IC-06 Acceleration due to gravity (Photo Gate)
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Aerospace Engineering
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Apr 3, 2024
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IC-06 - A
CCELERATION
DUE
TO
G
RAVITY
(P
ICKET
F
ENCE
AND
P
HOTO
G
ATE
) Rev 1-1-2023
6.1
OBJECTIVE
The purpose of this activity is to determine the acceleration due to gravity by
measuring the time of fall of a picket fence dropped through a photogate, as well as
by some other method.
6.2
EQUIPMENT
1.
Photogate
2.
Picket Fence (ME-9377A)
3.
Universal Table Clamp (ME-
9376)
4.
Science Workshop
5.
Capstone Software
6.3
THEORY
A freely falling object has a vertically downward acceleration. This is known as acceleration due to gravity and its values is almost the same all over the world. We start with the equations of motion for constant acceleration:
V = V
i
+ g
t
,
(1)
and Y = V
i t + (1/2)gt
2
(2)
Here, V
is the velocity of the object at time t
and V
i
is the initial velocity of the object (which is usually 0). ∆Y
is the distance traveled in time t
and g is the acceleration due to gravity. If V
i
is zero, from (1) we can write V = gt
(3)
And from (2) we can write
Y = ½ gt
2
(4)
From equation (3) we see that the graph of t vs V is a straight line and its slope is g. In the same way, from (4) we observe that the graph t vs ∆Y is a parabola. The graph t
2
vs ∆Y is a straight line and its slope is ½ g. Thus knowing the values of t, ∆Y, and V we should be able to find the value of g.
6.4
EQUIPMENT DESCRIPTION:
Picket Fence:
This is a clear plastic strip with uniformly spaced opaque bands at fixed distances.
Photo Gate:
The Photo gate has one Infrared beam. At the other side is a sensor that senses
the beams. When the beam is obstructed by an opaque object, a signal is sent to the Capstone
software. By noting the time the obstruction occurred and was removed, Capstone can calculate the position and speed of the moving object. With several obstructions of known size (as in the Picket Fence), the instantaneous velocity and acceleration can also be calculated. You do not have to calibrate the photogate.
6.5
PROCEDURE
Drop the “Picket Fence” through a Photogate. Each opaque band on the ‘Picket Fence’ blocks the Photogate beam and the time from one blockage to the next depends on the speed of the picket fence. Knowing the distance between the leading edge of each opaque band, the Capstone program calculates the average speed of the Picket Fence from one band to the next. The slope of the graph of average speed versus time gives the acceleration of the falling object.
PART I: Computer Setup
1.
Connect the Science Workshop interface to the computer, turn on the interface and then turn on the computer.
2.
Connect the Photogate’s stereo phone plug to Digital Channel 1 on the interface.
Click on Hardware Setup. A picture of the Science Workshop should appear. On the image of the Science Workshop, click at the slot where the Photogate has been attached. A dropdown list of equipment will open. Select “picket fence and photogate”. Close the Hardware setup by
clicking it again. Your instructor will show you the steps to follow.
PART II: Sensor Calibration and Equipment Setup
1.
The program assumes a 5 centimeter (0.05 m) spacing, leading-edge-to-leading-edge, for the opaque bands on the Picket Fence. Measure this distance on the picket fence. If you need to change the default setting to another value, double-click on the Photogate & Picket Fence icon in the Experiment Setup window to open the Sensor Setup window. Enter the correct value for the spacing of the opaque bands on your Picket Fence. Click OK to return to the Experiment Setup window.
2.
Set up the equipment as shown in Fig. 1. Mount the Photogate on the Pulley Mounting Rod. Turn the Photogate head sideways so that you can drop a Picket Fence vertically from above the Photogate and have the Picket Fence move through the Photogate’s opening without hitting it.
Trial Run of Data
1.
Before recording data for later analysis, experiment with the Photogate and Picket Fence by dropping the picket fence a few times and starting and stopping the program and looking at the graphs.
2.
Place a piece of foam, or a backpack or other cloth on the floor directly below the Photogate, so the Picket Fence has a soft place to land. 3.
When everything is ready, start recording data. Drop the Picket Fence vertically through the Photogate. Data recording begins when the Photogate beam is first blocked. Stop the recording once the Picket Fence has passed completely through the Photogate. 4.
Rescale the data to fill the Graph window. 5.
Erase your trial run of data.
PART III: Data Recording
1.
Prepare to drop the Picket Fence through the Photogate beam again. Hold the Picket Fence at one end between your thumb and forefinger so the bottom edge of the Picket Fence is above the Photogate beam.
2.
Start recording data and then drop the Picket Fence through the Photogate beam. The data collection will begin automatically when the Photogate beam is first blocked.
3.
After the Picket Fence passes completely through the beam, stop recording.
4.
