The μ of your shoe
Introduction:
If you were playing basketball in the NBA or the WNBA, what kind of shoes would you wear? The
basketball court is hard and smooth and can be very slippery so you need a shoe that will have a high
coefficient of friction on the court. The designers of athletic shoes think about this when they make their
shoes. That is why athletic shoe soles are different from dress shoes.
Mathematically, friction is equal to the force pressing two surfaces
together times the coefficient of friction: Ff =µ FN. [I remember by
saying : F of f equals ‘mu’Fin] The Greek letter µ (mu) represents the
coefficient of friction and N represents the normal force. If we are on
the basketball court, N is the upward force the court exerts on the soles
of our shoes. If we are not jumping or running this force is exactly
equal to our weight. With this in mind it is not hard to see that the court
exerts a much greater normal force on Shaquille O'Neal than it does on
you or me.
If we are familiar with Newton’s laws of motion it is easy to see what causes the normal force. The court
must exert an equal and opposite force to support our weight. Newton’s laws do not help us much with the
cause of the friction force however. Materials and their properties determine the coefficient of friction but
our friction equation also says that the normal force affects friction.
Do you think the force of friction would be greater if Shaq stood in his shoes or if you stood in his shoes?
Intuitively it makes sense that Shaq would be harder to push across the floor than you even if you were
wearing the same shoes. The reason why however is not so intuitive.
A microscopically rough surface is like a landscape of hills and valleys. For a
small normal force only the tallest hills(called asperities) touch each other.
As the normal force increases the hills press against each other and deform.
This increases the actual contact area. The amount of contact area depends
on how hard the material is and how great the normal force is.
We can now better explain the friction
force: Different materials and different
normal forces change actual contact area.
Atomic force
The greater the contact area the greater the
microscope picture
friction force. To get an idea of how much
of shoe sole
actual contact area occurs between materials choose a pair of materials
and a normal force (load). Note: for harder materials you may not even be
able to see the actual contact area until the load becomes very great.
Purpose: The purpose of this activity is to determine the coefficient of
friction for different shoes on a wooden surface.
Materials: spring balance or force probe, 3 equal masses, 2 different
shoes, wooden board
Procedure:
1) Use the data table to record Ff and FN for each shoe. You will need to record each force measurement
with no added mass, 1 added mass, 2 added mass, and 3 added masses. Each of these will be performed
three times.
2) Measure and record the weight of each shoe.
3) Drag your shoe at a constant velocity across the board. Make sure to keep the spring balance
PARALLEL to the board. Record this number in a data table for that shoe and repeat for a total of THREE
trials. Complete your table for all your other measurements.
6) Repeat with the addition of 1, 2, and 3 masses. Repeat for a second shoe.
Data:
Shoe with mass
(kg)
Shoe one: Detail shoe name and type:_______________________
Normal Force
(N)
Kinetic Friction (N)
Trial one
Trial two
Trial three
Average
Kinetic
Friction (N)
Shoe two: Detail shoe name and type:_______________________
Shoe with mass
(kg)
Normal Force
(N)
Kinetic Friction (N)
Trial one
Trial two
Trial three
Average
Kinetic
Friction (N)
7) Make a graph of your average Ff versus FN for each condition for each shoe. Use different symbols for
different shoes. Add a best fit line. Label each line and calculate the slope of each line. (You may use the
computer for this)
Analysis:
1. What does the slope of your line represent?
2. According to your graph, what is the equation that relates f and N? Use the appropriate symbol for your
slope.
3. What is the coefficient of friction for each shoe?
4. What would you use a high coefficient of friction shoe for? What would you use a low coefficient of
friction shoe for? Explain with examples from the sporting world.
5. Looking at your classmate’s data, does it appear that the coeffiecent of firction and cost are at all
correlated? If so, how?
Extension Activity:
Now for the easy way! You can use some simple trigonometry to deduce the coefficient of static friction
between a shoe and a surface with a simple ramp.
For this procedure you will attempt to determine the coefficient of as many different shoes as possible.
Procedure:
1. Determine a starting point on the board that you will place all shoes.
2. Place the first shoe on the board. Raise one end of the board very slowly until the shoe begins to slide. At
the same time, two other students should be at the axis point of the board with protractors or Astrolabes to
determine at what angle the shoe begins to slide.
Calculations: tan θ = μs = A/B
Brand
Shoe
Angle ()
Questions:
1. Which of the shoes had the greatest coefficient of static friction?
2. Speculate as to why the order of the shoes came out the way it did.
3. Why is it important to always start the shoe at the same part of the ramp?
Coefficient of Static
Friction ( μs)