FVCC Physics Laboratory
Free Fall Acceleration
J.K. Boger∗†
January 23, 2011
1
Objective
In this experiment we will measure the rate at which an object freely falls and then
calculate the acceleration due to earth’s gravity from the data. This is the first lab
using LabQuestTM and Vernier photogates.
NOTE: Please handle the lab equipment very carefully as we need to
make these things last for years. Thanks.
2
Theory
Any object in free fall will accelerate with a common acceleration. This acceleration is
a consequence of earth’s gravitational attraction at its surface and is nearly constant
at all points on the map with a generally accepted value of 9.8 m/s2 . We will
time the rate at which an object falls to measure this. The simple idea is that a
transparent plastic plank is painted with black opaque strips measuring 2.5 cm wide
and separated by 2.5 cm. As the so called picket fence falls through the photogate,
∗
†
(406) 756-3989
jboger@fvcc.edu
1
3 PROCEDURE
2
an electronic timer measures the time the gate is ’blocked’ and ’unblocked’. Since
you know the distance between the blocked state and the unblocked state (2.5 cm),
then you can use the measured time to calculate velocity. Doing this for a series of
bars (thus the picket fence), you can measure change in velocity which is of course
acceleration. Since the only force acting on the falling object is earth’s gravity, the
measured acceleration will be g. It is assumed that the air resistance is negligible in
this experiment.
3
Procedure
The procedure for doing this is contained the manual ”Physics with Vernier” and the
lab title in that manual is ”Picket Fence free fall”. Use that manual for details on
collecting data with the LabQuestTM data acquisition device. This write up guides
you for the FVCC version of the experiment.
3.1
Equipment
The basic equipment for this experiment is as follows:
1
2
3
4
5
3.2
LabQuest
Vernier Photogate
Lab stand
Pad to protect picket fence on impact with ground
USB thumb drive to port data to computer with Excel or equivalent
Collect & Process Data
The book assumes you will analyze the data on logger pro, which is Vernier software.
FVCC does not have this software so we will copy the raw data into a text file
(using export file) and read that file into Excel. Excel can open the text file as a tab
delimited file. You will do your data analysis in Excel.
1
2
3
4
Set LabQuest to collect datan with Photogate set to ”Picket Fence”
Keep the data collection number at 16 which is its default
Be certain the picket fence has a soft spot to land when dropped. (Or
catch it)
Collect data by dropping the picket fence through the photogate at least
6 times. The file drawer icon allows you to save individual runs.
3 PROCEDURE
3
0.4
3
0.35
2.5
0.3
y = 4.8946x2 + 1.1712x - 0.0002
R =1
0.25
Velocity (m/s)
Distance (m)
2
0.2
0.15
2
1.5
y = 9.812x + 1.1688
2
R =1
1
0.1
0.5
0.05
0
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (sec)
(a) Position Vs. Time
0.18
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Time (sec)
(b) Velocity Vs. Time
Figure 1: Example data plots with best fit lines shown
5
6
7
8
9
10
Transfer data by USB to computer or use USB thumbdrive. Use ”Export
Data” on Labquest.
Copy data onto computer. Open file with Excel. The file is a tab delimited
text file. Open file, then choose tab delimited. Excel will list all data
sequentially.
Use Excel to plot velocity verses time. The plot should be a straight line.
Use linear regression or Excel’s trendline option to find the slope of the
line. This is your determined value for g.
Use Excel to plot distance verses time. Note that distance values are
recorded only for 5 cm intervals, making your raw data look as though
every other distance value is missing. You can fill in the data so that
distance is given in 2.5 cm intervals. This will match the number of time
values in the raw data.
Use Excel’s trendline feature to match a parabola to the raw data. Read
the value of g from the resulting equation which Excel will display if the
option is checked to do so.
Examples of the plots you need to make from your data are given in ?? and ??.
In these plots, actual data from the experiment is plotted and a trendline is fitted to
the data. This is Excel’s method of regression analysis.
3 PROCEDURE
3.3
1
2
3
4
5
6
7
8
Reporting results
Average the accelerations calculated by LabQuest and report that value
at computed acceleration due to gravity.
Average the accelerations from the slope of the velocity vs. time plots
and report that as linear slope acceleration due to gravity.
Average the accelerations from the curve fit of the distance vs. time plots
and report that as polynomial fit acceleration due to gravity.
Compare each of these results to the accepted value of 9.8 m/s2
Which is more accurate, and why?
Using your data, estimate the initial velocity of the picket fence when it
enters the photogate for each run.
Knowing the initial velocity, calculate how far above the photogate the
picket fence had been upon release.
Comment on whether or not your height estimates are accurate.
Revision date: January 23, 2011
4