Coefficient of Friction

THE PHYSICS OF HOCKEY! Sliding Friction and Momentum on Ice

Coefficient of Friction

Misconceptions

Many texbooks make an assumption that ice is a frictionless surface: this is entirely untrue. People mistake ice for being frictionless because the ice seems to be a transparent, flat and smooth (it's slippery when you run your hand across the ice).

"At a macroscopic level, smooth surfaces exert frictional forces at least as large as do rough ones." (Sir Robert Robinson, 1965, p. 110)

Varying Coefficients

The coefficient of friction on ice is not constant; it is just too complicating to find the exact value. The reason for this is that the friction depends on many factors such as asperities, the mass of load, temperature, sliding speed, normal reaction, and the type of material.

Major Factors Affecting the Coefficient of Friction

1)Sliding Speed

(D.C.B Evans, "The Kinetic Friction of Ice." 493, 1976)

Click to view graph A

The graph above shows the relationship between the coefficient of friction of various materials according to different velocities. The low values of sliding friction arise when the speed exceeds 0.1 m/s. The other factors are kept constant.

For all three materials, they share a linear relationship on Graph A: it shows that the coefficient of friction of a slider on ice decreases in an straight line (inclined) as the speed increases. However you can see that the horizontal grid from for speed

We can conclude from this graph that the coefficient is extremely great when the sliding speed is too small; further, the friction drops as the speed increases.

The second graph below illustrates what happens when the sliding speed is less than 1m/s.

Click to view graph B

(Perssonn, 1998, p. 496)

This graph conveys the extreme high coefficient of friction when the slider is moving very slow.
For instance, at speeds around 10, exponent -7, m/s glass and granite are 0.3 and 0.9 respectively. Perssonn believes that adhesion occurs since there is no melting of ice at low speeds. Also, the data suggests the shearing of ice due to the slide which breaks open the adhesive contact.

2)Friction Depends on Asperities

Asperities, which are microscopic projections from the "average surface," play a major role in determining the coefficient of friction between materials.
The friction depends on the asperities of the surfaces in contact. The pressure on an asperity is greater than the normal force, that it may deform the contact area "plastically" (asperities can weld together). Therefore, frictional resistance arises from sliding objects breaking and creating bonds created by asperities.

In addition, you may notice that after a long hockey game, the surface of the pond or artificial pad you skated on is no longer smooth and shiny. You may see various sizes of scratches on the ice --your skates will have a difficult time, sliding on the roughness. It is time to call it "quits", or you simply have to ask the Zamboni man to clean the ice surface.

3)Temperature

(D.C.B Evans, p. 512, 1976)

Click to view graph C

This third graph is the relationship for the coefficient of friction of various materials at different temperatutes with a fixed velocity ( 3.14m/s on the graph ).
The temperature proportionally affects the amount of frictional force. From -1 to -25*C , the coefficient of static fricition for all three solids increases; thus there needs to be more energy exerted to slide an object at these temperatures.

Once again, mu, the coefficient of friction, rises with the falling temperature at a given speed; likewise, mu decreases as the temperature approaches the melting point of ice.

4)Load and Area of Real Contact

(N.J.Perssonn, 1998, p.444)

click to view graph D

This fourth graph indicates the relationship of a load on ice at two different temperatures. Since there was a 1kg load on the tip of a diamond, the area of real contact depends on the time the load is sitting. The two arrows on the graph indicates the approximation of the areas in contact if pressure-melting was the case.

The contact area increases linearly with the time of loading; similarly, the slower the object moves, the longer the time of loading, which leads to a more suface contact.
The amount of surface area which is in contact with the ice directly affects the coefficient of friction; a greater surface area will increase the amount of contact area between the load and the ice, therefore, allowing the area of friction increase.

Amonton's law states that the coefficient of friction is independent of the normal force.

However, Bowden (1953) proved that Amonton's law strictly applies when there is a lower load. The reason for this independence at lower loads is that there is less pressure for the asperities in contact to deform. Perssonn concludes from his extensive research that the amount of pressure influences asperities to deform "instantaneously."

Now, applying friction to ice and hockey in general, if the ice surface had no friction, nobody will dare bring oneself over the ice -- just as you will slip and fall with shoes, your skates will do no better.

Test it Yourself: Why not go to a skating rink and try it out? I advise that you wear a helmet and a pair of skates that fit well. When you're set, make one stride at the end of the rink. See how far you can go with this one stride. Make sure the your skates are facing toward the direction you are going. Depending on the sharpness of your blades, you may reach half the rink length with a powerful stride. It may seem you "flying" for a while, but will soon slow down. There is...friction!

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5)The Type of Material

The material of the slider is a crucial factor.

Looking at Graph A for "Sliding Speed", notice how the copper slider has a value of 0.02 at about 8m/s, whereas it is 0.05 at 1 m/s. The slope for copper is much steeper compared to that of mild steel and perplex; copper can have the coefficient dramatically altered at a higher speed.

Measuring the slopes of the lines for each material will show the ratio in which a certain speed will reduce the coefficient of friction.

However, this time using Graph B (showing the effects of temperature on the coefficient), the slopes of the lines are similar. Also, copper's values are higher than persplex and mild steel which are almost together.An explanation for this is that heat is conducted away through copper, while perspex and mild steel have heat conducted away through the ice.

Summary:

From these graphs, we can see that many factors play a role in determining the coefficient of friction on ice.

In particular, these graphs were created by the results of the experiments which were conducted by Evans and Perssonn. Their data have a great degree of accuracy and precision due to the careful procedure and to the utilization of advanced tools and apparatus. These graphs demonstrate the relationship of many conditions combined to showcase a better understanding of sliding friction on ice.
It is imperative to note that the science community can learn a great deal from the collected data of these scientist; further, these experimental results direct the nature of the theory. Certainly, with this data we can choose which theory or theories are pinpointing the true nature of sliding friction on ice.

That is why I conducted my own experiment, using the methods and tools that are accessible, to find similarities or irregularities with the results.

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