The type of surface did as the difference in values was large, at 72. %. (75 words) 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 paving 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 ass 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 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) FT is the force of tension in the string, mm 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 FT and find the following. (2) 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, FAN is the normal force acting on the block, M is the mass of the block, m is the mass added to the block, and ay is the acceleration in the arterial direction. Since the block isn’t accelerating in the vertical direction, we can set ay=O and solve the equation for FAN. ( ) (4) Now, we need to examine the forces acting in the horizontal direction by taking the sum of the forces. i ( ) (5) Fax 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 ax to O.
Also, since the string attached to the block is the same string that the hanging mass is attached to, we can also assume that FT is the same for both the block and the hanging mass. Solving the above equation for FT, we find the following. (6) From previous work, we know the equation force due to kinetic friction. It can be seen below. (7) The value PC 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. ) 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 he hanger. All of these values can be seen in the table below. Object Mass (keg) Wood Block 0. 0641 Trombone Paperclip 0. 001 Butterfly Paperclip 0. 003 Hanger 0. 005 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. Keg 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. Keg to the block up to a maximum amount 0. Keg. 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 efficient 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 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 iris 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.
We can also see in the table that side Co’s coefficient varies greatly from sides A and Bi’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 FT vs…
FAN 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 Figure 2- Graph of FT vs.. FAN to find values of PC We can see that the best-fit 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 best-fit 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.