Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
The effect of
different surfaces
to the limit of
static friction
by Myles Rankin
Candidate Number: 7181
Centre Number: 51519
Date: 12/02/2015
Word count: 2,768
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Introduction
Aim
In this lab report I will determine the best grain size of sandpaper for an object to move along its
surface with least amount of friction. The surface with the lowest limit of static friction will be
the best for this, as it shows the least amount of gravitational potential energy needed to move
down a slope. This can be related to snowboarding or skiing, to tell what best snow density and
particle size will be the best to be moving faster on.
To do this I will be finding the static limit coefficient of each surface tested, then I will be able to
use this to find the best material, which will be the one with the lowest static limit thus requiring
the least amount of force to overcome. Additionally, by plotting this data collected I wish to find
a trend to predict how further surfaces will act.
Theory
The static friction forces involved when the
interlocking of two surfaces occurs will increase to
prevent motion until a limit where motion will then
occur. This limit is characterized by coefficient of
static friction (This is usually larger than the
Fig 1 – A simple box and flat surface example I
made.
coefficient of Kinetic friction) and is denoted as the
greek letter mu (𝜇).
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
A basic example of this would be pushing a box along a flat surface (Fig 1). At a microscopic
level, the bottom of the box and the flat surface would interlock into each other causing a static
friction (Fig 2). If you were then to push on the box, it would not move up to a certain point of
which when it moves the static friction limit has been overcome. After this any friction
experienced after that is kinetic friction which is weaker, as it gets easier to push something
after its static friction limit has been met.
This can be shown in a graph by plotting
resistive frictional force against applied force
(Fig. 3).
Fig 2 – Interlocking representation of a surface and
object. [1]
Fig 3 – Graph of Static and Kinetic Regions of force on an
object. [2]
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Myles Rankin
A2 Physics Coursework
𝑓𝑠 = 𝜇𝑠 𝐹𝑛
Furze Platt Senior School
[3]
The experiment will be using a slope to apply force upon a block on a ramp. Therefore an
equation must be defined to find the static coefficient on a slope. This can be done by taking the
formula used for a flat surface ([3]) then
combining it with some basic trigonometry
shown below in Fig 4.
As 𝐹𝑛 was equal to mg in the case of a flat
surface (Fig 1), working out will be mg times
the cosine of the max angle of the slope when
the static frictional limit is met (When the
Fig 4
block slides down the slope). I then need to
know the force pulling the block along the
slope, and going against the frictional force. This will be mg times the sine of the max angle of
the slope. Now I can simply substitute these two formulae into the original flat surface formula
(Shown below).
𝐹𝑛 = 𝑚𝑔 𝑐𝑜𝑠𝜃 and 𝑓𝑠 = 𝑚𝑔 𝑠𝑖𝑛𝜃
𝑓 = 𝜇𝑠 𝐹𝑛 to get:
Substitute into 𝑠
𝑚𝑔 𝑠𝑖𝑛𝜃 = 𝜇𝑠 𝑚𝑔 𝑐𝑜𝑠𝜃
𝜇𝑠
𝑚𝑔 𝑐𝑜𝑠𝜃
𝑐𝑜𝑠𝜃
=
=
= 𝑡𝑎𝑛𝜃
𝑚𝑔 𝑠𝑖𝑛𝜃
𝑠𝑖𝑛𝜃
Therefore: 𝜇𝑠 = 𝑡𝑎𝑛𝜃
With this formula I can find the static limit coefficient by finding the angle using trigonometry of
the two lengths that I will be measuring. This will be the opposite length to the angle, and the
adjacent, of which the opposite length is the only that changes each time.
4
Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Initial Plan
A single metre long wood sheet is to be placed at an angle on an adjustable jack, different types
of sandpaper will be placed at the top of the sheet and secured with tape. A wood block, which
will be laminated underneath to reduce any friction due to the rough wood surface, will be
placed upon the section of the wood sheet that has been covered in sandpaper. The height of the
jack will then be adjusted, which will increase the angle of the board to the floor. Once the block
falls, the jack will no longer be raised and the height will be recorded. By using Pythagoras
theorem, the angle of the slope at the blocks static limit can be calculated as we know the length
of the board (hypotenuse), and now the height from the jack (opposite length).
