Lab 3 little g

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Physics

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Apr 3, 2024

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Phys 207 Lab CD4 Instructor: Luis A. Álvarez García Group: Rosemary Delgado Report 3: Little g Nicole Caringal Introduction (1pt) Through various experiments dealing with angle and mass, this lab helps to understand the relationships of mass vs. acceleration, angle vs. acceleration, and change in position vs. time due to acceleration from gravity. Procedure (1pt) Experiment 1: A rough measurement Take a 1 meter measuring stick and hold it vertically perpendicular to the floor. Take a wooden block and hold it up in the air where it is 1 meter above the floor, using the meter stick as reference. Have a timer ready to measure how long it takes for the wooden block to reach the floor from a height of 1 meter. Record the time. Repeat this process two more trials and record their time values. For each trial, calculate for acceleration [m/s^2]. Average these calculated acceleration values. Experiment 2: Slow-mo free fall Using the video provided, select one frame to use as your initial height value. Record the frame number and the height of the ball, in centimeters, of that frame. Select a second

frame value as the final height value. Record the frame number and the height of the ball in the frame. Based on these values, calculate for the acceleration value of the ball. Experiment 3: Leveling a ramp Ensure that the track is leveled. Do this by turning all the thumb-screws to the lowest level possible. Place the car on the track to check that it does not move. This will indicate that the track is leveled. On the side of the track opposite of the motion tracker, gradually increase the level of the track using the thumb-screws until the cart starts to move. Record the heights of both ends of the track. Using the length of the track and these recorded values, calculate for the angle of the track. This will be the angle of when the cart begins to move. Experimental Setup: Level the track again. Open the application LoggerPro3. Test that your motion sensor is connected, on, and working properly by clicking the collect button towards the top of the screen. When data is collecting, the device should emit clicking sounds, which indicates that it is working. Placing your hand in front of the motion detector should record a smaller position value than placing your hand farther away. This indicates that data is being recorded properly. Click the stop button to stop recording data. Experiment 4: The rolling cart at different angles Ensure that the track is leveled. On the end of track with the motion sensor, place 1 spacer under each thumb-screw. Measure and record the heights of both ends of the track. Use these values to calculate for the angle of the ramp. Place the cart against the stopper. Click collect on the application and immediately release the cart. Click stop once the cart has

reached the other end of the track. Save this data set. Repeat these steps two more times, each with different angle values. Experiment 5: The rolling cart with different masses Ensure that the track is leveled. Place 1 spacer under the thumb-screws on the side of the motion sensor. Record the height difference between both ends of the track and calculate for the angle value. Place the cart on the stopper and get ready to record data again with the motion detector. Repeat this process, but attach the hex-head bolt with the aluminum tube to the cart. Data and Calculations (3pts) Data Experiment: A rough measurement Figure 1: Recorded experimental time values to calculate for acceleration Trial # Recorded Fall Time (s) 1 0.33 2 0.35 3 0.27 Experiment: The rolling cart at different angles Figure 2: Calculated angle values according to ramp height values and length of ramp (122. cm)

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Trial # Ramp height 1 (cm) Ramp height 2 (cm) Angle (degrees) Trial 1 6.0 4.7 0.611 Trial 2 7.6 4.7 1.36 Trial 3 8.7 4.7 1.88 Figure 3.1.a: Trial 1 Position (m) vs. Time (s) Graph

Figure 3.1.b: Trial 1 Velocity (m/s) vs. Time (s) Graph Figure 3.2.a: Trial 2 Position (m) vs. Time (s) Graph Figure 3.2.b: Trial 2 Velocity (m/s) vs. Time (s) Graph

Figure 3.3.a: Trial 3 Position (m) vs. Time (s) Graph Figure 3.3.b: Trial 3 Velocity (m/s) vs. Time (s) Graph

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Experiment: The rolling cart with different masses Figure 4.1.a: Cart without mass Position (m) vs. Time (s) Graph Figure 4.1.b: Cart without mass Velocity (m/s) vs. Time (s) Graph

Figure 4.2.a: Cart with mass Position (m) vs. Time (s) Graph Figure 4.2.b: Cart with mass Velocity (m/s) vs. Time (s) Graph

Discrepancies Figure 5: Chart of the calculated acceleration values from different groups Group # Gravity (m/s^2) 1 -10.70 2 -11.11 3 11.77 4 -36.98 5 -9.615 6 -10.4 7 9.795 Calculations:

