LAB REPORT 3

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Apr 3, 2024

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Dean Taylor 6/7/23 PHY 133 L69 TA: Chamathka Thotamuna Wijewardhana The Force of Friction

Introduction: The force of friction is one that moves opposite to sliding motion. The goal of this lab report is to measure how friction changes with mass and to draw conclusions from collected data. While there are two key types of friction (static and kinetic), this lab will focus only on determining kinetic friction by an increasing mass of the IO Device and determining the coefficient of kinetic friction for a given surface. Prior to the movement of an object, static friction is in effect. If an object is in movement the force due to friction is described as being kinetic. The IO Device will be used to determine varying masses and accelerations with a given mass in order to solve for a coefficient of friction. It is expected that as mass increases, force of friction increases as well while the coefficient of kinetic friction should not change. The following equations will be used to make this determination: ࠵? = ࠵?࠵? ࠵? ! = ࠵?࠵? Procedure: Determination of Mass: 1. Ensure the USB is plugged in and the IO Device is powered on 2. Use the screw attachment on the force sensor 3. Place the IO Device such that the y-axis points towards the floor 4. Press record, wait 1 second, and lift the device by the screw (hold in place for a couple seconds) 5. Place the device down and press stop 6. Use the analysis tool to record mean acceleration prior to the lift as well as mean force during the lift 7. Use the formulas above to solve for the mass Finding Deceleration and Force Due to Friction 1. Ensure the USB is plugged in and the IO Device is powered on 2. Attach the plate attachment to the force sensor 3. Place the IO Device on face up (such that the “IO Lab” label faces the ceiling) 4. Press record and push the device from the plate in the “y-direction” 5. After the graph returns to its original values, press stop. 6. Use analysis mode to find the acceleration just after the applied force 7. Note this figure and use the equations found above in conjunction with the calculated masses to find force due to friction Measurements for Varying Masses 1. Tape a mass (such as a phone or lighter) to the wheel (or “IO Lab”) side of the IO Device 2. Follow instructions given in both sections above to determine new mass as well as new acceleration 3. Tape an additional mass to the IO Device (ensure you leave the originally added mass to the device) 4. Perform the experiment, again, using procedures above 5. Compile all data accordingly and calculate necessary values using the F=ma equation Results: Test # Average Fg Sigma Value for Fg Average g Sigma Value for g 1 -1.687 N 0.0032 N -9.818 m/s^2 0.013 m/s^2 2 -2.100 N 0.0047 N -9.816 m/s^2 0.014 m/s^2 3 -2.662 N 0.0039 N -9.820 m/s^2 0.013 m/s^2 Figure 1: All Data for all Values Used for Mass Determination

Figure 2a: Acceleration and Force (due to gravity) vs. time graph (at rest on surface) for Test 1 Figure 2b: Acceleration and Force (due to gravity) vs. time graph (being held from screw) for Test 1

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Figure 3a: Acceleration and Force (due to gravity) vs. time graph (at rest on surface) for Test 2 Figure 3b: Acceleration and Force (due to gravity) vs. time graph (being held from screw) for Test 2

Figure 4a: Acceleration and Force (due to gravity) vs. time graph (at rest on surface) for Test 3 Figure 4b: Acceleration and Force (due to gravity) vs. time graph (being held from screw) for Test 3 Mass # Average a Sigma Value for g 1 -2.499 m/s^2 0.25 m/s^2 2 -2.491 m/s^2 0.19 m/s^2 3 -2.177 m/s^2 0.20 m/s^2

Figure 5: All Data for all Values Used in Calculations for Force, Normal Force, and Coefficient of Kinetic Friction Figure 6: Acceleration and Force vs. time graph (after push) for Mass 1 Figure 7: Acceleration and Force vs. time graph (after push) for Mass 2

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Figure 8: Acceleration and Force vs. time graph (after push) for Mass 3 Mass # Normal Force Force of Friction 1 1.6876 N 0.4303 N 2 2.0962 N 0.5328 N 3 2.6568 N 0.5902 N Figure 9: Calculated Values for Force of Friction and Normal Force Figure 10: Force of Friction vs. Normal Force Graph Created Using Data from Figure 9 Slope = 0.1612

