APHY 145 Lab 2 (F2020) Linear motion 1 Linear motion Summary Using the data from the motion sensor (Fig. 1), make plots of position and velocity as functions of time, and compare different ways of calculating velocity. Theory For one-dimensional motion in a straight line, the displacement Δ is the net distance traveled during a specified time interval: Δ = − 0, (1) where 0 is the starting location, and is the final location. The average velocity v is = Δ Δ = − 0 − 0 , (2) where t is the elapsed time. For a constant velocity v, the final position is = 0 + Δ. If the velocity is not constant, there is non-zero acceleration. The average acceleration a has the same relationship to velocity as velocity has to displacement: = Δ Δ = − 0 − 0 . (3) Reference Serway & Jewett, “Physics for Scientists and Engineers,” Chapter 2. Color key for online labs The online versions of APHY 145 labs are based on the in-person versions and may retain most of the original lab instructions, regardless of whether you are performing the actual experiment. Green text highlights commentary to help you understand the lab or how to write your report. Blue text highlights key steps of the lab process that you should read carefully. Red text highlights steps important to recording data in Excel data sheet. Online vs. in-person For this experiment, the data has already been collected; your task is to carefully analyze it. Equipment Linear motion sensor LabPro interface Note: sonic ranger motion detector The motion detector emits short bursts of ultrasonic sound waves. Each burst is accompanied by a clicking sound from the detector. The computer calculates the distance from the time it takes an echo to Figure 1. Motion sensor. APHY 145 Lab 2 (F2020) Linear motion 2 return to the detector. The sound waves emitted from the detector fill a cone of about 20, as shown in Fig. 2. Stationary objects (stools, tables, lab partners) within that cone will cause echoes that interfere with the reading. The range of the detector is 0.5 - 2 m. Objects closer than 0.5 m or farther than 2 m away may not be detected. Procedure 1. SET UP Purpose: to test that the detector does not get interference from nearby sources. The motion detector should be plugged into the LabPro interface attached to the computer. Open the “Experiments” folder on the desktop, and click on the file “LinearMotion.” Place the motion detector on the edge of a table. Standing about 1 m away from the detector, click “Collect.” After 5 seconds, move to the point 2 m away. Verify that the graph of position vs. time displayed on the computer screen shows you starting at 1 m and ending at 2 m. Troubleshooting: occasionally the Logger Pro software cannot find the detector. Make sure everything is connected and powered, and restart the software. 2. WALKING AWAY SLOWLY Purpose: to produce constant velocity data and calculate average velocity in three different ways. 2.1 Position vs. time data Standing about 0.5 m from the detector, click “Collect,” and walk slowly and steadily, at a constant velocity, away from the detector. Your graph of position as a function of time should be close to a straight line. Practice a few times until it does. 2.2 Average velocity: manual slope calculation Using Screenshot 1 (at the end of this manual), read the time and position for the three pairs of data points: at 9 s and 1 s, 8 s and 2 s, and 7 s and 3 s. In this step, use the orange dots (data points), not the black fit line. Do your best to read the plot as accurately as possible. Record these measurements in an Excel spreadsheet. Calculate the change in position and time for each pair of points, and find velocity v (slope) for each pair using Eq. 2. Calculate the average velocity and its uncertainty (standard error) for all three trials. The standard error for n trials is = /√, where σ is the standard deviation of the set. 2.3 Average velocity: linear fit Another way to find the velocity is to fit the position vs. time curve to a straight line. Select a relatively straight portion of the data and use the Curve fitting icon to find the slope and its uncertainty. To fit a line, select “y = mt + b”. Click on “try fit,” then “Ok”. A box with the intercept, slope and uncertainties will appear. Read the average velocity and its uncertainty from the Linear Fit box shown in Screenshot 1. Record the results in your spreadsheet. detector Sound waves cone 20 Object being measured Figure 2. Sonic ranger motion detector. APHY 145 Lab 2 (F2020) Linear motion 3 2.4 Average velocity: velocity vs. time plot Change the graph to plot velocity vs. time. Click on the word “Position” on the y-axis. After a menu appears, select “Velocity” from the list. Select the linear portion of the time range and deploy the Statistics tool . Using the information provided in the Statistics box in Screenshot 2, determine the average (mean) velocity and its uncertainty (standard error). Record your results. Change the graph back to position vs. time. 3. WALKING AWAY QUICKLY Purpose: to compare the graphs for high and low velocity data. 3.1 Position vs. time data Repeat Section 0, but walk faster. 3.2 Average velocity Screenshot 3 employs one of the methods from Section 2 to find the average velocity and its uncertainty for the new data set. Record both the method and the measured value in Excel. 4. WALKING FORWARD Purpose: to compare the graphs for positive and negative velocity data. 4.1 Data Repeat Section 0, but start 2 m from the detector and walk towards it (either fast or slow). 4.2 Average velocity Screenshot 4 employs one of the methods from Section 2 to find the average velocity and its uncertainty for the new data set. Record both the method and the measured value in Excel. Lab Report Questions 1. What are the average velocities calculated in Section 2 by three different methods? Do they agree with each other within uncertainty? Which method do you judge the most precise, and why? If you have calculated uncertainties for a particular value, always report them as part of your results. Values agree within uncertainty if there is an overlap between their ranges. 2. Compare the slopes of the graphs in Sections 2 and 3 of the lab: which one is greater? Do the values make sense based on the type of motion observed in these experiments? Answer lab questions in complete sentences. 3. Compare the slopes of the graphs in Sections 2 and 4 of the lab: which one is greater? Do the values make sense based on the type of motion observed in each experiment? Remember that a negative value is smaller than a positive one. Lab reports (including Excel data sheets) should be submitted via Blackboard and have due dates listed on Blackboard. Use the data provided below to create your Excel sheet and lab report. APHY 145 Lab 2 (F2020) Linear motion 4 LAB DATA (provided as screenshots of LabPro interface) Screenshot 1 (Sections 2.2 and 2.3) Screenshot 2 (Section 2.4) APHY 145 Lab 2 (F2020) Linear motion 5 Screenshot 3 (Section 3) Screenshot 4 (Section 4)
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