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Experiment: A rough measurement 1st Acceleration: 1.0m / (0.33s)^2 = -18. m/s^2 2nd Acceleration: 1.0m / (0.35s)^2 = -16. m/s^2 3rd Acceleration: 1.0m / (0.27s)^2 = -12. m/s^2 Average Acceleration: (-18 + -16. + -12.) / 3 = -16. m/s^2 Experiment: Slo-mo free fall Initial frame: 0 | Initial height: 0cm Final frame: 50 | Final height: 125cm Calculated Acceleration: [(125. cm / 100) * -2] / [(50 - 21)/ 60]^2 = -10.7 m/s^2 Experiment: Leveling a ramp Height 1: 5.8cm | Height 2: 4.9cm Minimum angle for movement: sin^-1 [(5.8 - 4.9) / 122] = 0.423° Experiment: The rolling cart at different angles Trial 1 angle: sin^-1 [(6 - 4.7) / 122] = 0.62° Trial 2 angle: sin^-1 [(7.6 - 4.7) / 122] = 1.4° Trial 3 angle: sin^1 [(8.7 - 4.7) / 122] = 1.9° Report Question 2

Uncertainty: (0.9 ± 0.01) / (122 ± 0) = (0.9 / 122) [1 ± (0.01/0.9 + 0/122)] = (0.9/122) ± 0.011 Report Question 6 (-10.70 + -11.11 + -11.77 + -36.98 + -9.615 + -10.4 + -9.795) / 7 = -14.34 m/s^2 Questions (3pts) Report question 1: Why is this method not very good? What are the limitations? This method is ineffective as it depends on a person’s reaction time of when the wooden ball begins to fall and when it hits the ground. A person’s reaction time, the limitation, will be off of the actual times, hence the imprecision in time values. When comparing the actual value of gravity, -9.81 m/s^2 compared to the experimental average value, -16. m/s^2, it shows how a small error in time can greatly impact the experimental acceleration value. Report question 2: Let's consider how 'level' this track really is. Using uncertainty analysis, what is the uncertainty in the angle measurement of the track? Based on this uncertainty, our tracks are probably not exactly at θ = 0.000 .... In an ideal physics set up, even a very small angle θ should create an acceleration. So, why can you get the car to stand still? Uncertainty in the angle measurement is ± 0.011. The car is able to stand still due to friction. Potentially, there is friction between the track and the wheels of the car. There could also be friction in the car in the axels. Friction acts as an opposing force that acts against a force trying to get the car in motion.

Report question 3: Based on this angle, estimate the static (or rolling) friction coefficient that is acting on the car when it's on the ramp. The mass of the cart is ~ 500grams. The coefficient of static friction acting on the 500-gram car is equal to tan(0.423) = 0.0074. Report question 4: For each angle, perform the analysis separately. Do the three measurements all produce similar results for g? Why or why not? Comment on reasons why they might be different. Trial 1 has a g value of 8.19 m/s^2. Trial 2 has a g value of 6.79 m/s^2. Trial 3 has a g value of 9.47 m/s^2. The three measurements do not produce similar results for gravity. This can be due to a misinterpretation of the time when the car actually makes impact with the other end of the track for each trial. This can also be due to the bump present in the track that caused irregular data to be recorded while the car was moving, affecting the acceleration value. The lack of precision concerning the heights of the track and the car’s length of travel can also cause errors. Report question 5: Doing a similar analysis to this data as you did in the question above and determine the acceleration of the cart with and without the mass. Use your analysis to make a claim either that the mass affected the acceleration or that it did not. Would you expect it to based on our understanding of kinematics? The acceleration of the cart without the mass is 0.0942 m/s^2. The acceleration of the cart with the mass is 0.11 m/s^2. There is a slight increase in acceleration with the added mass. This result was not expected since mass is inversely proportional to acceleration in Newton’s Second Law of Motion. Essentially, as mass increases, acceleration decreases.

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Report question 6: More than likely, there are differences between some groups' estimation of g shown in the table above. Comment on these discrepancies. If everyone had access to the same raw data (i.e. the video), shouldn't their results be the same? What could lead to variations in these results? Calculate the average value from g based on these measurements. Is it within the uncertainty you would expect from the experiment? Varying results in the data can be attributed to estimated height values. Since the height value of the ball in each frame is not exactly given, it has to be estimated based on the 5- centimeter subintervals. The estimated value can be give or take 0.025 meters of the actual height. The average acceleration based on these measurements is -14.34 m/s^2. It is not within the expected uncertainty from the experiment. Conclusion (2pts) Through various experiments dealing with angle and mass, this lab helps to understand the relationships of mass vs. acceleration, angle vs. acceleration, and change in position vs. time due to acceleration from gravity. Mass does not have a significant impact on acceleration. The greater the angle of a system, the greater the acceleration. With acceleration from gravity, there is an exponential increase in position vs. time.

Lab 3 little g

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