PCS 120 Lab 03 report

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School

Toronto Metropolitan University *

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120

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Mechanical Engineering

Date

Apr 3, 2024

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docx

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Uploaded by ProfessorUniverseKookabura30

1 Introduction In this experiment, we studied static and kinetic friction on an object with non-zero normal force, varying weights, and on two different materials, carpet and plastic. The objective of the experiment was to determine the effects of static and kinetic friction, with varying factors involved (as stated above), and to quantify them using formulas and the data collected. Procedure This experiment's procedure consisted of 1 wooden block, a 500g weight, three 1kg weights, and two materials to test the static and kinetic friction on, 1 carpet strip and 1 plastic strip. We attached 1 end of a string to the wooden block, and the other end to a measurement device. We pulled the measurement device that was attached to the wooden block and dragged it across the material (carpet or plastic). First starting with 500g on the wooden block, then 1500g, 2500g, and finally 3500g. We did this on each material, and used the vernier graph analysis linked to the measurement device to calculate the data (In this case, Force) collected each time we dragged the wooden block across the material strip with varying weights. Results and calculations Force data tables for Carpet path: Raw data plot for mass 500g

2 In order to find maximum static friction force working on the log, the peak of the graph was chosen, which was 4.31 Newtons at 0.46 seconds. After that, the graph can be seen dropping and going on a rather constant path, where the applied force on the log overcame maximum static friction force and converted into kinetic friction force, hence a mean of the values of force from 0.47 seconds to 2 seconds in order to the mean kinetic friction force values, 2.44 Newtons. Normal force was calculated by the formula, N= mg, where m was the mass, 0.5kg in case of first attempt and g was 9.8m/s², hence normal force for 500g was 4.9N. In order to calculate the static friction and kinetic friction coefficients were calculated by dividing the Normal force by static friction and kinetic friction force respectively. So, for 500g, μ static = 4.31/4.9= 0.88 μ kinetic = 2.44/4.9= 0.50 The calculations for 1500g, 2500g and 3500g were carried out using the same formulas. The results for each mass for both forces on the carpet path can be found in the table given below:

3 Mass (g) Static friction (Newtons) Kinetic friction (Newtons) Normal force (Newtons) μ static (Static friction coefficient) μ kinetic (Kinetic friction coefficient) 500g 4.31N 2.44N 4.9N 0.88 0.50 1500g 9.26N 6.05N 14.7N 0.63 0.41 2500g 16.29N 10.55N 24.5N 0.66 0.43 3500g 22.05N 15.61N 34.3N 0.64 0.46 Force data tables for Plastic path Mass (g) Static friction (Newtons) Kinetic friction (Newtons) Normal force (Newtons) μ static (Static friction coefficient) μ kinetic (Kinetic friction coefficient) 500g 3.78N 2.42N 4.9 0.77 0.49 1500g 8.88N 5.81N 14.7 0.60 0.40 2500g 13.26N 9.60N 24.5 0.54 0.39 3500g 18.08N 13.67 34.3 0.53 0.40 All in one force vs mass graph

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4 Calculation of R² values R²= 1- Σ ( y i − y i, fit ) ² Σ ( y i − y ) ² In order to find R² for the max. Static friction force on the carpet surface, the values used were as follows, y i, fit = mx+b, where m= 6.025 and b= -2.085 y = 4.31 + 9.26 + 16.29 + 22.05 4 = 12.98 x y i y i, fit ( y i − y i, fit ¿ ² ¿ ❑ ( y i − y ¿ ² 500 4.31 0.9275 11.44 75.17 1500 9.26 6.9525 5.325 13.84 2500 16.29 12.978 10.97 10.96

5 3500 22.05 19.003 9.284 82.3 Sum 37.02 182.27 So, R²= 1- 37.02 182.27 = 0.79689 ≈ 0.8 Forces R² Static friction (Carpet) 0.80 Kinetic friction (Carpet) 0.994 Static friction (Plastic) 0.91 Kinetic friction (Plastic) 0.998 Discussions 1.) Some other contributors that the model does not account for are, surface roughness, Temperature, and Wear and Tear. Surface Roughness: The roughness of the surfaces play a significant role in friction, although we ran tests on 1 rough surface and 1 smooth surface, there are surfaces with varying roughness which the model doesn’t account for. Temperature: Temperature can influence the friction between two surfaces, as the temperature changes, the coefficients of friction can also change. Wear and Tear: Over time, the carpet can wear down, and lose its roughness, which would lead to changes in friction. 2.) When pulling the block across the surfaces, you might have had to hold the surface such that the surface itself does not slide on the table. What statement can you make about the coefficients of friction between the block and surface compared to the surface and table?

6 If you need to hold the surface, such that it does not slide on the table while pulling a block across it, it implies that the coefficient of friction between the surface and the block is higher than the coefficient of friction between the surface and the table. 3.) The R 2 value is still a rather vague quantifier and typically requires further justification to truly indicate whether the result is ‘trustworthy’. Instead, reflect on the experiment and explicitly highlight specific aspects of the experiment which can be improved that would possibly increase the R 2 value. Some aspects that can be improved that would possibly increase the R 2 value are: Data quality, Sample size, and measurement errors. Ensuring data quality in the experiment is accurate and free from errors can impact the R2 value in a positive way. Increasing the sample size can improve the reliability of the R2 value. Reducing measurement errors can improve the precision of the model and increase the R2 value. Conclusion The higher R² values here suggest that model was a good fit for the data and there is a strong relationship between mass of an object and the frictional forces working on it. The lower values also suggest a strong relationship however they might have been affected by variables other than mass, such as- error in calibration or variability in force while pulling the wooden log. In terms of the coefficients of static friction (carpet) , it can be concluded that more force was needed to overcome static friction on the carpet for 0.5kg than 3.5kg, hence higher the mass, the easier it is to move the object on that specific carpet material. Moreover, for coefficients of kinetic friction, it can be said that less force was needed to maintain motion than what was needed to overcome maximum static friction. In regard to the values of coefficients of static and kinetic friction (plastic), as they had lesser values than the coefficients of the carpet material, it can be concluded that it was easier to move all masses on plastic that it was on the carpet surface.

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