THE CALCULATION OF THE COEFFICIENT OF FRICTION
in a laboratory setting
Nienke Adamse
2/10/2010
ABSTRACT
The purpose of this experiment was to determine the coefficient of friction by two methods:
1. Pulling a friction block with a newton meter over various surfaces. With the equation Ffr = μk FN, the
measured friction force and the weight would give the value of the kinetic friction coefficient.
These trials resulted in a larger kinetic friction coefficient when pulling the block with the sandpaper
and the glass on the contact side than those with the wood-on-wood surface, the block on its side and
the wood/carpet surface.
Calculating the static friction coefficient, the newton meter was read at the moment the block started to
move, this force was larger than the force needed to maintain motion with a constant speed; therefore
the static friction coefficient was also larger.
2. Using an inclining surface to the point where the block started sliding, the angle at which the plane
was held at that moment was measured. With the equations tanθ= h/b
the limiting angle of repose was calculated, the value of the friction coefficient μ. The static friction
coefficient here came close to the static friction coefficient found in the first method.
INTRODUCTION
This experiment's objectives are to study the concept of friction by measuring the friction forces (static
and kinetic) using two different methods.
Wherever we are, we experiment friction. Without friction, we cannot walk or drive a car. Friction
forces are considered non-conservative forces: The friction forces always work against you. The force
necessary to overcome friction depends on the nature of the materials, their roughness or smoothness.
It also depends on the normal force but not on the area of contact or on the speed of the motion. When
graphing the friction forces against the weight of the object that feels the friction, the slope of the graph
represents the friction coefficient. Thus, the friction coefficient is proportional to the normal force
(N=mg on a horizontal surface and N=mg cosθ on an inclined surface).The equation with which we
calculate the friction coefficient is Ffr = μk FN.
The experiments should show a larger friction coefficient when using rough contact surfaces and a
smaller friction coefficient when using smoother surfaces. We should also find a larger static friction
coefficient than a kinetic friction coefficient because we need to use more force to start sliding the
object from rest.
The static friction coefficient we will find in the second method (on the inclined plane) should be the
same static friction coefficient as the one we find in method 1 (wood on wood).
1
MATERIALS AND METHODS
Materials needed:







Ramp board: 30” long, 8” wide
1 Can of soft drink or item of similar weight
1 Friction block set-PK
1 Protractor
1 Scale-Spring-500-g
1 Tape measure, 1.5-m
1 Tape measure, 3-m
1. A board of 30” by 8” horizontal was placed on a table, taped down to prevent sliding. The wooden
block plus the extra weight on top of it (a jar with paint) were weighed. The newton meter was attached
to one of the wooden blocks with an eye hook. The Newton meter with the block was pulled with a
constant speed over the board; the force was measured by the reading on the Newton meter. This trial
was repeated three times. The average value was calculated and written in the results table. This was
the force of kinetic friction.
2. In this step the meter was read at the point where the block just started moving; this trial was
repeated 3 times for 3 values. And then the average value was calculated. This was the force of static
friction.
3. Steps 1 and 2 were repeated, but this time the wooden block laid on its long side. The average kinetic
and static force values were calculated and noted.
4. Steps 1 and 2 were repeated for various surfaces. A block with sandpaper attached on one side and
glass on the other was used. This way the various surfaces being tested were: sandpaper-surfaced block
on wood, glass-surfaced block on wood and woodblock on carpet.
5. The kinetic friction coefficients and the static friction coefficients for all trials were calculated with
the equation Ffr (max) = μs/kFN
μs/k= Ffr/FN(mg)
6. One side of the board was lifted up with the wooden block and weight on it. The height and the angle
it made with the table surface at the point where the block started sliding down were measured. This
experiment was repeated three times and the values were noted in the table. The friction coefficient was
calculated by taking tanθ and by calculating height/base of the triangle that the board formed with the
table surface.
2
OBSERVATIONS
Experiment 1: wood on wood
When pulling the block over the board the Newton meter showed a higher reading at the start and a
lower reading when the block was moving. The readings were not very accurate because of the
difficulty of pulling and reading the values at the same time. At each trial the readings were different.
The board was quite short (30”), and there was little time to do the readings. Pulling the block faster
did not change the readings much.
Experiment 2: wood on wood with smaller contact surface (block sideways)
The beginning pulling force was smaller than in experiment 1. When the block was moving with
constant speed, the force was a bit larger than in experiment 1.
Experiment 3: The block with the sandpaper and the glass attached to it is heavier than the plain
wooden block. The forces measured are greater than in experiment 1 and 2. The static friction forces do
not differ much from the kinetic friction forces for the glass surfaces. The static friction forces of the
sandpaper experiment do differ from the kinetic friction forces. The static friction forces of the carpet
surface are much greater than the kinetic friction forces.
Experiment 4: The measurements in this experiment were not very accurate: it was difficult to measure
the angle of the board and keep the board steady at the moment of sliding. There was much difference
in the angles measured and therefore in the friction coefficient calculated.
