Acceleration of Gravity

Objectives:

1. To determine the acceleration of gravity for a freely falling object.
2. To gain experience using the computer as a data collector.

Materials:

1. Windows based computer
2. LabPro interface
3. LoggerPro software
4. Motion detector
5. Rubber ball
6. Wire basket

Procedure:

1. Gather the necessary materials and then proceed to connect the LabPro to the computer and the motion detector to the DIG/SONIC2 port on the LabPro. Turn on the computer and load the LoggerPro software by double clicking on its icon located within the PhysicsApps folder. A file named graphlab will be used to set up the computer for collecting the data needed for this experiment. To open this file, select File, Open, and then open the mechanics folder. When this folder opens, open the graphlab file.
2. Upon opening the file, you should see a blank position vs. time graph. The y-axis (position axis) should be from 0m to 4m while the x-axis (time axis) should be from 0s to 4s. 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. Enter in the desired numbers and push the Enter key.
3. Place the motion detector on the floor, facing upward, and place the wire basket (inverted) over the motion detector to protection the detector from the impact of the falling ball. Check to see that the motion detector is working properly by holding the rubber ball about 1m above the detector. Click the Collect button to begin taking data and then move your hand up and down a few times in order to 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 the equipment does not seem to be working properly, seek assistance from the instructor.
4. Give the ball a gentle toss straight up from a point about 1 meter above the detector. The ball should rise 1 or 2 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 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.
5. Select the data in the interval that corresponds to the ball in freefall by clicking and dragging the mouse across the parabolic portion of the graph. Release the mouse button at the end of this data range. Any later 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 a quadratic function [t^2+ b t + c] 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. Use unit analysis to give a physical interpretation and the proper units for each of these quantities. Find the acceleration, g_exp, of the ball from this data and calculate the percent difference between this value and the accepted value, g_acc, (9.80 m/s2).
6. Look at a graph of velocity vs time for this motion by double clicking on the y-axis label and select “velocity” and deselect “position”. Examine this graph carefully. Explain (relate them to the actual motion of the ball) the regions where the velocity is negative, positive, and where it reaches zero. Determine the slope from a linear curve fit to the data. Use unit analysis to find the values of m and b that best fit the data. Give a physical interpretation and the proper units for each of these quantities. 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. Finally, select Experiment, then Store Latest Run to prepare for the next trial.
7. Repeat steps 4 - 6 for at least five more trials. Obtain an average value for the acceleration of gravity and a percent difference between this value and the accepted value.
8. Obtain a printout of one representative graph for position vs time and velocity vs. time and include this in your lab report. Put both graphs on a single page.
   
   Conclusion:
   
   The purpose of this lab was to discover through observation and measurement the constant we know to be gravity (g) of roughly -9.8 m/s^2. Human error is the source of any discrepancies in data. Considering I worked by myself, I do not think I did so poorly. Shout out to Tito for helping me set it up.