Introduction: A wise man once said “Recently in my physics class my imagination caught fire.” As far back as I can remember I have always been intrigued and captivated by motion. Whether I was playing with toy cars or riding my bike, I was always interested in why and how things moved and also why they stopped. Even after many years, this interest and intrigue has stuck with me to this day. Last year in my physics class we learned that the two forces of friction and gravity affect all motion on earth, so when we began learning about friction I was very excited. Fast forward to this year, when it became time to start work on our Internal Assessments for physics, I saw the perfect opportunity to delve a little deeper and to expand my understanding on the relationship between friction and moving objects.
Background: The coefficient of friction is defined as the ratio between the force required to move one surface horizontally over another and the force holding the two together. This relationship can be represented mathematically by the formula μ=FkNwhere μ represents the coefficient of friction. Throughout history, the work of many famous names including Leonardo Da Vinci, Guillaume Amontons and Charles-Augustin de Coulomb have told us that many factors such as roughness, hardness and elasticity all affect the amount of friction between two surfaces. Just like the coefficient of friction itself, the relationship between temperature and the coefficient of friction is a complicated one that interestingly enough depends on the two materials that come into contact. Many factors that contribute to the physical makeup of a material such as molecular structure, molecular density and characteristics such as thermal expansion, contribute to how easily an object slides across a surface, and many of these properties change along with temperature. A real world example of this is how race car drivers warm up their rubber tires in order get a better grip on the race track. This example, along with all of my research led me the hypothesize that I would see very much the same outcome in my own experiment and that I would find that the coefficient of friction increases as temperature increases.
Procedure:
Due to my love for winter sport including sledding and skiing, I initially decided to try and conduct my experiment by measuring the friction force between a miniature plastic sled and a block of ice, all while manipulating the temperature of the sled. I found out through some frustration that this was not a feasible way to collect accurate data especially in a room temperature environment and as a result of this I had to scrap the use of ice in my testing. After some trial and error I eventually decided on measuring the friction between a sliding piece of rubber and a wooden surface. I also took several steps to modify the way in which I collected data in the hopes of modifying accuracy.
Here is a diagram of the setup I eventually decided upon:
In this setup, the weight was released which pulled on the string and the force probe and dragging the rubber sled across the wooden surface. During the this process the force probe recorded data in the form of a Force (N) vs Time (s) graph. The peak data value was recorded as the value for static friction (Fs) and a median data point within the “plateau” was used to measure the kinetic friction force (Fk). Using a freezer and a toaster oven I was able to manipulate the temperature of the rubber sled and conduct trials at varying temperatures. An infrared thermometer was used to measure the surface temperature of the bottom of the rubber sled.
Uncertainty:
According to the distributors specifications for the Digital Thermodetector GM700 infrared thermometer, the uncertainty for objects 0 – 700℃ ( 32 – 1292 oF) is ±1.5℃ and for objects -50 – 0℃ (-58 – 32 oF) is ±3℃. These are the uncertainty values I therefore used for my temperature measurements. According to Vernier, the uncertainty for the Dual Range Force Sensor is ± 0.05 N. This is how I came upon my uncertainty for my friction force values.
