Running head: TRACTION OF SPORTS SHOES
Coefficient of Static Friction and Traction of Sports Shoes
Student Name Here
Jacksonville High School
November 28, 2012
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TRACTION OF SPORTS SHOES
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Abstract
Finding the traction of sports shoes by finding the coefficient of static friction, μs, of the
shoes is important to physicists who are concerned with safety of people in sports and in
everyday life. This experiment found μs for two different shoes with four different masses added
both longitudinally and laterally. It found that mass has no effect on μs because μs stayed
relatively constant throughout the experiment. Also, some shoes, such as the Reebok tested, have
greater static frictional force longitudinally while others, like the Nike tested, have greater static
frictional force laterally. The Nike had greater overall traction, consistent with the hypothesis.
Unfortunately the basis for the hypothesis (that the shoe with the greater surface area would have
the greater traction) could not be tested, because too many variables were present. Another
experiment under controlled atmospheric conditions with same-size shoes that have the same
sole materials and have been worn under the exact same conditions would be necessary to
determine a relationship between a shoe’s contact surface area and its μs.
TRACTION OF SPORTS SHOES
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Introduction-(needs to break up the introduction into paragraphs)
This experiment tested 2 sports shoes to determine their coefficient of static friction (μs—
read myu sub s).First of all, the static friction coefficient between two solid surfaces is defined as
the ratio of the frictional force (Ff) required to produce sliding divided by the normal force
between the surfaces (FN) (Beardmore, 2012). Traction can be defined as the adhesive force of
friction of a body on some surface (Dictionary.com, 2012). Normal force (FN) can be determined
by the mass of an object multiplied by the acceleration due to gravity pulling the object toward
Earth (9.80m/s2). Similar experiments have been performed with a focus on safety of athletes on
synthetic turf fields and on accident prevention in the workplace. The sports experiment cited
two important facts about traction: it depends on contact geometry and dynamics and traction
coefficients on turf surfaces vary with temperature (Torg, 1996). The research focused on
accident prevention was more like this experiment in that it was concentrated on slip resistant
materials’ effect on static friction. It made an important advance in the idea that a method needs
to be developed so that slip resistance, which is such an important factor in accident prevention,
can be given as much attention as other features of the sole (Tisserand, 1985). It is important to
do experiments such as this to determine which shoes are best for which activities. For example,
cross country would need shoes with higher longitudinal traction since runners are almost always
exerting force forwards while basketball may require shoes with greater lateral traction for
planting and changing directions side-to-side. Although Shoe 1 was larger from front to back,
shoe 2 was larger from left to right and had a greater overall surface in contact with the lab table,
which is reason to believe that shoe 2 would have a greater μs and greater traction.
TRACTION OF SPORTS SHOES
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Method
On November 15th and 16th of 2012 at Jacksonville High School, an experiment was
tested to determine the coefficient of static friction of two different sports shoes. The first was a
Nike Free men’s size 10.5 shoe with a fair amount of wear and a custom orthotic insert. The
second was a Reebok Realflex size 12 with minimal wear and a Dr. Scholls gel insert. Following
the 2009 The Physics Classroom Mu Shoe Physics Lab, each shoe was weighed using a triple
beam balance, then masses of 100g, 200g, 500g, and 1000g were added for each respective test
with the mass distributed as evenly as possible throughout the shoe to mimic the force of a
human’s weight. With a Vernier interface, LoggerPro software, and a force sensor, the force
exerted by the sensor on a string tied to the shoe could be seen on a Force-Time graph on
LoggerPro. Before beginning the experiment, the force sensor was calibrated, and before each
trial, a zero point was determined when no force was being exerted. Tests were conducted both
laterally and longitudinally for the shoes with 100g, 200g, 500g, or 1000g added for each test.
On LoggerPro each graph would have a maximum force, which was the static frictional force,
because once that force was reached, the force sensor would sense less, as the shoe was
accelerating. With the normal force (FN equals mass of the shoe plus the added mass [in kg]
times acceleration due to gravity [9.80 m/s2] ) and the static frictional force (Ff), the coefficient of
static friction could be calculated: Ff/FN= μs.
TRACTION OF SPORTS SHOES
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Results
For every test (all four masses longitudinally and laterally) but one (mass of shoe plus
200g mass longitudinally), the Nike shoe (TABLE 1) had higher static friction and therefore a
greater μs than the Reebok (TABLE 2). For each set of tests (shoe 1 longitudinally, shoe 1
laterally, shoe 2 longitudinally, and shoe 2 laterally), μs remained basically constant.
TABLE 1
Nike Free
size 10.5
Mass (kg)
0.4182
0.5182
0.8182
1.3182
Normal Force
(N)
4.10
5.08
8.02
12.9
Frictional Force
Longitudinal (N)
2.589
3.131
4.996
8.013
Frictional Force
Lateral (N)
2.640
3.292
5.127
8.473
μs
Lateral
0.644
0.648
0.639
0.657
μs
Longitudinal
0.631
0.616
0.623
0.621
TABLE 2
Shoe 2 Reebok
Realflex size 12
Mass (kg)
0.4500
0.5500
0.8500
1.3500
Normal
Force (N)
4.41
5.39
8.33
13.2
Frictional Force
Longitudinal (N)
2.567
3.377
4.759
7.225
Frictional Force
Lateral (N)
2.436
3.091
4.666
6.877
μs
Lateral
0.552
0.573
0.560
0.521
μs
Longitudinal
0.582
0.627
0.571
0.547
TRACTION OF SPORTS SHOES
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Discussion
This experiment reveals a lot about μs, traction, and frictional forces. One revelation is
that the mass of an object has no direct relation to its coefficient of static friction. When the mass
of the shoe was tripled, the μs stayed the same. Also, the size of the shoe has no correlation to its
μs when the shoes are different styles, have differing sole surface areas and material, have been
worn under varied conditions, and may be under different atmospheric conditions such as
temperature (Torg, 1986). Because of all of these different factors going into the experiment, a
specific and accurate conclusion cannot be made with any decent amount of certainty.
Consequently the reasoning for my hypothesis can’t be accepted or denied although my
hypothesis itself, that the Nike shoe would have higher traction than the Reebok was accepted.
Other than eliminating the aforementioned variables by using shoes of the same size just out of
the factory in a temperature-controlled room, the experiment can be improved by spreading the
added mass evenly throughout the shoe and pulling the force sensor at the center of the mass to
eliminate inconsistencies. Even simply doing multiple trials for each test and averaging the
results would make the data more accurate and μs would be even more constant.
TRACTION OF SPORTS SHOES
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References
Beardmore, R. (2012). Friction factors. In Roymech. Retrieved from
http://roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm
Tisserand, M. Institut National de Recherche et de Securite, (1985). Progress in the prevention of
falls caused by slipping (AQF03). Retrieved from TAYLOR & FRANCIS LTD website:
http://www.tandfonline.com/doi/abs/10.1080/00140138508963225
Torg, J.S., Stilwell,G., and Rogers,K.: The effect of ambient temperature on the shoe-surface
interface release coefficient. Am J Sports Med, 24:79-82, 1996.
Traction. In (2012). Dictionary.com. Dictionary.com, LLC. Retrieved from
http://dictionary.reference.com/browse/traction