Da Vinci said that:
-magnitude of friction is independent of macroscopic contact area between the objects
-magnitude of friction does depend on microscopic contact area
-microscopic contact area is proportional to normal force


Does anyone understand the 3 points above? I don't get any one of them at all. Could someone explain?

1 - if you slide a brick along a tabletop, the frictional force's magnitude won't depend on how much of the brick's area touches the table.

Actually, it's not entirely independent - if nothing touches, there's no friction. But if more than a certain minimum touches, you don't have to worry about how much.

2 - if you could look at the bottom of the brick through a microscope while it was sliding along the table, you'd see little rough bits catching on the table and causing the frictional force. These microscopic bits make up the 'microscopic contact area'. Obviously, the more there are, the stronger the frictional force will be.

3 - 'normal force' here is the force pushing the brick into the table, i.e. perpendicular to the table surface. Assuming a normal horizontal table: the vertical component of the total force on the brick would be the 'normal force'.

The greater this force, the more the tiny rough bits will dig into the table. Experiment has found that the frictional force's magnitude is proportional to the normal force.

1 - if you slide a brick along a tabletop, the frictional force's magnitude won't depend on how much of the brick's area touches the table.

Actually, it's not entirely independent - if nothing touches, there's no friction. But if more than a certain minimum touches, you don't have to worry about how much.

2 - if you could look at the bottom of the brick through a microscope while it was sliding along the table, you'd see little rough bits catching on the table and causing the frictional force. These microscopic bits make up the 'microscopic contact area'. Obviously, the more there are, the stronger the frictional force will be.

3 - 'normal force' here is the force pushing the brick into the table, i.e. perpendicular to the table surface. Assuming a normal horizontal table: the vertical component of the total force on the brick would be the 'normal force'.

The greater this force, the more the tiny rough bits will dig into the table. Experiment has found that the frictional force's magnitude is proportional to the normal force.

Sorry, but I still don't get the macroscopic independence and microscopic dependence business. How is it possible? How come there are "2" frictional forces at the same time? Does it matter whether it is macroscopic or microscopic? Ff= (mu) Fn, the frictional force can't be different ...

So if you put a rectangular box on the table and slide it, and then put the same box with the "less contact area" side in contact with the table, that frictional firce won't change, right??

How about a hard-covered book? First, lay it flat and slide horizontally (the entire side is in contact with the table). And then, put the book with the "less contact area" side in contact with the table (this side has pages not touching the table, only the covers are). Will the friction force be the same in each case?

we had an "experiment" in elementary school that demostrated this.

our teacher hooked a wooden brick to a dynamometer(the spring thingy that measures force). she dragged the wooden brick on the table and measured force needed to do this. then she flipped the brick on the side - the smaller surface and dragged it again at aproximately the same speed and measured the same force. i forgot if she actually dragged it or had some electric motor drag it, it doesnt mater

so, the force of friction does not depend on the surface area. it depends only on the weight of the brick and the coefficient of friction between the wood of the brick and the wood of the table - this is the microscopic nature of the two materials.

this is not entirely correct though as some materials do have more friction when the surface is bigger - like rubber - wide car tires etc. they have adhesive properties and so on. so it is only aproximately correct. it is pretty much accurate when hard materials like wood and metal are involved.

also, if huge weight is placed upon very small surfaces - heavy speakers on wooden pointy "legs"(high end speakers usually have pointy legs to reduce vibration heh), and dragged along a rough surface the friction will be greater because the rough surface will actually rip of material off the pointy legs and that will require some extra force..they will probably also scratch the rough surface which is also ripping of material off the rough surface etc..