Kinetic Friction. Experiment #13


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1 Kinetic Friction Experiment #13 Joe Solution E Partner Jane Answers PHY 221 Lab Instructor Nathaniel Franklin Wednesday, 11 AM1 PM Lecture Instructor Dr. Jacobs Abstract The purpose of this experiment was to examine kinetic friction and what factors affect it. We pulled a wood block across a surface to determine whether the surface area of the block or the type of surface affects friction. The surface area did not appear to affect friction, since there was a small percent difference of 6.16% between different surface areas. The type of surface did as the difference in values was large, at 72.2%. (75 words)
2 Introduction The purpose of this experiment is to examine kinetic friction and the factors that affect it. The two factors that are examined within this experiment are the surface area of the object and the type of surfaces in contact with one another. Both of these will be tested and compared to see which affects the value of kinetic friction Friction is a force that always opposes the motion of an object. Friction can be divided into two different types. One is called static, and one is called kinetic. Static friction is a force between two objects that are not moving relative to one another. For example, an object resting on a slope, but not sliding down the slope, is kept in its position by static friction. Static friction must be overcome to cause an object to move across a surface. Once enough force has been applied to an object, it will begin to slide across a surface and kinetic friction will then act on the object. Kinetic friction occurs when two objects are moving relative to one another with one object sliding across the surface of the other and it opposes the motion of the object. Both types of friction are described by different coefficients. These values are known as the coefficients of static and kinetic friction respectively. The coefficient of static friction is usually higher than that of kinetic friction. A small wooden block was used, with one side covered in Teflon tape to examine the coefficient of kinetic friction. The Teflon tape on one side of the block allowed us to see the effect of different surface types on the coefficient of friction. The small block was attached to a string. This string was threaded over a pulley, which was then connected to a mass hanger. Paperclips were used to add mass to the hanger, increasing the weight of the mass hanging on the string, until the block began to slide across the surface of the table. Mass was also added to the top of block to increase the normal force between the block and the table. The apparatus can be seen in the figure below. Figure 1 A picture of the experimental set up
3 In order to calculate the coefficient of kinetic friction, we can look at the set up and begin by examining the forces acting on the hanging mass. Using Newton s Second Law on the hanging mass, we find (1) F T is the force of tension in the string, m h is the mass of the hanger and paperclips, g is the acceleration due to gravity, and a is the acceleration of the hanger. If we assume that the hanging mass is not accelerating, we can solve the above equation for F T and find the following. Next, we can look at the forces acting on the block resting on the table. Since the forces act in two different directions, we must sum the forces separately. To begin, we can look at the forces acting in the vertical direction. (3) In the above equation, F N is the normal force acting on the block, M is the mass of the block, m is the mass added to the block, and a y is the acceleration in the vertical direction. Since the block isn t accelerating in the vertical direction, we can set a y =0 and solve the equation for F N. (4) Now, we need to examine the forces acting in the horizontal direction by taking the sum of the forces. (5) F k is the force due to kinetic friction in the above expression. If we assume that the block only just starts to move and is not accelerating, we can set a x to 0. Also, since the string attached to the block is the same string that the hanging mass is attached to, we can also assume that F T is the same for both the block and the hanging mass. Solving the above equation for F T, we find the following. From previous work, we know the equation force due to kinetic friction. It can be seen below. The value µ k is known as the coefficient of kinetic friction. We can solve equation 7 for this value and substitute equation 6 into equation 7 to solve for the coefficient of kinetic friction. (2) (6) (7) (8)
4 This final equation is what we can use to calculate the coefficient of kinetic friction for this experiment. Results We used an electric balance to measure the mass of the wooden block, one trombone paperclip, one butterfly paperclip, and the hanger. All of these values can be seen in the table below. Object Mass (kg) Wood Block Trombone Paperclip Butterfly Paperclip Hanger Data Table 1 Masses of Objects In order to get the block moving across the surface of the table, we added paperclips to the mass hanging until the block just started to move. We were able to find the tension in the string using equation 2. The mass of the hanger was 0.005kg and for this trial, it took 3 butterfly paperclips to cause the block to move. This calculation was completed for each trial that was run. Next, we used equation 4 to calculate the normal force acting on the block. The example seen below was done on the trial that just used the mass of the block itself with no added mass. With these two values, we can then use equation 8 to calculate a value for the coefficient of kinetic friction for this trial s set of data. We started with no mass on the block as was shown in the above sample calculations. For each successive trial we added 0.050kg to the block up to a maximum amount 0.250kg. The same calculations were run for each trail. Once we had run all of the trails, we took an average of the values found for the coefficient of kinetic friction. That calculation can be seen below. After finishing these 6 trials, we then turned the block so that a different side with a different surface area was in contact with the table. The procedure was then repeated with this new surface to find the coefficient of friction. The block was then flipped again, this time placing the side with the Teflon tape in contact with the table. The same trials and calculations
5 were repeated in order to obtain a value for the coefficient of kinetic friction. The table below shows all of the data collected from each part. Part A represents the first set of trials. Part B represents the second set where the surface area was changed. Part C represents the trials run with the Teflon tape side in contact with the table. M+m (kg) F N (N) Hanging Mass (kg) Tension (N) Coefficient of Kinetic Friction A B C A B C A B C Average Data Table 2 Finding the Coefficient of Kinetic Friction There are a few observations that can be made upon examining the table above. Firstly, we can see that as the mass of the block increases, the total force of tension also increases. We can also see that despite the change in surface area, the coefficients of friction do not vary by much between parts A and B. If we take a percent difference between these two values, we find the following results. This percent difference is relatively small and leads us to conclude that sides A and B have the same value for the coefficient. We can also see in the table that side C s coefficient varies greatly from sides A and B s coefficient. If we take an average of the coefficients in side A and B, 0.206, and compare it to side C in a percent difference, using the same calculation as above, we see that the percent difference is 72.2%. One last trend is that the first trial of each part is slightly higher than the rest and the value of the coefficient seems to decrease slightly as we increased the mass of the block. We then used the data in the table above to graph F T vs. F N to allow trends in the data to be seen more clearly. According to equation 8, the slope of these lines should be equal to the coefficient of friction for each set of trials