RESULTS
DATA TABLE 1: Mass of block: 0.43 Kg Weight 4.24 N
Flat Board
Force of Kinetic
Force of Static
Friction, N
Friction, N
Trial 1
0.8
1.2
Trial 2
0.7
1.3
Trial 3
0.7
1.4
Average
0.7
1.3
Average kinetic friction coefficient:μ= 0.17 Average static friction coefficient: μ= 0.30
DATA TABLE 2: Mass of block: _0.43_ Kg Weight _4.24 N
Flat Board –
Force of Kinetic
Force of Static
Block Sideways
Friction, N
Friction, N
Trial 1
0.8
1.1
Trial 2
0.9
1.0
Trial 3
0.8
1.0
Average
0.8
1.0
3
Average kinetic friction coefficient:μ= 0.18 Average static friction coefficient: μ= 0.24
DATA TABLE 3: Weight= 4.59 N
Surfaces Tried:
Force of Kinetic
Glass Surface
Friction, N
Trial 1
1.5
Trial 2
1.6
Trial 3
1.4
Average
1.5
Force of Static
Friction, N
1.6
1.6
1.5
1.6
Average kinetic friction coefficient:μ= 0.33 Average static friction coefficient: μ= 0.34
DATA TABLE 3a:Weight= 4.59 N
Surfaces Tried:
Force of Kinetic
Sandpaper
Friction, N
Trial 1
2.3
Trial 2
2.1
Trial 3
2.2
Average
2.2
Force of Static
Friction, N
2.5
2.7
2.6
2.6
Average kinetic friction coefficient:μ= 0.48 Average static friction coefficient: μ= 0.57
DATA TABLE 3b: weight 4.24 N
Surfaces Tried:
Wood on Carpet
Trial 1
Trial 2
Trial 3
Average
Force of Kinetic
Friction, N
0.9
0.8
0.8
0.8
Force of Static
Friction, N
2.4
2.1
2.2
2.2
Average kinetic friction coefficient:μ= 0.19 Average static friction coefficient: μ= 0.52
DATA TABLE 4:
Height, cm
Trial 1
Trial 2
Trial 3
Average
26.0
27.0
25.5
26.2
Base Length,
cm
66.5
66.0
67.0
66.5
4
θ
20
21
19
20
max
μs
tan@ 0.36
0.38
0.34
0.36
EXPLANATION
The static friction coefficients of all trials are larger than the kinetic friction coefficients
because there is a greater force needed to make the block start sliding than the force to pull it
with a constant speed. This is a logical outcome since the theory about static friction states
that the static friction force is larger than the kinetic friction force: “static friction is the force
between two stationary objects that resist their relative motion. Static friction is maximal when
f(s)=μ(s)N, where μ(s) is the coefficient of static friction, μ(s) is always greater than μ(k.).”
(Pollock, 2001, Unit: The Forces of Friction)
The friction coefficients (both static and kinetic) of rough surfaces like sandpaper are larger
than the coefficients of wood on wood (see table 1and 3a). The friction coefficients of glass
are also larger than those of wood on wood. These results are plausible because the friction
depends on the normal force of the object. The friction block with the sandpaper and glass
was heavier than the plain wooden block. Thus the normal force was larger. The contact
surface area has no influence on the friction coefficients (see table 2). This is a logical result
because the friction only depends slightly on the shape and size of the object. The smooth
surface of glass did result in a smaller friction coefficient than the sandpaper surface (see
table 3). This is justifiable because friction varies with the texture of the contact surfaces.
Sandpaper has a coarser texture than glass. The carpet on wood surface did not result in a
much larger kinetic friction coefficient from the plain wood-on wood experiment, while the
static friction coefficient of carpet on wood did increase (see table 3b). This is credible when
the resistance to motion for the carpet surface is larger than that of wood.
The limiting angle of repose and the friction coefficient that could be derived from it showed a
nearly similar static friction coefficient than the one found in table 1 (see table 4). The method
with the inclined plane is a good method to determine static coefficients of materials.
The variations in measurements in all trials and the difference between the static friction
coefficients of experiment 1 and experiment 4 are due to the inaccuracy of measurements.
The Newton meter readings were executed while in motion and the values of readings of the
angle between board and table surface were not very precise.
CONCLUSION
This lab has increased my understanding and knowledge of friction forces and friction
coefficient. It was possible to measure and compare the friction coefficients of various
surfaces and, although the measurements were not very precise, I was able to calculate the
friction coefficients by using two different methods: by measuring the friction forces directly
with a Newton meter in experiments 1-3, and by determining the limiting angle of repose and
thus the friction coefficient in experiment 4.
5
REFERENCES
Jeschofnig, P. (2008).Physics I: Lab Manual of Experiments for the Independent Study of
Physics.Englewood, CO: Hands-On Labs, Inc.
Pollock, S. (2001). Dynamics. The Forces of Friction. Retrieved on February 14, 2010 from
www.Thinkwell.com.
6