Equipment List:
1) 1x 1.38m x 0.1m x 0.005m wood sheet
2) 1x Adjustable height jack
3) 1x 1m Rule (Uncertainty +-0.5mm)
4) 1x A laminated wood block 100mm x 50mm x 20mm (0.042 kg)
5) 1x Roll of tape
6) 2x Clamp stands + Clamps
7) 1x Weight/Support to keep slope in place
8) Sandpaper:
1x P60 Sandpaper square
1x P80 Sandpaper square
1x P100 Sandpaper square
1x P150 Sandpaper square
1x P180 Sandpaper square
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Type of Sandpaper
Average particle size (µm)
P60
269
P80
201
P100
162
P150
100
P180
82
Initial method
Fig. 5 – Sandpaper Average Particle table [4]
1) Setup equipment as described in plan, and
shown in Fig 6.
2) Secure sandpaper to be tested on slope.
3) Lower slope to minimum angle.
4) Place block onto slope where sandpaper
has been placed.
5) Gradually increase angle by adjusting the
height of the slope using the jack.
6) Wait until block slides down slope, then
stop increasing height of the slope.
7) Measure the height at which caused the
block to slide down, as this is the limit.
Fig. 6 – Initial setup
8) Reset and repeat three times for each different type of sandpaper.
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Preliminary Results and Analysis
Sandpaper Average
Particle Diameter
Opposite Length
Hypotenuse length θ (= Sin^-1(O/H))
Static
Diameter Uncertainty Length Uncertainty Length Uncertainty
Material
(µm)
(%)
(m)
(%)
(m)
(%)
Angle (°)
Uncertainty
Limit
(%)
Coefficient
Laminate
0
0.00%
0.427
0.12
1.38
0.04
18.0
0.15
0.325
Laminate
0
0.00%
0.765
0.07
1.38
0.04
33.7
0.10
0.666
Laminate
0
0.00%
0.435
0.11
1.38
0.04
18.4
0.15
0.332
P180 Sandpaper
82
0.61%
1.046
0.05
1.38
0.04
49.3
0.08
1.162
P180 Sandpaper
82
0.61%
0.971
0.05
1.38
0.04
44.7
0.09
0.990
P180 Sandpaper
82
0.61%
1.072
0.05
1.38
0.04
51.0
0.08
1.234
P150 Sandpaper
100
0.50%
1.096
0.05
1.38
0.04
52.6
0.08
1.307
P150 Sandpaper
100
0.50%
1.102
0.05
1.38
0.04
53.0
0.08
1.327
P150 Sandpaper
100
0.50%
1.034
0.05
1.38
0.04
48.5
0.08
1.131
P100 Sandpaper
162
0.31%
1.082
0.05
1.38
0.04
51.6
0.08
1.263
P100 Sandpaper
162
0.31%
1.091
0.05
1.38
0.04
52.2
0.08
1.291
P100 Sandpaper
162
0.31%
1.061
0.05
1.38
0.04
50.2
0.08
1.202
P80 Sandpaper
201
0.25%
1.054
0.05
1.38
0.04
49.8
0.08
1.183
P80 Sandpaper
201
0.25%
1.042
0.05
1.38
0.04
49.0
0.08
1.152
P80 Sandpaper
201
0.25%
1.196
0.04
1.38
0.04
60.1
0.08
1.737
P80 Sandpaper
201
0.25%
1.083
0.05
1.38
0.04
51.7
0.08
1.266
P60 Sandpaper
269
0.19%
0.973
0.05
1.38
0.04
44.8
0.09
0.994
P60 Sandpaper
269
0.19%
0.921
0.05
1.38
0.04
41.9
0.09
0.896
P60 Sandpaper
269
0.19%
1.043
0.05
1.38
0.04
49.1
0.08
1.154
P60 Sandpaper
269
0.19%
0.962
0.05
1.38
0.04
44.2
0.09
0.972
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Preliminary Results
Static Friction Coefficient
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
Average Particle Diameter (µm)
As seen in the graph, as the average particle diameter increases the static coefficient also
increases, though after 201µm the graph declines which is an unexpected result. From this I can
make a prediction that the lower particle size of the surface requires less force to overcome the
static friction limit. This being said, due to the incline at the end there might be an issue with the
initial method so improvements may be needed to fully conclude a trend. Though, there might
be a more complex underlining trend in which the coefficient reaches a turning point, this is
something to look out in an improved method. Lastly, the initial uncertainty percentages seen in
the table have room for improvement.