Raw Data:
Table 1: Complete Raw Data Set Friction vs. Temperature
Temperature of Rubber Sled (±1.5oF)
Static Friction
(± 0.05 N)
Kinetic friction (± 0.05 N)
30
15.1
10.9
30
15.0
10.3
45
13.7
7.50
55
11.7
8.56
60
11.6
8.19
60
11.1
7.85
80
8.62
6.82
80
7.89
6.20
90
7.25
5.68
90
8.13
5.35
90
7.34
5.78
90
7.55
5.47
105
7.81
6.68
110
7.34
5.38
110
8.18
6.01
Table 2: Mean Friction vs. Temperature
Temperature of Rubber Sled (±1.5oF)
Mean Static Friction (± 0.05 N)
Mean Kinetic friction (± 0.05 N)
30
15.0
10.6
45
13.7
7.50
55
11.7
8.56
60
11.4
8.02
80
8.26
6.51
90
7.57
5.57
105
7.81
6.68
110
7.76
5.70
Graphs:
Graph 1: Complete Raw Data Set Friction vs. Temperature
Graph 2: Mean Friction vs. Temperature
Data Manipulation, Calculating Coefficient of Friction:
Although the relationship between friction and temperature can easily be observed from my two completed graphs, I decided to take my investigation one step further by calculating the coefficient of friction for the sled at each temperature as well. As a whole, I felt as if the collected values for static friction were generally more accurate than the sliding friction values due to the nature of my data collection. Because of this I decided to calculate the coefficient of static friction (μs). The formula for μs is as follows:
μs = FsN, where Fs is static friction and where N = normal force. The equation for normal force is N = mgcosθ. In the case of this experiment this equation can be simplified to
N = mg, where m = mass and g = gravity, because the sliding occures on a level surface.
Here is an example of how I calculated μs between the rubber sled and the wooden surface at 30o F using the first value of static friction in Table 2:
Temperature of Rubber Sled (±1.5oF)
Mean Static Friction (± 0.05 N)
30
15.0
Givens: g = 9.806 m/s2, mass of sled = 1.408 kg
μs = 15.0 N(1.41 kg)(9.81m/s2)= 1.08
I used this method to calculate μs for the rest of the values in table 2:
Table 3, Coefficient of friction vs temperature:
Temperature of Rubber Sled (±1.5 oF)
Static Friction
(± 0.05 N)
μs( ± 0.05)
30
15.0
1.08
45
13.67
0.990
55
11.74
0.850
60
11.35
0.822
80
8.26
0.598
90
7.57
0.548
105
7.81
0.566
110
7.76
0.562
I then graphed this newly calculated data in order to finally see what I set out to find in the first place, the relationship between the coefficient of static friction of a sliding object and temperature.
Graph 3: Coefficient of Static Friction Vs. Temperature
Conclusion and Data Analysis:
After conducting my procedure, collecting data and processing the data, I was able to determine that temperature did in fact have an impact between the wooden surface and the rubber sled used in the trials. According to my results the lower the temperature, the larger the coefficient of friction between the rubber and the wood. Essentially I found the relationship to be inverse. Unfortunately it is difficult to verify the accuracy of my results mainly because there is no one value or even a general equation that can expresses the coefficient of friction for any two materials that come into contact. In all honesty, with my prior knowledge and research in mind I expected the results to be much the opposite and I didnt expect the relationship to be inverse. Much like the example of race car tires, I expected the coefficient of friction to increase as temperature increased, but my results do not support this original hypothesis. Through a bit more research I was able to shed a bit of light on my findings. Although it’s generally accepted that materials tend to expand when heated and contract when cooled some, like certain types of rubber actually do the opposite. According to PhysLink.com “a rubber band will actually become softer, or easier to stretch, when the temperature gets colder.” This would potentially explain my somewhat counterintuitive results.
Improvements and Potential Sources of Error:
As with any experiment there are always improvements that can be made to increase accuracy and to eliminate potential sources of error. This experiment is no different, and this mostly has to do with the manipulated variable in the experiment, temperature. Whenever objects are being heated or cooled and then placed in a room temperature environments they begin to return to thermal equilibrium with their surroundings instantaneously. The amount of time this takes depends on many things such as specific heat capacity and others. Because of this constant change in temperature towards equilibrium I find it likely that many of my of my temperature readings, although accurate at the instant I took them, were not an accurate measure of the temperature of the object by the time I started the data collection. Even if the delay was only 5-10 seconds. I also think factors such as heat created during the sliding process could have changed the temperature of the rubber and therefore impacted the results as well. For the most part I feel that most of these potential sources of error are due to the variables being tested and not necessarily a flawed setup. Because of this I do not see an easy way to significantly improve these issued if a second test was to be conducted.
Originally published 15.10.2019