Addis Ababa University

College of Natural and Computational Sciences

Department of Physics

3. Calculating Coefficients of Friction

Name I.D. Number

Nathan Girma UGR/5650/14
Nathan Mesfin UGR/0534/14
Nathnael Alemu UGR/8888/14
Nathnael Efrem UGR/9074/14

Date of Experiment: 26th of May 2022

Date of Submission: 2nd of June 2022

Name of Instructor:
Name of Lab Assistant:
 Table of Contents
Table of Contents .....................................................................................................1
Abstract ......................................................................................................................2
Objective ...................................................................................................................2
Introduction/Theory ................................................................................................2
Apparatus Used ........................................................................................................3
Procedure ..................................................................................................................3
Data/Results ..............................................................................................................4
Table 1.1: Static Friction........................................................................................................................ 4
Table 1.2: Kinetic Friction...................................................................................................................... 4

Analysis/Discussion ..................................................................................................5
Static Friction .......................................................................................................................................... 5
Table 1.3: µs values for subsequent trials ............................................................................................ 6
Kinetic Friction ....................................................................................................................................... 6
Table 1.4: µk values for subsequent trials ............................................................................................ 6

Conclusion, Evaluation and Closing Remarks ......................................................7

Table of Content

1
 Calculating Coefficients of Friction

Abstract

A single mass-pulley system was used to determine the values of the static and kinetic
friction of a wooden surface. A block of wood was attached to one end of the string which
was held by a scale pan on the opposite end. The coefficient of static friction was found by
meticulously calculating the force required to move the wooden block from its docile
state. The coefficient of kinetic friction, on the other hand, was found by moving the
wooden block and estimating the force at which the block would continue moving at a
constant velocity. The resulting values for the coefficient of Static and Kinetic friction are
0.65 ± 0.03 and 0.45 ± 0.03 respectively. This agreed with the general assumption
that coefficients of static friction are greater than that of kinetic.

Objective
To calculate the static and kinetic coefficients of friction using measured data from a non-
inclined, mass-driven pulley system

Introduction/Theory
Friction is a natural phenomenon caused by uneven surfaces that resists the sliding/rolling
motion of two solid objects over each other. Fundamentally, it is of two types: Static and Kinetic.
Static friction is the friction that an object must overcome before starting a motion, while kinetic
friction is one that is encountered by an object that is already in motion. Naturally, the values of
the two is different, with static friction being the harder to overcome. Calculating the values of
static and kinetic friction usually requires the use of Dynamics. While static friction can be more
accurately measured due to its motion-free nature, the same can’t be said about kinetic friction.
Regardless, the use of a mass-pulley system and the basic laws of Dynamics should allow the
revelation of results within an acceptable range of accuracy.
In the measurement for static friction, it is assumed that the point of limiting equilibrium lies
between the value of the mass that was large enough to overcome the limitation, and the value of
that mass minus the smallest increment that was available, which happens to be 5g. At the
limiting equilibrium, in other words, at the verge of motion:
Ff = T

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 T = m*g & Ff = FN*µs
µs = mg / FN…. (Further simplification is done later in the report)
In the measurement for kinetic friction, it is assumed that the point at which the wooden block
moves at a constant velocity (net force is zero) is between the value of the mass that was large
enough to keep the block moving, at a constant velocity, as opposed to letting it stop and that
mass minus the smallest increment available. At this point:
FNet = T – Ff = 0
T = Ff
m*g = FN*µk
µk = mg / FN…. (Further simplification is done later in the report)
Prediction: It was predicted that the coefficient of static friction will be greater than the
coefficient of kinetic friction in every given trial.

Apparatus Used

Apparatus Quantity
Wooden Board 1
Wooden Block (180g) 1
Scale Pan (25g) 1
Multiple weighted bars (5g, 10g, 2 each for the 5g, 10g & 20g and 1 each
20g, 50g, 100g and 200g) for 50g, 100g & 200g
Scale 1
String 1
Pulley Wheel 1

Procedure
1. The system was adjusted with the long wooden board having an attached pulley wheel on
one end.
2. The wooden block, with no additional mass, was setup on one end of the string, which was
coiled around the pulley wheel and attached to a scale pan.
3. Mass was added in fixed amounts onto the scale pan until the wooden block started to move,
and the details were recorded. The wooden block was readjusted after every increase in mass
to avoid any errors that could potentially arise from keeping the wooden block motionless for
an extended period of time.

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 4. The wooden block was moved, at a constant velocity, and released against varying masses to
measure the kinetic friction. The minimum mass that would cause the block to continue
moving along the board was recorded.
5. Procedure number 3 and 4 were repeated with varying masses on top of the wooden block.
The masses added were 5g, 10g, 20g, 25g, 50g and 100g. The numbers were chosen for the
purpose of convenience and representation.