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Improvements and Final Method
From the preliminary results and after conducting the initial experiment, a few discrepancies
and issues can be noticed. The first issue observed is that when using the wood sheet as a slope,
it found to be too thin and started to bend for each test. This means the force needed to
overcome the static limit will be higher, as the normal force will be differently distributed and
there will be more ‘digging’ and perhaps jumping from the block to the surface which will not
reflect the proper results for the flat surface model derived earlier as the surface will be curved.
To improve this, a thicker slope block that doesn’t bend will be substituted. Additionally, the
length has been increased for so the percentage uncertainty will affect the length less if it is
longer.
Another issue was that, when measuring the height of the slope the metre rule was not always
level and was hard to line up the top of the slope with a measurement on the rule. To improve
the measurement of the height, an ultrasonic measurement tool was used which has a much
smaller uncertainty (fixed at 0.005%) than a metre rule when measuring a distance under 15m.
It was secured on a pivoting point with a small level fixed on top of it. The pivot allowed the tool
to be pointing directly down at the ground, and the level was used to verify this. Additionally,
after using the lengths measured from the ultrasonic tool I used an adjustable angle
measurement tool to verify if any of the angles measured were anomalous results.
The last issue was when using the weights to keep the slope in place occasionally moved slightly
when the block slid down. To fix this, the bottom of the slope was propped up against a wall
which prevented it from shifting at all. To add to this, I decided there was safety risk in doing
this on a desk at a height which the slope could drop and hit someone, therefore I moved the
experiment onto the floor next to a wall.
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Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Additional Equipment
1) 1x Thicker & longer wood slope 0.045m x 0.085m x 1.52m
2) 1x Ultrasonic measurement tool (Fixed uncertainty of +-0.005%)
3) 1x Small level
4) 1x Pivot fixture
5) 1x Structural Support (Wall)
Improved Plan
The thicker/longer wood slope to be placed as before on an adjustable jack but with the bottom
propped against a wall. The different types of sandpaper to be secured as before, and the wood
block laminated. Then the height is to be adjusted, but once the static friction limit has been met
the ultrasonic measurement tool should be levelled out on the pivot (using the level to check
this) then used to find the height. After this, the adjustable angle measurement tool is to be used
to measure the angle to verify that the ultrasonic measurement has been done correctly. Lastly,
as before the lengths measured can be used to find the angle using trigonometry and thus can be
used to find the static coefficient.
Improved Method
1) Equipment setup as described in improved plan.
2) Secured sandpaper being tested onto slope.
3) Place block onto sandpaper.
4) Increase the jack height, once block falls stop increasing.
5) Adjust the ultrasonic measurer on its pivot so it’s level, use level tool to do this.
6) To have an angle to verify the ultrasonic measurer is correct, use the adjustable
measurement tool to measure an angle manually.
7) Test each sandpaper 3 times then remove.
8) Repeat method.
10
Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Improved Results and Analysis
Sandpaper Average
Material
Hypotenuse
Particle Diameter
Opposite Length
length
Diameter Uncertainty
Length Uncertainty
Length Uncertainty
Angle Uncertainty Static Limit Angle Uncertainty
(µm)
(m)
(m)
(°)
(%)
(%)
Angle Measured
θ (= Sin^-1(O/H))
(%)
(%)
Coefficient
(°)
(%)
Laminate
0
0.00
0.68
0.005
1.52
0.005
26.6
0.01
0.500
27.5
0.30
Laminate
0
0.00
0.74
0.005
1.52
0.005
29.1
0.01
0.557
28
0.30
Laminate
0
0.00
0.77
0.005
1.52
0.005
30.4
0.01
0.588
29
0.29
P180 Sandpaper
82
0.61
1.13
0.005
1.52
0.005 48.0
0.01
1.112
47.5
0.18
P180 Sandpaper
82
0.61
1.09
0.005
1.52
0.005
45.8
0.01
1.029
44.5
0.19
P180 Sandpaper
82
0.61
1.1
0.005
1.52
0.005
46.4
0.01
1.049
45
0.19
P150 Sandpaper
100
0.50
1.06
0.005
1.52
0.005
44.2
0.01
0.973
43.5
0.19
P150 Sandpaper
100
0.50
1.07
0.005
1.52
0.005
44.7
0.01
0.991
43
0.19
P150 Sandpaper
100
0.50
1.01
0.005
1.52
0.005
41.6
0.01
0.889
40.5
0.21
P100 Sandpaper
162
0.31
0.95
0.005
1.52
0.005
38.7
0.01
0.801
