Scott Gardner wrote:
> The coefficient of friction
> between to surfaces does not rely on the amount of surface area in
> contact, only on the weight of the object being moved.
Technically, it does matter, it's just that it is cancelled
out in the math.
The holding power of an object is technically the coefficient
of friction times the number of square units of contact area
times the weight distribution, which is the weight divided by
the number of square units of contact area. Those two terms
cancel out, leaving weight and coefficient.
> static friction is like a wheel rolling across the floor--no
> points on the floor and wheel ever
> actually slide relative to one another, but there's still friction,
> also known as rolling resistance).
Static friction and rolling resistance are actually very
different.
Static friction is the maximum coefficient of friction that
can be developed before the object "breaks free". The quickest
way to measure it is to make a ramp of one surface and an
object of the other. Tilt the ramp up slowly until the object
slips, take the tangent of the angle, that's the coefficient
of friction.
Static friction is always larger than dynamic friction, the
simple explanation is that it takes less effort to KEEP something
sliding than to START it sliding. This is why if you brake to
a stop with a steady foot, the car will come to a slow stop and
then pinch right at the end to come to an unpleasant jerky stop.
(new drivers learn quickly after the passengers complain)
To relate to our "ramp", also notice that once the object
breaks free and starts to slide, it's resistance drops from the
static value to the dynamic value, which is why it slides off
in a real hurry. If you try to "catch" the object by lessening
the ramp angle really quickly, you'll notice you have to bring
the angle way back to much less steep than the object was actually
holding before.
Another term for this is "stiction", which you've all probably
noticed when doing things like turning wheels or crankshafts
by hand. Once the initial "snap" of motion begins, it goes easy.
Typical values are (materials hidden to protect the innocent)
0.55 for static and 0.47 for dynamic. This means if you put a block
on a surface that has enough mass to make 100N of vertical force,
it will take 55N of horizontal force to start it moving but only
47N of force to KEEP it moving.
> Here's his question. If the coefficient of friction is only
> dependent on the two surfaces in question and the weight of the
> object being moved, and not the amount of surface area in contact
> with the ground, why do drag racers use such wide tires?
The coefficient of friction is a fairly inexact measure
anyways, since it depends on so many things.
One of the key relative things it depends on is PERFECTLY
SMOOTH SURFACES. It only takes into account force transferred
between objects contacting only perpendicular to the force
applied.
In the real world, this isn't true. Tire rubber will deform
and "grip" into the pavement such that force is actually
applied to vertical surfaces of the pavement.
Think of climbing a smooth wall, where you can only use friction. If
the wall is anywhere near vertical it becomes impossible. Compare this
to
a rough rock cliff that you can hook your fingers into and get enough
grip to climb even if it is slightly MORE steep than vertical
(overhang).
Back to the drag car, this is also why spinning the tires loses
races. When the tires are sticking, you can apply the torque up
to the weight of your car times the static coefficient. Once you
lose it, you only get the weight times the dynamic coefficient which
again is always less. One you lose traction, you have to back way
off before you'll get it back.
This is also how antilock brakes (or really good brake technique) will
stop quicker than a four wheel lockup, same effect backwards.
--
Trevor Boicey
Ottawa, Canada
tboicey@brit.ca
http://www.brit.ca/~tboicey/
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