What is “Theoretical Acceleration” in this experiment, and how to derive it? 2. What is the average of “experimental accelerations” in this lab, and how to obtain percent difference with theoretical one?
What is “Theoretical Acceleration” in this experiment, and how to derive it? 2. What is the average of “experimental accelerations” in this lab, and how to obtain percent difference with theoretical one?
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1. What is “Theoretical Acceleration” in this experiment, and how to derive it?
2. What is the average of “experimental accelerations” in this lab, and how to obtain percent difference with theoretical one?
Transcribed Image Text:Procedure:
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0. NEVER MOVE THE RIDER ON THE
TRACK WITHOUT THE AIR SUPPLY
TO THE TRACK TURNED ON
(DOING
SO
WILL
CREATE
SCRATCHES AND FRICTION ON THE
TRACK)
1.
2.
3.
4.
6.
Make sure your air track is level. (How?
There is another way besides using a
level.)
7.
Raise the air track at the end with the single leg by placing two blocks under it; the
height of the blocks is h.
5. Repeat, with the rider moving up the ramp. Start with the rider at the top of the track
but start taking data after it bounces upward at the bottom.
Determine sine of the ramp by measuring h and H. Note that sin = h/H.
Measure the acceleration of a rider of mass M≈ 400 grams moving down the ramp
(see Appendix I, below). Your Instructor will demonstrate a "run" on the air track.
Determine the acceleration for each run by graphing velocity vs. time.
The acceleration is equal to the slope of this graph (see Appendix II, below).
From these two graphs, take the average of the two slope values as your
experimentally measured acceleration aexp. (The average will tend to cancel certain
systematic errors in the measurement.)
8. Compare the average acceleration aexp with the theoretical acceleration atheo
obtained from Equation (1). For g, use the local acceleration of gravity: g = 979.9
cm/s².
"Comparing" your experimental results with theory means computing the percent
difference between the experimental value and the theoretical prediction. This is
given by:
%Difference =
Experiment-Theory
Theory
-x100%
Transcribed Image Text:APPENDIX II: Determination of the Acceleration
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Create two plots of the rider's average velocity versus time: one graph for the downward run and a second
graph for the upward run. The acceleration is equal to the slope of the line obtained from plotting average
velocity versus time. If this line is a straight line (as it should be here) we conclude that the acceleration is
constant for the run. Therefore, the acceleration for each run in this experiment is obtained by
determining the slope of the straight line of the run. Check that your slope (rise/run) has units of
acceleration, (cm/s) / (s), or simply cm/s².
Your Instructor will assist you in graphing techniques. See "Supplementary Notes on Graphs, Errors and
Taking Good Data" for more information. As a minimum, every graph must have the following
information on it:
1. A graph title (preferably more informative than just reiteration of the axes)
2. A readable choice of scales must be chosen for each axis
3. The axes must be labeled
4.
The units for each axis must be shown next to the title axis
5.
Data should be plotted as a small point surrounded by a circle (or some other shape) so you can
find the point even after a line passed through it
6. The graph should be as large as possible, filling most of the page of your lab notebook
Note that your data points may not fall
exactly on a straight line, but instead may
have a random scatter about the line.
Draw the best-fit straight line through
your data as follows:
Compute the average of the time values and
average of the velocity values. Mark this
point on your graph and use it as a pivot
point. Then draw a straight line through the
pivot point that best matches the data points.
It is not necessary for the line to actually pass
through any of the data points. This line
represents your data from now on.
To find the acceleration, measure the slope
of the line. Do this by choosing two
positions on the line, but not actual data
points. These positions should be as far
apart as is practical, i.e., near the ends of the
line. Use the coordinates of these positions
to determine the slope of the line
(slope rise/run= Av/At = a). The result is
the measured acceleration for the particular
run. Once you have determined the slope
values, take the average of both slopes (from
your two graphs), and call this aexp.
Velocity in cm/sec
50
45-
40-
35-
30-
25
20
15
10-
5
0
Velocity vs Time for Sloped Air Track
0.2
0.4
23
0.6
D
Pivot Point
1.6 0.2 14 sec
slope
0.8
Time in seconds
36.0-8.5
= 27.5
cm/sec
= 27.5/14 = 19.7 cm/sec2
1.2
1.4
1.6
1.8
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