forces that is applied by the surface irregularities on the book is less as compared to when book was open.

Now when the surface area increases it results in increase in interlocking as mentioned above.
So where Am I going wrong? Is it the 'PRESSURE' part that I am not understanding?

 

[A.T.]

You say that the pressure is halved, but how does it offset the increase in area?

With less pressure each irregularity is pressed together less, so the interlocking is easier to overcome.

Consider a simple contact area like this for both bodies in contact: /\/\/\/\
Compute the horizontal force needed to slide the upper body of a given weight up the slopes.
Does it depend on the number of teeth?

 

[jackwhirl]

But when the surface area in contact increases there are more irregularities kind of interlocked. So more force would require to overcome it.

This does not follow.

I understand it is a little counter intuitive. Think of those irregularities as 'opportunities' where interlocking could occur. They are proportional to the area. The rate at which interlocking does occur is proportional to the pressure, which as we've covered is inversely proportional to area. So you can multiply by the area and then divide by the area, but it's easier to just ignore it.