# 6. Coefficient of Friction ```Experiment 6
The Coefficient of Friction
Equipment:
1 ULI with force probe
1 Inclined plane (see Fig. 6-1)
1 Wooden block
1 Triple beam balance
Masses
Pulley
Objectives:
To measure the coefficients
of static and kinetic friction
between a wooden block and
a wooden plane.
Figure 1- Block on incline plane
Theory
Friction is the force that resists the
relative motion of one surface in contact
with another. There are two types of
friction: static and kinetic. Usually, the
kinetic frictional force is less than the
maximum value of the static frictional
force. The maximum value of static
frictional force is given by fs,max = µ s N
and the kinetic frictional force is given by
fk = µ k N , where µ s is the coefficient of
static friction, µ k is the coefficient of
kinetic friction and N is the normal force.
If f k versus N is graphed, the slope of the
line is µ k for the system. Similarly, if
fs,max versus N is graphed, the slope of
the line is µ s .
The angle of repose is defined as the
angle at which an object just starts to
slide down an inclined plane. If ! is the
angle of repose, it can be shown that
µs = tan! . We will call this method to
determine the static coefficient of friction
the angle of repose method. It can also
be shown that when an object slides
down an incline at constant velocity,
µ k = tan ! .
In this experiment, the frictional force
between a wooden block and the wooden
surface of a horizontal and inclined plane
will be measured, and from these plotted
data, the coefficients of static and kinetic
friction will be obtained.
The angle of repose method will also be
used to determine the coefficient of static
friction. Lastly, the coefficient of kinetic
friction will be determined by a second
method (called constant velocity method)
by noting the angle ! that the block
slides down an incline without
accelerating and then using µ k = tan ! .
Procedure:
1. Turn on the ULI and the computer.
Open the Logger Pro application. Go to
the Experiment/Setup sensors/LabPro1
menu and choose the port which force
probe sensor is plugged in. Go through
list of probes and highlight Dual Range
50N Force Probe.
2. Calibrate the force probe by using the
path Experiment/Calibrate/LabPro1:
Dual Range Force. Click on calibrate
now and follow the directions given to
you on the screen. Use 1/2 kilogram on
the weight hanger for the calibration. Be
sure to use units of force (not mass)
when calibrating the force probe.
to Statistics. This will print the value of
the slope at the bottom of the graph. If
Ffr, the frictional force is proportional to
FN, the normal force (Ffr=µkFN), then the
slope of this line should be the coefficient
of kinetic friction between the two
surfaces. Determine this value from the
graph.
Block on an inclined plane
3. Measure the mass of the wooden
block with the Triple-Beam balance and
calculate its weight in newtons.
4. With plane in the horizontal position,
place 500 grams on the block and pull the
block across the plane at a constant speed
with the force probe. Be sure to pull
horizontally. Note the "bump" at the start
of the graph. This peak represents a
maximum force which can be used to
calculate µs . See fig 6-2 below and
theory section.
5. Highlight the constant force portion of
your run. Determine the mean force. The
force needed to pull the block is your
frictional force and the combined weight
of the block and mass is your normal
force. Note that normal force here is also
used in step 4 to determine µs .
6. Repeat steps 4 & 5, adding 500 grams
each time until a total of 3000 grams has
been added to the block. Record the
frictional and normal forces needed for
each trial.
7. Plot a graph of the frictional force vs.
the normal force using Graphical
Analysis, with the frictional force on the
Y axis and the normal force on the X
axis. Plot a "best fit line" between the
points by pulling down the Graph menu
to Regression line. To obtain the slope
of this line, pull down the Graph menu
8. Calculate the force needed to pull the
block up a plane inclined to 300 at a
constant speed when loaded with 500
grams. Draw a force diagram labeling all
the forces acting on the block as it moves
up the inclined plane. Use the coefficient
9. Measure the force needed to pull the
block up the plane (same angle as part 8)
at a constant speed. If there is a large
difference between the calculated and the
experimental values, check the
calculations carefully. (Common
mistakes: Neglecting the mass of the
block and improper force diagrams)
Calculate the percentage difference
between this value and the calculated
value.
Angle of repose method
10. Add 500 g to block. Find the
coefficient of static friction by slowly
raising the incline plane until the block
just starts to slide. Note the angle and use
µs = tan! . Repeat with 1000g total
Constant Velocity Method
11. Add 500g to block. Find kinetic
coefficient of friction by tilting the
inclined plane and noting the angle at
which the block slides at a constant
Experiment 6
The Coefficient of Friction
speed. You should have to tap the block
in order to get it started. Use µk = tan ! .
Add a total of 1000g to block and repeat
this step.
Questions:
1. Show that µk=tanθ for the constant
velocity method. Include a diagram of all
the forces on the block as it slides down
the inclined plane.
2. When the mass on the block is was
doubled, what happens to the angle of
repose? Were your results as expected.
Explain.
3. Why was it necessary to tap the block
to get it started in section 11 of the lab?
4. Why can anti-lock brakes stop a car in
a shorter distance than regular brakes?
Force (Newtons)
5. Which method do you think would
yield the more accurate value for the
coefficient of kinetic friction and why?
Time (sec)
figure 6-2
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