6 Figure 2 Graph of F T vs F N to find values of µ k We can see that the bestfit lines for data sets A and B are very close to one another and have very similar values of slope. This should have been expected as the average values from A and B were also very close. C is also very different from A and B and this should have been expected as the difference in the averages was also quite large. Finally, we can compare the slope of each best fit line to the corresponding average for each part of the experiment in a percent difference. Using the same calculation shown on the previous page, we found a percent difference of 3.09% in part A, 11.0% in part B and 10.9% in part C when comparing the average to the corresponding slope of the bestfit line. Error Analysis One source of error was the assumption that the block was not accelerating in the horizontal direction. We made this assumption by setting all of the accelerations in equations 1 and 5 equal to 0. I noticed that the block did appear to accelerate once enough mass was added to the hanger to cause the block to move. If the block accelerated, we would need to alter our equations used throughout out the experiment. Looking back over the equations, our values of F T and F k would change. F T and F k would become slightly smaller due to the acceleration. This would mean the coefficients for each trial would also decrease. The calculations below show how the formulas for the tension force and friction would change. (9)
7 (10) Since the hanging mass and block are connected by the string, they should accelerate at the same rate, so a=a x. Next, we can plug in the value of F T from equation 9 into equation 10, noting that F k should still be equal to µ k F N Solving this equation for µ k, we find a new formula for our value of µ k. If we use this new formula to calculate our coefficients assuming that there was a small acceleration of 0.02m/s, we would see that each of the coefficients found in parts A, B and C would decrease. Below is a sample calculation as well as a recreation of Data Table 1 using the new calculation to find µ k F N (N) Hanging Mass (kg) Tension (N) Coefficient of Kinetic Friction A B C A B C A B C Average Data Table 3 Factoring in Acceleration into the Coefficient of Kinetic Friction Using this new data, we can also recreate Figure 2, the graph of F T vs. F N.
8 Figure 3 Recreation of Figure 2 Accounting for Acceleration The slopes have slightly changed compared to the slopes found in the experiment. If we then compare the new averages and slopes that account for acceleration just as we did before using a percent difference, we find a percent difference of 1.80% for part A, 9.8% for part B, and 8.4% for part C. With a reduction of percent difference, this source of error can be held accountable for some of the error in the experiment. Another source of error is that there was friction in the pulley that was not accounted for. The string and pulley were in contact. Two surfaces in contact will generate friction as one surface moves past the other. This would mean that the friction between the pulley and the string was not accounted for. We can alter our equations to include this term. F S represents the force of friction due to the string sliding along the pulley. As we can see by the final equation, this factor would reduce the values we calculated for the coefficient of friction. For example, if we estimate the force of friction between the string and pulley to be 0.002N, we would find the following new results given the data we collected in the experiment. A sample calculation is shown below as well as a new data table that used the new calculation for the coefficient.
9 M+m (kg) F N (N) Hanging Mass (kg) Tension (N) Coefficient of Kinetic Friction A B C A B C A B C Average Data Table 4 Factoring in the Friction Between the Pulley and String Again, we can see that the averages are lower for each part of the experiment when compared to previous values. We can then compare these values to the graph of F T vs. F N in a percent difference as was done previously. When compared, we find a percent difference of 2.24% from part A, 10.3% from part B, and 9.3% for part C all of which are reduced when compared to the percent differences found during the experiment. Conclusion In this experiment, we examined kinetic friction and looked at the factors that affect the value of the coefficient of kinetic friction. First, we examined whether or not the surface area of the objects affects the coefficient. We can conclude that the surface area does not appear to have an effect on the coefficient, and therefore the friction between two objects since there was a percent difference between part A and part B, which had different surface areas, of only 6.16%. We next tested whether or not the type of surface has an effect on the coefficient. Comparing the average of Part A and B to Part C, we found a percent difference of 72.2%. This leads us to conclude that the type of surface has a large impact on the force of friction and coefficient as part C had a different surface type than parts A and B. The value of friction does depend on the normal force between the two objects. We saw this in equation 7,. We can see that the frictional force is proportional to the normal force through the coefficient of friction. As the normal force increases, the frictional force increases. The percent difference between my graphs and the corresponding averages appear to be close to one another. The percent differences were 3.09%, 11.0%, and 10.9% for parts A, B, and C respectively. These percent differences are under 15% and are reasonable when comparing averages to best fit lines. Looking at the graphs and averages, we have found a few different values of the coefficient. Of our values found for µ k, I think that the slopes found for our best fit lines give us the most accurate measurement. Excel uses the method of leastsquares when calculating the bestfit line for a given data set. This is a much more accurate approach for finding a best fit value than one found just taking an average. Finally, if we wanted to reduce error in the experiment, we may want to use a material with a higher value of µ k, like rubber. By using a higher coefficient, any small changes in the value of the coefficient will be harder to detect as the actual value will be much higher. If we can keep the uncertainty at about the same value, but increase the value it applies to, like the coefficient, we can reduce the error.
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