Is friction still a linear relationship at high pressures?

[lavalamp]

My questions is reasonably simple and requires no difficult equations, just a lot of puzzling over (for me at least).

OK, Consider a rubber mat of mass 10Kg and an area of 1m^2 in contact with the ground. The maximum frictional force that exists between the mat and the ground is force F.

Now if you were to fold the mat exactly in half, so that the area in contact with the ground is now 0.5m^2 but everything else stays equal, what is the new frictional force that exists between the mat and the ground? Is it 2F, is it 0.5F or is it still F?

 

[Doc]

Think about it. Double the force per area of the mat. I remember doing this experiment and it doesn't change when you reduce the contact area. We used cement blocks on side, edge, and end. NO CHANGE in the force required to get the block to slide, and NO CHANGE in the force required to maintain sliding.

 

[jimmy p]

Couldnt have put it better myself...all you are doing is doubling the force on half the area. There..i suppose there wasnt much point in my posting this except to boost my posts HAHA

 

[lavalamp]

That's what I thought but upon questioning my teacher wasn't too sure about it.

This then leads me on to another point, why do race cars (and various road cars) have wide tyres? As you both put above the width of the tyres will not affect the friction.
Is it to disperse water when it's raining, or to reduce tyre wear, a combination of both or perhaps something else?

 

[jimmy p]

OK this i am not too sure about but i will give it my best shot. Actually, first i think it is how the tyre tread is set out is how water is removed (on bikes, the wheel has rounded sides to cut through surface water).

Cars have wide tyres to distribute the weight of the car more evenly ( i think ) and save any damage if the tyres were thin. With race-cars, becauese they are so low to the ground and travel at such high speeds, it is important there is a lot of surface area touching the ground. Friction is reduced on race-car tyres because they use slicks on dry surfaces.

Maybe i should review my first answer. Because there is the same mass, then it would spread over a larger surface area the friction, F would be the same but spread over a large area. If the surface area is small, then F is the same but spread over a smaller area...

Garn i have confused my self.. If i have helped, send my a present but if I am wrong, send me an email-bomb!

 

[jimmy p]

Lol i forgot. ps, i love your signature..'dont worry its inflammable'

 

[lavalamp]

Friction is reduced on race-car tyres because they use slicks on dry surfaces.

I fail to see why, just because they use slick tyres, this reduces friction. I also don't see what the advantage of using slick tyres is in the first place.

Because there is the same mass, then it would spread over a larger surface area the friction, F would be the same but spread over a large area. If the surface area is small, then F is the same but spread over a smaller area...

I think you confused me here as well.

By the way, I took that from the simpsons. Dr. Nick said it just before some NO2 tanks exploded in his surgery.

"What? Inflammable means Flammable. Ach, what a country!"

 

[Njorl]

Race cars don't have too take road surface quality and rain into account. This allows them to use "slicks". The advantage of wide slicks is that there is less pressure on the surface touching the road. Pressure on the surface increases wear. Also, when a treaded tire's surface touches the road, it compresses and deforms. This interferes with adhesion to the road, and causes the tires to heat up and wear faster.

Njorl

 

[lavalamp]

So less pressure = less wear. Seems simple enough.
Although would wider tires cause more, for want of a better word, drag on the road surface?

 

[KLscilevothma]

Friction is independent of the area of contact between two surfaces. It depends on the nature of the two surfaces and the normal reaction between them instead.

Friction = coefficient of friction * normal reaction

where coefficient of friction depends on the nature of the surfaces.

Reducing the area of contact doesn't change the coefficient of friction between two surfaces, thus the friction remains unchanged.

 

[lavalamp]

I know the equation F = [mu] R, but it was just whether the area incontact with the ground changed [mu]. I guess not.

 

[Soveraign]

I'm surprised nobody has mentioned this. Tires generally do not follow the regular friction relation. When tires heat up, they get sticky (very slightly). This is why dragsters burn out before a run, and also why you see race cars weave back and forth when there is a caution on the track and they must slow down.

Since the tire is sticky, the force due to stickiness would be a function of the area of the tire touching the road. So in effect, the total "adhesive" force of a tire to the road is:

F = friction + stickiness

where the stickiness is something like C*A where C itself is a function of temperature and A is the area of contact.

Of course you don't run on flat tires though since there is also a rolling resistance when a tire is not perfectly rigid. Thus the big game about adjusting tire pressures to get the "best" performance you can get..

 

[turin]

Originally posted by lavalamp
I know the equation F = [mu] R, but it was just whether the area incontact with the ground changed [mu]. I guess not.

Like every other linear equation in Physics that I can think of, this is an approximation. Of course our linear equations are not exact representations. There is a limited range over which the equation is valid. I don't know specifically about the race car, but, in general, if you press two objects together hard enough, they will fuse, and the precious linear relation melts away. There is also probably a compression of this relationship for certain materials (like tyre stuff). If you think of the friction in terms of pressure, then you get a force per area, multiplied by the area of contact. If the force per area is large enough, it most certainly can change the coefficient, and I'm imagining for the worse. Spreading the weight of the car over a greater area reduces the pressure and alleviates the compression problem. This is just a guess, though.