School Papers

Xiaobing 1/31/18 Group: Xiaobing Liu, Aliyah Saber, Riya

Xiaobing Liu                                                                                                Lab Performed: 1/24/18PHYS 2021-044                                                                                      Report Due: 1/31/18 Group: Xiaobing Liu, Aliyah Saber, Riya Patel, Shauna Ballin         TA: Shuo Jia   Experiment 1– The Physic Laboratory — Picket FenceIntroduction: The first lab is “The Physics Laboratory” the purpose of this lab is to use computer for data acquisition and analysis. The data is acquired from the probe and the sensor that connect to the computer via an interface and then analysis by Excel. The goal of the lab is to practice graphing and analyzing data in Excel and also to gain and understand the concept of velocity, acceleration and time. The lab is divided up into three part the first paper is Experimenting with Capstone, the second part is Plotting Data in Excel and the last part is to Further Data Analysis: Reproducibility and Distributions. Lastly, the goal of the lab is to have 6 runs to test the position, time, speed, and the acceleration (slope obtain from graph) of the picket fence being dropped into the photogate. Procedure: Apparatus and Measurementscomputer with PASCO interface PASCO Capstone softwarephotogate on a standpicket fence (84.4g) Part I: Experimenting with CapstoneSet up the photogate with it extending out of the table.Connect the photogate to Digital Input 1 of the PASCO interface.Then check if the photogate is working properly. That there should be a red light on the photogates that will blink as your hands pass through. If it is not working properly check the power button on the PASCO interface.Open the PASCO Capstone software on the desktop. Input the photogate that is connected and on the drop-down menu for the measuring device.After the photogate is selected the Setup Timer should appear. Choose Pre-Configured Time, on the menu and then click Picket Fence timer. Then have the data being collected for time, position, and speed. Also, make sure to have the correct Flag Spacing to measure the speed.Then look at the Data Summary to make sure all setup of the photogates quantities that are required is right.Click on the Hardware Setup and the Time Setup and the menu button will be hidden. Then from the Display menu on the right, drag the Table to the middle area. Then click Select Measurement buttons to show Time, Speed, Position. Make sure foam pad is on the floor. Click Record to start data collection. Hold the picket fence vertically as it falls through the photogate beam.Click Stop to end data collection. Copy and paste data table into Excel.To make sure measurement are reliable and reproducible, repeat the data collection five more times for a total of 6 runs.Part II: Plotting Data in ExcelOpen excel and make a scatter plot of velocity vs. time for the first trial. Then right-click on the plot and choose Select Data and all other runs. So there will be 6 runs in one graph. Each run will be plotted as individual data series.     For each trial add it’s trendline. Choose the linear fit and select the option to display the equation of trendline. The graph should appear with label, title, and units.Use the data from the last run and make a plot of vertical distance vs. time. Add title, label, and unit do the graph. Part III: Further Data Analysis: Reproducibility and DistributionCompare Equation 1 to the equation of the trendline and that the value for slope represent acceleration. Record the acceleration into a new table on spreadsheets.Step one is data analysis to find the average. Second Step of data analysis is the standard deviation of the mean of the 6 acceleration value. Compare my value and the acceptable. And explain my error. Set Up Precautions and Source of Error: PrecautionsThe set up of the Digital Input 1 is connected to the PASCO interface. The light of the photogate should be on. Also that there should be a foam pad on the floor that the picket fence can fall through onto. Source of ErrorThe weight or the mass of the picket fence.  The height of the picket fence drop each trial could be at different.The person dropping the picket fence and the person clicking start on the computer could be different. That one person could have started dropping the picket fence and then that other person could then have click start. Also that the picket fence could have dropped onto the floor before the person clicks stop or the picket fence didn’t reach the floor before the other person clicks stop.Data Calculations Fitting:Slope: (velocity)(m/s)Runs 1-6  (Distance vs. Time)1.59261.42891.58761.51661.79731.5335Slope: (acceleration )(m/s2)Runs 1-6  (Velocity vs. Time)8.75378.72348.51748.72259.035810.011Standard deviation: 0.493488347 Average: 8.960633333Standard deviation / Average: 0.055072932 Data Table: (distance vs. time)Run #1Run #1Run #2Run #2Run #3Run #3Run #4Run #4Run #5Run #5Run #6Run #6 Times (s)Position (m)Times (s)Position (m)Times (s)Position (m)Times (s)Position (m)Times (s)Position (m)Times (s)Position (m)2.8703.0900.1400.2400.0600.0102.930.053.160.050.190.050.30.050.110.050.060.052.960.13.20.10.230.10.340.10.140.10.10.12.990.153.230.150.260.150.370.150.160.150.130.153.020.23.260.20.280.20.390.20.190.20.150.23.040.253.280.250.310.250.420.250.210.250.170.253.060.33.30.30.330.30.440.30.230.3N/AN/A Data Table: (velocity vs time)Run #1Run #1Run #2Run #2Run #3Run #3Run #4Run #4Run #5Run #5Run #6Run #6Times (s)Speed (m/s)Times (s)Speed (m/s)Times (s)Speed (m/s)Times (s)Speed (m/s)Times (s)Speed (m/s)Times (s)Speed (m/s)2.870.983.090.690.141.010.240.850.061.210.011.012.931.43.161.240.191.420.31.320.111.570.061.422.961.723.21.590.231.730.341.650.141.860.11.742.991.993.231.870.261.990.371.920.162.110.131.993.022.223.262.110.282.230.392.160.192.330.152.433.042.433.282.330.312.460.422.370.212.530.172.623.062.633.32.520.332.60.442.590.232.72N/AN/A Graph: Distance (m) vs. Time (s) Graph: Velocity (m/s) vs. Time (s)Calculation:? ± ?g ? 