Data/Results
Due to the lack of smaller increments, there is assumed to be an uncertainty of ± 5g in the
measured mass of the scale pan. The recorded data for the motionless block (Static friction
calculation) is as follows:

Trial Mass added on the wooden Mass added on the scale pan when the block
Number block (g) started moving (g)
1 0 85
2 5 85
3 10 90
4 20 100
5 25 110
6 50 130
7 100 200
Table 1.1: Static Friction

The recorded data for the block moving with constant velocity (Kinetic friction calculation) is as
follows:

Trial Mass added on the wooden Mass added on the scale pan when the block
Number block (g) moves with constant velocity (g)
1 0 35
2 5 40
3 10 50
4 20 75
5 25 85
6 50 95
7 100 115
Table 1.2: Kinetic Friction

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Analysis/Discussion
Refer to the two figures below regarding the analysis.

Static Friction

In this case, it is assumed that the Limiting point is within 5g of the calculated figure, hence
the uncertainty. At this point:
Static Frictional Force = Tensional Force from Mass 2
F s = m2g
Fs is equal to the product of the normal force and the coefficient of static friction. m 2 is the
total mass on the scale pan. Therefore:
(m1g)µs = m2g
µs = m2 / m1
The static friction for the experiment for the given trial is given as follows. Note that this
information is based off the data given in Table 1.1. The uncertainty values for the coefficient
of static friction have been omitted in the final calculation of µ s due to its overwhelming
insignificance in the grand scheme of things.
Trial m1 – total mass of the block m2 – total mass of the Coefficient of Static
Number (g) scale pan (g) Friction (µs – unitless)
1 180g + 0g (25g + 85g) ± 5g 0.61 ± 0.03
2 180g + 5g (25g + 85g) ± 5g 0.59 ± 0.03
3 180g + 10g (25g + 90g) ± 5g 0.60 ± 0.03
4 180g + 20g (25g + 100g) ± 5g 0.62 ± 0.02
5 180g + 25g (25g + 110g) ± 5g 0.66 ± 0.02
6 180g + 50g (25g + 130g) ± 5g 0.67 ± 0.02

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 7 180g + 100g (25g + 200g) ± 5g 0.80 ± 0.02
Table 1.3: µs values for subsequent trials

Final Calculations:
. . . . . . .
 Mean = = 0.65
( . . ) ... ( . . )
 Variance = = 0.005
 Standard Deviation = √0.005 = 0.07
.
 Standard Error = = 0.03
√

The value for the coefficient of static friction, µ s, is 0.65 ± 0.03.

Kinetic Friction

In this case, it is assumed that there is a point within 5g of the calculated value of m 2 where
the kinetic friction equals the tensional force, and the block mass continues at a constant
velocity. At this point:
Kinetic Frictional Force = Tensional Force from Mass 2
F k = m2g
(m1g)µk = m2g
µk = m2 / m1
Based off Table 1.2, the value of µk for all seven trials is as follows:
Trial m1 – total mass of the block m2 – total mass of the Coefficient of Kinetic
Number (g) scale pan (g) Friction (µk – unitless)
1 180g + 0g (25g + 35g) ± 5g 0.33 ± 0.03
2 180g + 5g (25g + 40g) ± 5g 0.35 ± 0.03
3 180g + 10g (25g + 50g) ± 5g 0.39 ± 0.03
4 180g + 20g (25g + 75g) ± 5g 0.50 ± 0.02
5 180g + 25g (25g + 85g) ± 5g 0.54 ± 0.02
6 180g + 50g (25g + 95g) ± 5g 0.52 ± 0.02
7 180g + 100g (25g + 115g) ± 5g 0.50 ± 0.02
Table 1.4: µk values for subsequent trials

Final Calculations:
. . . . . . .
 Mean = = 0.45

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 ( . . ) ... ( . . )
 Variance = = 0.008
 Standard Deviation = √0.008 = 0.09
.
 Standard Error = = 0.03
√

The value for the coefficient of kinetic friction, µ k, is 0.45 ± 0.03.

Conclusion, Evaluation and Closing Remarks

At the end of the experiment, we have been able to determine the static and kinetic frictional
coefficient of the surface in question. As it was mentioned in the opening theory and prediction, the
value of the static coefficient is greater than that of the kinetic in every trial undertaken by the team.
However correct the calculations may be, there were fundamental limitation in the data collection
process. Some that are too rudimentary to account for, and others that are inherent to the procedure
that was followed. It is necessary to mention that although the data on this report can be used to
demonstrate the difference between static and kinetic friction, it is not recommended to use the
values on further calculations.