Acceleration of Gravity

Tuesday August 28,2012

Purpose: To determine the acceleration for a freely falling object.
               To gain experience using the computer as a data collector.

Lab Equipment: Windows based computer, lab pro, logger pro software, motion detector, rubber ball and wire basket.

Procedure:
1. Connect lap pro to the computer and the motion detector to lab pro. turn the computer on and load logger pro software. open the graphlab file on the mechanics folder.
2. There will be a blank position vs time graph. the position axis is set 0 to 4m (meters) the time axis is set 0 to 4s (seconds). these could be changed if need be.
3.Now we placed the motion detector on the floor and we started to test out the equipment by doing trial ball tosses 1m above the detector. it takes a few tries to get a nice parabola on the computer.
why is it a parabola? because the ball is going up, evens out then comes down, gravity is the only thing acting on the ball after it leaves the hand.
4. Select the data in the interval. analyze/curve fit the data and chose quadratic t^2+bt+c and let the computer find values of a, b, and c that best fit the data. select try fit, a box will appear that contain the values of a,b,c.

                                                                    Trial 1 position vs time
5. 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 the velocity vs time graph.

                                                                   Trial 1 velocity vs time
why does the curve have a negative slope? because acceleration is negative.
what does the slope of the graph represent? change in velocity but acceleration stays the same.
determine the slope  from a linear curve fit to the data. find values of m and b that best fit the data.
find the acceleration of the ball g exp find percent difference between this and accepted value g acc.
put together a spread sheet of the data.
7. we did 5 trials and calculated the percent error by
                            percent error   =  measured-actual
                                                                 actual               X  100%

                                                    a,b,c and m,b values for all 5 trials
                                         
                                                 Results from Falling Body Experiment

 Errors: motion of the hands after releasing the ball can cause interference with the motion detector.
             the motion detector being not being on a level surface and the wire basket also interfering
             with the ultrasonic waves.

Conclusion: one of the purposes was to gain experience using the computer as a data collector, that
                    was accomplished by doing all of trials in the lab and by analyzing the data and
                    performing curb fit and by finding the values of a,b,c in quadratic and m,b in linear.
                    the other was to determine the acceleration of gravity for a freely falling object, that
                    was accomplished by the calculations of the results of our trials of the ball toss.
                    the percent difference between the acceleration of the trials and the accepted value
                    of acceleration were minimal thus proving that 9.80m/s^2 is free fall acceleration.
                    our trials acceleration was negative because the slope was negative.

Graphical Analysis

Tuesday August 21,2012

Purpose: To gain experience in drawing graphs and in using graphical software.

Lab Equipment: Computer, graphical analysis, lab pro interface, logger pro software, motion detector, rubber ball, wire basket.

Procedure:
1. we turned on the computer and logged in
2. opened the physics apps folder > loaded graphical analysis. there's a text, data, graph window.
    any can be closed and opened at nay time.
3. click file > open > physics > functionplot
    it shows a graph of a function and the data used to create the graph.
4. we chose a function of our own and it must include a title, x and y axis and units
    our function was y= - cos^2 x

5. our graph with title and its labels.
6. then we connected the motion detector to the computer and loaded logger pro and began to graph
    lab. we practiced recording pos vs time graphs by dropping the rubber ball on motion detector        protected by the wire basket. once a nice curve was achieved we did a curve fit.

                                                                x = At^2 + Bt + C
                                                                x = -4.948t^2+ 14.16 - 9.04
   we had to confirm the distance fallen was      d alpha gt^n where g= 9.8 m/s^2
   the acceleration due to gravity.
   what is n in this equation? it is 2 because its a quadratic equation.
7. verify the equation using dimensional analysis and unit analysis.
    m = m / s^2
    [L][T]^2 / [T]

Errors: possible errors include the motion detector not being on a level surface, the basket getting in the way of the detector, body movements after the drop of the ball.
Conclusion: The purpose of this lab was to gain experience in using graphing software. I believe that was achieved because of setting up the lab and practicing gathering data with the motion detector, and being able to analyze the data and curve fit. With the data collected, we were able to test that the acceleration due to gravity is at of 9.8m/s^2.