9.8 ± 0.9 m/s2m ± ?m ? 84.4 ± 0.05 gF ± ?F ? 0.8 ± 0.073 N84.4g × (1 kg1000 g) = 0.08 kg F= m × a(unit) N= (kg) × (mss) F= (0.08 kg) × (9.8 (mss)) F= 0.8  (kgmss) F= 0.8 N?F= F(?m?mmm)+(?g?ggg)?F= 0.8((0.05)(0.05(84.4)(84.4))+((0.9)(0.9)(9.8)(9.8))?F= 0.073 NQuestions: Question 1. Looking at the data, you should notice that the time difference between successive data points is smaller and smaller the farther the picket fence falls. Why is this? The time difference between successive data point gets smaller and smaller as farther the picket fence falls is because of the gravity accelerates faster and faster. So as the picket fence drops the gravity pulls it faster and faster so the velocity will increase and the time will decrease.Question 2. How does the computer know the velocity when all it is measuring is time? Hint: what is the other part of the equation for average velocity? The computer knows the velocity because it is setup to measure the time, speed and position. Since the computer is measuring the speed which is also the distance, it can use the velocity formulas distance divide the change in time to get the velocity. Also the average velocity is calculated by ?s / ?t.Question 3. If we want the slope to be the acceleration, which variable, velocity or time, goes on the x-axis? Why? To have the slope as the acceleration the time goes as the x-axis and the velocity go on the y-axis.Question 4. Describe in words the shape of the velocity vs. time graph. (Does the slope stay constant? Is the Y-intercept zero?) The velocity vs. time graph is a straight linear line that the slope is constant and the y-intercept does not equal to zero.Question 5. Describe in words the shape of the distance vs. time graph for the free fall. How should this look (linear, quadratic, etc.)? The distance vs. time graph is quadratic because the equation for it is S=V0t + 1/2at2 the square on the a time t indicate the shape to be quadratic.Question 6. Look at your list of 6 slope values (i.e. acceleration values) and, in one or two qualitative sentences, report how reproducible your acceleration results appear (e.g. very similar values, widely varying from one trial to the next, etc.). The value of the six slope is reproducible and consistency, that the slope of the six trials is very close to each other.Question 7. Is your standard deviation low when compared to the value of your average? As a rough guideline, a standard deviation less than 10% of your average is OK (but the lower the better!). Does this standard deviation seem reasonable with what you put for your quantitative description of reproducibility in Question 6? This shows how standard deviation is a measure of reproducibility. The standard deviation of the six trials is 0.493488347 and the average of the trials is 8.960633333. Dividing the standard deviation by the average (0.493488347 / 8.960633333) = 0.055072932 which is about 5.5% and is less than 10% so my data shows that it is reproducible.Question 8. Looking at this equation, what would the standard deviation be if all of your measured values were the same? Explain. Looking at the equation if all the measure value were the same it would be zero because of the number very similar and is closer to each that (Xi-Xavg) will be near zero. Question 9. It is very useful to understand the effects of errors, both to prevent them and to account for unexpected results. When you drop the picket fence, the markers are perpendicular with the photogate beam. How your results be affected if the picket fence was dropped at an angle through the photogate? If the picket fence was drop at an angle some of the distance will we lose. That the photogate beam can’t read it at an angle it read the picket fence up and down.Question 10. Using calculus, how do you determine (1) velocity from position, and (2) acceleration from position? In calculus, velocity is the derivative of position and acceleration is the slope of velocity and the derivative of velocity or its rate of change. Results and Discussion: In conclusion, this lab is dropping the picket fence through the photogate and then it will calculate its speed, velocity and time. Then analyzing all the data through excel and plotting two graph the first graph is the velocity vs. time and the second graph is distance vs. time. The expected results were about 8.9 m/s2 and the actual value was 9.8 m/s2 which is relatively similar to earth gravity. Since the result came to similar, the slope (acceleration) is said to be reproducible and consistency with each other, that the number of my six slopes are relatively closed to each other. This experiment also proves that the object falling to earth will have experience relatively the same gravity due to acceleration. And that there are other sources of errors and precaution that affect my results to be more accurate. But overall my result seems to be reproducible and consistent.

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