Figure 11: Free Body Diagram of Forced Acting on Device Calculations: ࠵? ! = ࠵?࠵? ࠵? = ࠵? ! ࠵? Test 1 Mass Determination: ࠵? " = # ! ! = $".&’( * $+.’"’ ,/.^0 =0.17218…=0.1722 g Test 2 Mass Determination: ࠵? 0 = # ! ! = $0."11 * $+.’"& ,/.^0 =0.213936…=0.2139 g Test 3 Mass Determination: ࠵? 2 = # ! ! = $0.&&0 * $+.’01 ,/.^0 =0.271079…=0.2711 g Normal Force (N) for Mass 1: N=mg (0.1722 g)(9.8 m/s^2)=1.68756 N= 1.6876 N Normal Force (N) for Mass 2: N=mg (0.2139 g)(9.8 m/s^2)=2.09622 N= 2.0962 N Normal Force (N) for Mass 3: N=mg (0.2711 g)(9.8 m/s^2)=2.65678 N= 2.6568 N Force of Friction for Mass 1: ࠵? " =0.1722 g Average a=-2.499 m/s^2 ࠵? = ࠵?࠵? =(0.1722 g)(-2.499 m/s^2)=0.4303278 N=0.4303 N Force of Friction for Mass 2: ࠵? 0 = 0.2139 g Average a=-2.491 m/s^2 ࠵? = ࠵?࠵? =(0.2139 g)(-2.491 m/s^2)=0.5328249 N=0.5328 N Force of Friction for Mass 3:

࠵? 2 =0.2711 g Average a=-2.177 m/s^2 ࠵? = ࠵?࠵? =(0.2711 g)(- 2.177 m/s^2)=0.590184 N=0.5902 N ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵? ࠵? 3 = ࠵?࠵? * ࠵? = ࠵? 3 ࠵? * Calculation of ࠵? for Mass 1: ࠵? = ࠵? 3 ࠵? * = 0.4303 ࠵? 1.6876 ࠵? = 0.254932164 = 0.2549 Calculation of ࠵? for Mass 2: ࠵? = # " # # = 1.420’ * 0.1+&0 * = 0.25417422 =0.2542 Calculation of ࠵? for Mass 3: ࠵? = # " # # = 1.4+10 * 0.&4&’ * = 0.222146944 =0.2221 Average of ࠵? ࠵? 3 = (࠵? " +࠵? 0 + ࠵? 2 )/3 = (0.2549 + 0.2542 + 0.2221 )/3= 0.24375 Error Analysis: ࠵? ! = ࠵?࠵? ࠵? " = # ! ! = $".&’( * $+.’"’ ,/.^0 =0.17218…=0.1722 g Acceleration σ= 0.0013 m/s^2 Force σ= 0.0032 N ࠵? B ࠵? ࠵? E = |࠵?࠵?|G H ࠵? 5 ࠵? I 0 + H ࠵? 6 ࠵? I 0 ࠵? H $".&’( * $+.’"’ ,/. $ I = J(−1.687 ࠵?) ࠵?(−9.818 , . $ )J M H 1.1120 * $".&’( * I 0 + H 1.11"2 ,/. $ $+.’"’ ,/. $ I 0 =0.03149405146 Relative Error For F g : ∆࠵? ࠵? = B 0.0032 ࠵? 1.687 ࠵? E = 0.001896858328 = 0.001897 For g: ∆࠵? ࠵? = O 0.0013 ࠵?/࠵? 0 ࠵?/࠵? 0 Q = 0.0001324098594 = 0.001324 Discussion: In assessing whether the hypothesis can be accepted or rejected, it is clear the results are in line with what was expected and so we accept the hypothesis. Throughout this experiment while most values were consistent, there were some discrepancies which point towards noteworthy error. One such example was the gap between calculated coefficient of friction and the slope generated by excel. The calculated average for coefficient of friction was found to be 0.2438 while the slope was generated to be 0.1612. This is somewhat significant of an error and could be a result of human error in carrying out the experiment as well as random error. One important aspect to note, however,

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is that all experimentally calculated values of the coefficient of friction were quite close with one minor “outlier.” The respective values were as follows: 0.2542, 0.2549 , and 0.2221. However, even with any gaps, some amount of error is expected and the two calculated values are close enough to state that the hypothesis is supported by the generated slope. The slope of Normal Force and Force of Friction represents the coefficient of friction which is why the two values are being compared. Masses for each test were determining using acceleration due to gravity while the object was a rest in addition to acceleration due to gravity in order to use F=ma and determine that m=f/a, or in this case, m=Fg/g. Furthermore, by using the accelerometer, accelerations and previously calculated masses were used to determine the force of friction. Using the force of friction (and noting that FN=Fg), values for the coefficient of friction were calculated with the equation. ࠵? 3 = ࠵?࠵? * oritsrearrangement: ࠵? = ࠵? 3 ࠵? * In assessing error, values were all quite low implying conclusions made from data assessment are firm. As a result, it is clear that the coefficient of friction is unaffected by mass and mass and force due to friction have a direct positive relationship. Link to Video of Proof: https://drive.google.com/file/d/145oNBsQDbVmUIBYBMSH-- VtVupiSL9tS/view?usp=drivesdk