The Force of Friction

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Stony Brook University *

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121

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Mechanical Engineering

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Oct 30, 2023

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Shiv Thakur 9/30/2023 PHY 121 TA: Yue Chen The Force of Friction

Introduction: The purpose of this laboratory activity is to study how the force of friction changes with mass and to solve for the coefficient of kinetic friction between the surface and the device. There are two main types of friction, kinetic and static. Static friction refers to the force needed to begin sliding an object and once the object begins moving, kinetic friction takes over. In this lab we investigate how the force of kinetic friction changes as the mass of the iOLab increases by attaching masses to it. We can determine the coefficient of kinetic friction, μ, from the equation for friction, 𝐹 ? = μ𝐹 𝑁 . As the coefficient of friction depends on the materials the two surfaces are made of, the value should be constant as the mass changes throughout the experiment. Procedure: • Plug in the iOLab dongle into your computer, start the iOLab device, and open the software on your computer. • Attach the screw to the force probe and turn the device so the y-axis is pointing downwards. • Hit record and let the device sit for one second before using the screw to lift the device and holding it steady before placing it down again. • Find the average force and acceleration in the y direction once you pick up the device, this gives you the force due to gravity and the acceleration due to gravity, respectively. • Use the gravitational force equation, 𝐹 ? = 𝑚𝑔 , to find the mass of the iOLab. • Replace the screw on the iOLab with the plate and place the device wheels up on a flat surface. • Push the device on the plate in the y direction and use Analysis mode to find the acceleration after the push. • Attach a mass using tape to the side of the iOLab device. • Find the mass of the new system using the same methods as previously used. • Add a second mass on top of the first and repeat the process. • Use the force of gravity to calculate the normal force. • Use Excel to plot the force of friction vs. the normal force and add a linear trendline. • Calculate μ for each trial and average the values. • Using the slope of the force of friction vs. the normal force plot, find μ. • Compare the two values of μ generated.

Figure 1 Finding the "Known" Value of the Mass Figure 2 First Push Figure 2 Mass Number 2 Figure 4 Acceleration Number 2 Figure 5 Acceleration Number 3 Results: y = -0.399x - 1.1687 R² = 0.7594 -5 -4 -3 -2 -1 0 0 1 2 3 4 5 6 7 Force of Friction (N) Normal Force (N) Force of Friction vs. Normal Force

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Calculations: Discussion: We begin by finding the known value of the mass of the iOLab device. Using the information extracted from Figure 1, I used the equation 𝑚 = 𝐹 ? ? to find the known mass of the iOLab device to be 0.159 kg. When you stop pushing the device it still has an acceleration because it can still be accelerating positively due to the force applied followed by a negative acceleration caused by friction slowing the iOLab down. Using the mass and acceleration, you can find the force acting on the device using the equation F = ma. You can find the force of friction by taking the negative of the calculated force, as every force has an equal and opposite force. The normal force was calculated using the formula 𝐹 𝑛 = 𝑚𝑔 using the mass calculated previously and g coming from the acceleration due to gravity given by the accelerometer on the iOLab. Gravitational Force (N) Acceleration due to Gravity (m/s 2 ) Calculated Mass (kg) Acceleration When pushed (m/s 2 ) Normal Force (N) Force of Friction (N) Coefficient of Friction μ iOLab -1.561 -9.81 0.159 16.487 1.56 -1.90 -1.22 iOLab + Mass -4.184 -9.81 0.422 5.633 4.14 -2.377 -0.57 iOLab + 2 nd additional mass -4.984 -9.81 0.508 6.778 4.98 -3.49 -0.64

The coefficient of friction, μ , was calculated using the formula μ = 𝐹 ? 𝐹 𝑁 where the force of friction and normal force were calculated using the methods previously mentioned. The value for μ was calculated for the trial with the iOLab alone, the iOLab with one mass added, and the iOLab with two masses added. The values calculated came out to be -1.22, -0.561, and -0.69, the inconsistencies with these values could be explained by the surface that was used for this experiment being my mousepad, as the surface has uneven wear from use. The average coefficient of friction was calculated to be -0.827. The value for the coefficient of friction gathered from the excel plot was -0.399 which is quite different from the value found experimentally, this could be explained from the iOLab not being properly calibrated and the unit being a rental and could have been slightly damaged from previous owners. An error analysis was conducted using the multiplication / division formula from the error analysis manual for the calculations of mass, force of friction, and normal force. The average error for mass was 0.022, the error for force of friction was 0.094, and the error for the normal force was 0.094. The low values for the average error of the calculations show that the values generated are fairly accurate. As the coefficient of friction only varies with the materials used the values should have been more consistent than they were, variances could be explained by issues with the iOLab and inconsistencies on the surface that the experiment was conducted on. Conclusion: The value for the coefficient of friction was not found to be constant with changes in mass but this doesn’t invalidate the theory as inconsistencies could be explained by the errors discussed above. Proof: