Static vs. kinetic frictional force

[bezgin]

Why is the kinetic frictional force always less than the static?

One other question, when a car moves along a curved road, the direction of the static frictional force is toward the center. But we were told, since the elemantary school, that the frictional force is always at the opposite direction of velocity. I'm really confused.

 

[arildno]

1)"Why is the kinetic frictional force always less than the static?"
Assume it was greater.
Then, assume that you push with a force equal to maximal static force.
Static force then gives way to kinetic; the kinetic force, being oppositely directed of the pushing force, but, due to our assumption GREATER than the pushing force, would start accelerating the object TOWARDS you, rather than reducing its acceleration AWAY from you.
Get it?
2) Since we're talking static friction, it opposes the direction the object would TEND to move in if the static friction wasn't present.
Any object starting to move in a circular motion would TEND to move in the direction of increasing radius, if it weren't a centripetal force (acting inwards) holding it in place.

 

[Doc Al]

Why is the kinetic frictional force always less than the static?

Interesting question. Would having a static friction less than the kinetic friction even make sense? Say the maximum static friction was 5 N, but the kinetic friction was 10 N. What's the minimum force needed to move the thing? 5 N won't do. But neither would 6 N... the kinetic friction would stop you dead! You'd need at least 10 N to get it moving. But we'd call that the static friction.

One other question, when a car moves along a curved road, the direction of the static frictional force is toward the center. But we were told, since the elemantary school, that the frictional force is always at the opposite direction of velocity. I'm really confused.

It's the relative velocity between the surfaces that counts. As long as the tires aren't skidding, the patch of tire in contact with the road has zero speed with respect to the road. But a better way to say it is that friction always acts to oppose slipping between surfaces. And note that for static friction, there is no velocity between the surfaces.

(arildno beat me again! )

 

[bezgin]

I'd thought the static friction = kinetic friction. Why isn't that the case?

Another thing, they say the static frictional force, in curved roads, "takes the place" of the centripetal force, meaning the static frictional force AND the normal force * sinx (x being the angle of the road's incline) ACTS AS the centripetal force. What does it mean? It's the same thing when you rotate an object tied to the end of a rope - the tension force in the rope ACTS as the centripetal force.

 

[Doc Al]

I'd thought the static friction = kinetic friction. Why isn't that the case?

When there is friction between two surfaces those surfaces aren't really smooth, but have jagged peaks. In the static case, those peaks come in contact and form relatively strong bonds. But in the kinetic case, the relative motion gives less time for those stronger bonds to form. So the kinetic friction is weaker.

Another thing, they say the static frictional force, in curved roads, "takes the place" of the centripetal force, meaning the static frictional force AND the normal force * sinx (x being the angle of the road's incline) ACTS AS the centripetal force. What does it mean? It's the same thing when you rotate an object tied to the end of a rope - the tension force in the rope ACTS as the centripetal force.

Don't think of "centripetal force" as a kind of force like gravity, or friction, or tension in a string. The word "centripetal" just means "towards the center". (Another term often used is "radial force".) Whenever something is moving in a circle there must be some force pulling it towards the center.

In your examples: For a car going around a curve, the centripetal force is provided by friction and the normal force (if the road is banked). For something twirling at the end of a rope, the tension in the rope provides the centripetal force. Those forces don't "take the place of" the centripetal force, they are the centripetal force!

 

[Clausius2]

One other question, when a car moves along a curved road, the direction of the static frictional force is toward the center. But we were told, since the elemantary school, that the frictional force is always at the opposite direction of velocity. I'm really confused.

Your first question seems to be clarified, but the second doesn't. In fact, there is a frictional force in the same direction of movement of the car in the curve, owing to the proper friction of both surface. Moreover, an expertise car driver can use this effect for not being pushed out of the curve when he's running at high speed.

The resulting fricton coefficient is the sum of the radial friction coefficient $$\mu_r$$ pointing towards the center of the curve, and the circumferential friction $$\mu_{\theta}$$ pointing towards the contrary way of the car direction. Then, the effective friction coefficient is:

$$\mu=\sqrt{\mu_r^2+\mu_{\theta}^2}$$

Some expertise car driver would accelerate a bit when he's turning a curve. That increases the $$\mu_{\theta}$$ coefficient and also the total grip force $$\mu$$.

 

[rcgldr]

Why is the kinetic frictional force always less than the static?

It isn't in all cases. There are a few exceptions, like certain types of Teflon on Teflon, where they are essentially the same (.04 for Kinetic and Static). There's a pratical use for such surfaces, no "jerk".

Further, by combining special surfaces with liquid lubricants on "slideways", you can end up with more kinetic than static "friction", but what this really means is that kinetic friction increases with speed, and is at it's minimum when there's no motion on the slideway. As I understand it, fluid is force injected into the slideway, so there's always a thin film present. The fluid creates a drag that increases with speed, so the result is a very controllable motion.

http://www.skc-technik.de/e/e_prod_eigensch.html (Click on the anti-stick-slip behavior button).

and

http://www.hjlube.com/english/product_1(6).htm

The comments made about more kinetic than static friction is what I was referring to above,
$$F_v > F_0$$ as long as $$v \neq 0$$

 

[rcgldr]

One other question, when a car moves along a curved road, the direction of the static frictional force is toward the center. But we were told, since the elemantary school, that the frictional force is always at the opposite direction of velocity.

What you're missing here is that kinetic frictional force is always opposing velocity.

If you push sideways on a car, after everything stabilizes, there's no motion. The tires exert a sideways force on the pavement, and the pavement reacts with an equal and opposite force. It's the pavement's force that causes a car to corner (it's the only inwards force).

Both surfaces flex whenever there is a force, but most of the flexing is at near the contact patch of the tire. When a tire is rolling and generating a cornering force, the area near the contact patch flexes. There will be a difference in the direction the tire is pointed, and the direction that the tire is actually moving. This difference is called slip angle, although it's mostly due to the tire flexing near and at the contact patch. There's also some slippage at the edges of the contact patch. As slip angle increases, conering force increases up to a maximum, then it starts decreasing as excessive slippage occurs at the contact point.

Exceed the slip angle of maximum grip at the rear and a car spins, exceed it at the front and a car plows.