Introduction
The purpose of this lab was to determine the acceleration of gravity for a freely falling object and to gain experience using the computer as a data collector. We used the computer to collect
some position (x) vs time (t) data for a ball tossed into the air. Since the
velocity of an object is equal to the slope of the position vs time curve, the computer can also construct the graph of velocity vs time by calculating the slope of position vs time at each point in time. We will use both the position vs. time graph and the velocity vs. time graph to find the free fall acceleration of the ball.
Data
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Trial 3
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Trial 5 |
Calculations
Position (m) vs Time (s)
Trial 1
x=At^2+Bt+C
x=(-4.863^2)+(7.7)t-(1.3)
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(2A-0.5*9.8)/ 0.5*9.8] x 100%
percent error = [((2*4.863)-9.8)/ 9.8)] x 100%
percent error = -2.04%
Trial 2
x=At^2+Bt+C
x=(-4.718^2)+(8.7)t-(2.2)
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(2A-9.8)/9.8] x 100%
percent error = [((2*4.718)-9.8)/ 9.8)] x 100%
percent error = -3.71%
Trial 3
x=At^2+Bt+C
x=(-4.703^2)+(7.7)t-(1.6)
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(2A-9.8)/9.8] x 100%
percent error = [((2*4.703)-9.8)/ 9.8)] x 100%
percent error = -4.02%
Trial 4
x=At^2+Bt+C
x=(-4.804^2)+(7.9)t-(1.8)
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(2A-9.8)/9.8] x 100%
percent error = [((2*4.804)-9.8)/ 9.8)] x 100%
percent error = -1.95%
Trial 5
x=At^2+Bt+C
x=(-4.708^2)+(7.821)t-(1.496)
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(2A-9.8)/9.8] x 100%
percent error = [((2*4.708)-9.8)/ 9.8)] x 100%
percent error = -3.91%
Velocity (m/s^2) vs Time (s)
Trial 1
y=mt+b
t = time
m = slope
b = y-intercept
y=9.885t+7.87
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(m-9.8)/9.8] x 100%
percent error = [(9.885-9.8)/ 9.8)] x 100%
percent error = 0.86%
Trial 2
y=mt+b
t = time
m = slope
b = y-intercept
y=9.892t+8.835
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(m-9.8)/9.8] x 100%
percent error = [(9.892-9.8)/ 9.8)] x 100%
percent error = 0.94%
Trial 3
y=mt+b
t = time
m = slope
b = y-intercept
y=9.306t+7.609
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(m-9.8)/9.8] x 100%
percent error = [(9.306-9.8)/ 9.8)] x 100%
percent error = -5.04%
Trial 4
y=mt+b
t = time
b = y-intercept
y=9.886t+8.219
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(m-9.8)/9.8] x 100%
percent error = [(9.886-9.8)/ 9.8)] x 100%
percent error = 0.877%
Trial 5
y=mt+b
t = time
m = slope
b = y-intercept
y=9.449t+7.825
percent error = [(measured - actual)/(actual)] x 100%
percent error = [(m-9.8)/9.8] x 100%
percent error = [(9.449-9.8)/ 9.8)] x 100%
percent error = -3.58%
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Results from Falling Body Experiment
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Trial | gexp (2a)(m/s^2) | % diff | gexp (m)(m/s^2) |
% diff2
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1 | 9.726 | -2.04 | -9.885 |
0.86
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2 | 9.436 | 3.71 | -9.892 |
0.93
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3 | 9.406 | -4.02 | -9.306 | -5.04 |
4 | 9.608 | -1.95 | -9.886 | 0.87 |
5 | 9.416 | -3.91 | -9.449 | -3.58 |
Conclusions
In this lab we used logger pro software and logger pro interface to record the accelaration of gravity on a rubber ball. We simulated the ball falling on top of the motion detector with a wire basket on top of the motion detector (for protection) From this lab we concluded that the acceleration of gravity is 9.8(m/s^2) by taking of the acceleration from the position vs time parabola graphs multiplied by 2, from the equation by taking the average slopes of the velocity vs time graphs of y=mx+b where m = slope. The slope is the acceleration of gravity.
Hi Edwin,
ReplyDeleteThanks for this nice lab write up. I think you may have included the data table twice by accident.
The % differences look very good --
In the future though you do need to include all the data collected in a table, you only need to show a few representative data plots with fits.
You do a very nice job showing all the sample calculations; again just a couple are necessary for future write ups.
Make sure in the future you include a discussion of errors in your conclusions as well as answer all the questions posed in the lab. For instance, in #5 you are asked to use unit analysis to interpret the quantities in the equation used to fit the data ... I don't see you've included that in your report. For the future be sure to include the answers to questions like that for full credit.
grade == s