# Sliding Friction

## Laboratory Exercise no. 9

"Laboratory Manual
for General Physics", Bernard D.Kern. Part One: Mechanics, Heat and
Sound, Revised Printing, 1996 Copyright C 1968, 1971, 1996 by Bernard Donald
Kern

### Discussion

An object which is made of wood, when sliding on another object of wood,
has its motion retarded by a frictional force. It is generally true that
the frictional force is

- proportional to the force
*N* which pushes the two objects together;
- independent of the area of contact area;

- mostly independent of the velocity;

- such that the frictional force is smaller after the motion has started
than it is when the two objects are both at rest.

Consider a wooden block which is being pulled with constant velocity
by a horizontal force *F* applied along a horizontal plane; i.e.,
with zero acceleration, *a* = 0. The vertical reaction force on the
block is *N*. Then by Newton's Second Law,

where
is a proportionality constant called the coefficient of sliding friction.
In this particular example, the reaction force N is equal and opposite
to the weight W of the block, and

The coefficient may be obtained directly by measuring the two forces.

If the plane is inclined, as in our case, see the diagran above,
then a component F of the weight W acts to move the block
and the other component
presses the block to the plane. Since the block does not move perpendicularly
to the plane (the acceleration is zero),
. If the block is made to slide with constant velocity by the adjustment
of the angle of inclination:

We see the interesting result that the coefficient of friction can be
measured in terms of the angle, and with no dependence upon the size and
mass of the block itself.

The static frictional forces are always larger than the kinetic frictional
forces and not so reproducible, experimentally. We can use Eqn.4, but assume
that the block is at rest. As angle
is increased, an angle will be reached at which the block suddenly starts
to slip. At this point the component,
, has become greater than the static frictional force,
, and it is difficult to determine by how much. However, by use of the
concept of an inequality, we can rewrite Eqn.6 using the "equal to
or greater than" and "less than or equal" symbols
and
:

This gives a measured upper limit limit to the coeficient of static
friction,

Run
Virtual Java Experiment "Sliding Frction"

Return to PHY211 Homepage