Acceleration of Gravity Lab

Acceleration of Gravity Lab

Lab Partners :  Kevin Hilario, Becca Causey, and Raychel Kolofske

Purpose : 

To determine the acceleration of gravity for a freely falling object, and to gain experience using the computer as a data collector. (We have to be able to determine the acceleration due to gravity by observing an object in free fall, and practice recording data using the computer's data collector.)

Equipment Needed :

• 1 Windows based computer with the Logger Pro software

• 1 Lab Pro interface

• 1 motion detector

• 1 rubber ball

• 1 wire basket

 Procedure :

1.  Connect the lab pro to computer and motion detector to DIG/SONIC2 port on lab pro. Turn on the

computer and load the Logger Pro software by double clicking on its icon located within the Physics

Apps 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, first select File/Open and then open the mechanics folder. 

When this folder opens, open the graphlab file.

2.  You should see a blank position vs. time graph.  The vertical scale (position axis) should be from 0 to 4m while the horizontal scale (time axis) should be from 0 to 4 s.  These values can be changed if you desire 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 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 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 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.  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 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 t^2+ b t + 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.  Give a physical interpretation and the proper units for each of these quantities (Hint: use unit analysis).  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/s^2).

  

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.  Why

does the curve have a negative slope?  What does the slope of this graph represent?  Determine the slope from a linear curve fit to the data.  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 (Hint: use unit analysis). 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. Finally, select Experiment/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.

Results:

Position vs Time Graph w/ best fit Parabola

Velocity vs Time Graph w/ best fit Line

%Difference Spreadsheet for 5 Trails

Motion Diagram for Position vs Time

We labeled the origin and the positive direction. Also, we showed the direction of acceleration. Where the purple arrow is, it shouldn't say a=0, but say v=0 instead. On the left side it shows that the ball is decreasing in motion in the positive direction. On the right side, the ball is moving in the negative direction and is increasing. The point where there is a break in the motion diagram, connected by the pink, dashed,curved line, is where v=0 because there is the point where the ball begins to descend.

Conclusion:

In this lab we found the velocity and acceleration from the path of a ball being tossed in the air. With those we found the difference in what we found and what is actual. Nothing was perfect, because a ball thrown by a person can not be a perfect parabola. That is why we did more than one trial so that we can  get as close to perfect as possible. For all of the velocity, the differences were less than four percent. However, over all the difference for acceleration beat velocity except for one trial. Trials 2-5 were all less than four percent as well. The first trial was less than seven percent. Trial five for acceleration was less than one percent leaving it to be the best over all.