Lab 5 Acceleration of Gravity-1-1

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San Francisco State University *

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Physics

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Apr 3, 2024

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Acceleration of Gravity Purpose: 1. To determine the acceleration of gravity for a freely falling object 2. To gain experience using the computer as a data collector. Equipment: Windows-based computer, Lab Pro interface, Logger Pro software, motion detector, rubber ball Introduction: In this laboratory, you will use the computer to collect some position (x) vs time (t) data for a rubber ball tossed into the air. Since the velocity of an object is equal to the slope of the x vs t curve , the computer can also construct the graph of v vs t by calculating the slope of x vs t at each point in time. In this experiment, we will use both the x vs. t graph and the v vs. t graph to find the free-fall acceleration of the ball. Procedure: 1. Connect the lab pro to the computer and motion detector to the DIG/SONIC1 port on the lab pro. Open the Vernier software. 2. You should see two blank graphs—one of position vs. time and the other of velocity vs time . A couple of changes are needed to make the graphs fit today’s experiment. Configure the vertical scale of the position axis so that it runs from 0 to 2 m while the horizontal scale (time axis) should be from 0 to 4 s. These values can be changed by pointing the mouse at the upper and lower limits on either scale and clicking on the number to be changed. Type in the desired numbers and push the Enter key. Change the velocity axis's minimum and maximum values to +5 m/s and -5 m/s respectively. The time axis for this graph should also run from 0 to 4 s. Finally, change the length of the data collection time to 4 s by selecting Experiment/Data Collection on the menu bar and entering 4 s in the length box. Click “Done” to close the Data Collection window. 3. Place the motion detector on the floor facing upward and place the basket (inverted) over the detector for protection from the falling ball. Check to see that the motion detector is working properly by holding the rubber ball about 1 m above the detector. Have your lab partner click on the Collect button to begin taking data and then move your hand up and down a few times and verify that the graph of the motion is consistent with the actual motion of your hand. After 4s the computer will stop taking data and will be ready for another trial. If your equipment does not seem to be working properly ask for help. 4. Give the ball a gentle toss straight up from a point about 1 meter above the detector. The ball should rise to 1 m above where your hand released the ball. Ideally, your toss should result in the ball going straight up and down directly above the detector. It will take a few tries to

perfect your toss. Be aware of what your hands are doing before and after the toss as they may interfere with the path of the ultrasonic waves as they travel from the detector to the ball and back. Take your time and practice until you can get a position-time graph that has a nice parabolic shape . Why should it be a parabola? 5. Select the data in the interval that corresponds to the ball in free fall by clicking and dragging the mouse across the parabolic portion of the position graph. Release the mouse button at the end of this data range. Any data analysis done by the program will use only the data from this range. Choose Analyze/Curve Fit from the menu at the top of the window. Choose At 2 + Bt + C (Quadratic) and let the computer find the values of A , B , and C that best fit the data. If the fitted curve matches the data curve, select Try Fit . Click on OK if the fit looks good. A box should appear on the graph that contains the values of A , B , and C . Record these values. Give a physical interpretation and the proper units for each of these quantities (Hint: Compare with the motion equation: x f = x i + v i t + ½ at 2 ). In other words, what do the constants A, B, and C that you found correspond to? Find the acceleration, g exp , of the ball from these data and calculate the percent difference between this value and the accepted value, g acc , (9.81 m/s 2 ). 6. Look at the graph of velocity vs time just below the position graph. Examine this graph carefully. Explain the regions where the velocity is negative, positive, and where it reaches zero by relating these regions to the position graph at the corresponding times. Why does the curve have a negative slope? What does the slope of this graph represent? Determine the slope from a linear curve fit (select Analyze/Curve Fit and choose linear fit ) to the data. Record the values of m and b that best fit the data. Give a physical interpretation and the proper units for each of these quantities (Hint: compare with the motion equation: v f = v i + at). In other words, what do the slope and the intercept correspond to? Find the acceleration of the ball, g exp , from this data and calculate the percent difference between this value and the accepted value, g acc . Put together an excel spreadsheet for your data like the one shown below. Falling Body Results Table Trial g exp (from position graph) m/s/s % error g exp (from velocity graph) m/s/s % error 1 2 3 4 5 Average

7. Repeat steps 4 - 6 for at least four more trials. Obtain an average value for the acceleration of gravity from all of your data and a percent difference between thi value and the accepted vale. Present this information in your conclusion. % error = | g exp − g acc g acc | × 100% 8. Your lab report shows at least one representative graph for position vs time and velocity vs. time. Put both graphs on a single page (one under the other).

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