37.5
0.22
P100 Sandpaper
162
0.31
0.93
0.005
1.52
0.005
37.7
0.01
0.774
36
0.23
P100 Sandpaper
162
0.31
1.03
0.005
1.52
0.005
42.7
0.01
0.921
41
0.20
P80 Sandpaper
201
0.25
1.12
0.005
1.52
0.005
47.5
0.01
1.090
46
0.18
P80 Sandpaper
201
0.25
1.11
0.005
1.52
0.005
46.9
0.01
1.069
44.5
0.19
P80 Sandpaper
201
0.25
1.13
0.005
1.52
0.005 48.0
0.01
1.112
46.5
0.18
P60 Sandpaper
269
0.19
1.19
0.005
1.52
0.005
51.5
0.01
1.258
50
0.17
P60 Sandpaper
269
0.19
1.15
0.005
1.52
0.005
49.2
0.01
1.157
48
0.17
P60 Sandpaper
269
0.19
1.14
0.005
1.52
0.005
48.6
0.01
1.134
47
0.18
11
Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Improved Results
1.4
Static Friction Coefficient
1.2
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
Average Particle Diameter (µm)
The graph from the improved results gives a general upwards but
unexpected trend line, as seen there is a spike around the 82 micro
For 82 µm:
metre point. Initially this seems like an anomalous result, but when
Static Limits
looking at the results table it can be seen that the calculated coefficient
is consistent each time it is tested. Each set of 3 results were
calculated:
1.1
1.03
repeatable, for example for 82 micro metres all values were within
1.05
3.8% (See Fig.7) therefore the data must be reliable. If it is not an
Range: 0.08
anomalous result, then the reason behind a high coefficient at the
Average: 1.06
beginning of graph could be due to the particles being the right size to
(½*0.08)/1.06 = 3.8%
perfectly interlock with the laminate. This would mean it would
Fig. 7
interlock at the beginning, requiring a higher static friction coefficient but then drop down when
the particles become to big to interlock initially. Otherwise, if we ignore this spike from our
results the graph does match a pattern like the first, with a general upwards trend; then a
turning point towards the end where the static coefficient needed drops.
12
Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Conclusion
As outlined in both analysis of the preliminary and improved results, a general upwards trend
then a turning point wards the end of the data can be seen in the graphs. This initially tells me
that the bigger grain size means more interlocking happens, therefore more force is needed to
overcome the static limit. Which means for snowboarding, you would want a very small particle
size of snow to be able to move most efficiently with least friction. However, as mentioned in my
improved analysis, there is a slight spike at the beginning of the results. This has lead me to
believe this is either a anomalous result or, due to the particles being so small during the test
they actually perfectly interlocked with the laminate underneath the block. Therefore,
potentially it could mean a slightly higher grain but within the lower quartile of sizes could be a
more efficient particle size. Though this may vary to each different surface, as they will interlock
differently depending on material.
In terms of improvements and how the test was executed, there was an improvement. The
improved method allowed me to identify a spike, which in the initial method was not discovered.
However, If I had been given more time I would have liked to double the number of times I
tested each surface and also increase the amount of surfaces tested (more specifically, higher
particle sized surfaces). Furthermore, trying different laminate and surfaces to coat the block
may have been a potential way to further the experiment. This would’ve allowed me to
conclusively find if the spike in the improved method was just a localised issue with the laminate
used in that test. I could also test a waxed surface, as snowboarders wax their snowboards to
prevent getting stuck on flat terrain, in other words reducing the friction between the board and
terrain.
Lastly, the accuracy and ease of data gathering was adequate. The uncertainties/error bars were
small as shown in the graphs (almost unnoticeable in the improved graph), and the methods of
measuring were fast allowing me to make more tests in the limited time I was given.
13
Myles Rankin
A2 Physics Coursework
Furze Platt Senior School
Bibliography
[1] - http://qph.is.quoracdn.net/main-qimgb9a6cd376d1962e05cfb83758ca84fd2?convert_to_webp=true – 05/02/15
[2] - http://images.tutorvista.com/cms/images/83/graph-showing-static-and-kineticfriction.PNG - 01/02/15
[3] - http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html - 26/01/15 - 01/02/15
[4] - http://en.wikipedia.org/wiki/Sandpaper - 01/02/15
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