Repeat a few times, and find the mean values of ‘g’. Figure 1: Right Way to Drop Picket Fence
Figure 2: Wrong Way to Drop Picket Fence
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6.6
ANALYZING THE DATA
Determine the value of ‘g’ by three methods: Velocity-Time graph, Position-Time graph, and Acceleration-Time graph:
1.
Set up your graph display so it shows the values of velocity on the Y-axis, and time on the
x-axis. If necessary, rescale the graph’s x- and y-axes to fit the data.
2.
Examine the plot of Velocity versus Time. This should be a straight line. The slope of the ‘best fit’ line for velocity versus time data is the value of ‘g’. Record your results. (Hint: In Capstone
, select ‘LINEAR’ from the ‘FIT’ menu to get the best fit line.)
3.
Now change the y-axis to Position. The data that you have already taken will now show as a position versus time graph. Examine the plot of Position versus Time. This should be
a parabolic curve. Draw the best fit parabola (y = Ax
2
+ Bx + C) through the data points. The value of ‘g’ will be 2A. Record your results. (Hint: In Capstone
, select ‘QUADRATIC’ from the ‘FIT’ menu to get the equation of the best fit parabola.)
4.
Now change the y-axis to acceleration. The plot of acceleration versus time will show large variations in ‘g’. Instead of plotting the line representing the data, find the average value of acceleration. Record your results. (Hint: In Capstone
, select ‘MEAN’ from the ‘STATISTICS’ menu to get the mean value) 5.
Repeat the experiment (i.e. drop the picket fence) four times. Find the average values of acceleration from each type of graph for the four runs and calculate the percent errors from the accepted value of ‘g’. 6.
Attach Capstone screenshots with your report.
6.7
OTHER METHOD TO FIND g
Devise and perform an experiment to measure the acceleration due to gravity by some other method. Devise the data sheet and write a short report on this part (theory used, procedure, results, conclusions, and possible errors). Keep this to one to two pages.
Extra Credit 5 points
: Determine and discuss the effect on the measured value of ‘g’ of increasing the data collection rate to 50 and 100 Hz.
6.8
IC-06 Acceleration due to gravity – Picket Fence
REPORT FORM
Trial 1
Trial 2
Trial 3
Trial 4
Mean
Value
along
row Percent
error
‘g’ from velocity versus time graph
‘g’ from the position versus time graph
‘g’ from acceleration
versus time graph
Overall mean value of ‘g’: ______________
Percent error in ‘g’: ___________
6.9
PRECAUTIONS
1.
Make sure that the Photo Gate is horizontal, and picket fence is vertical.
2.
When dropping the Picket Fence, hold it at the middle of the short edge with a finger and thumb, as shown in Fig. 1.
3.
Make sure that the picket fence does not hit the Photo Gate or any wire as it falls down.
4.
The Picket Fence should fall perpendicular to the IR beam of the Photo Gate.
5.
The Picket Fence may be dropped from a few to several cm above the Photo Gate.
6.
The Picket Fence should be dropped after Recording has started. You do not have to drop the Picket Fence at the same instant that Recording is started.
7.
Open Capstone AFTER connecting the Photo gate.
8.
When selecting data for curve fit, do not try to include the very last data points on either end.
6.10
REPORT SUBMISSION
Upload the following in the Report for this Lab:
Points in
report
1.
Completely filled up “Report Form”.
10
2.
Capstone Graphs (at least one for each type) showing curve fits.
3*5=15
3.
Other Method for finding ‘g’
10
4.
Sources of Error in this experiment.
5
5.
Discussion of your results / Conclusions. (Discuss the accuracy and precision of the results. Do you see any substantial difference between the results from different graphs?)
10
Total
50
6.11
ADDITIONAL INFORMATION
Using time of fall (2.35 min) https://www.youtube.com/watch?v=wBIydqBHFes
Using picket fence (1.26 min)
https://www.youtube.com/watch?v=RVtDqF_bHEg
Using picket fence (2:53 min
)
https://www.youtube.com/watch?v=VxpbyOsYj4o
6.12
POINTS TO THINK ABOUT
1.
What range of errors are “acceptable”?
2.
What are the most likely sources of error? 3.
Should each graph give the same result for ‘g’. If not why?
4.
Would the measured value of ‘g’ be different if the picket fence is dropped from different heights above the photogate?
5.
Would the value of ‘g’ change if the picket fence is dropped with an initial downward or upward velocity?
6.
Would it matter if the picket fence is tilted instead of being vertical?
7.
How does the system use the picket fence to get the required data?
8.
What error would be introduced in measurements of position, velocity and acceleration if the spacing between bands in the picket fence is more / less than the value in the software (5.00 cm)?
9.
Calculate the value of acceleration due to gravity from the data in the video:
https://www.youtube.com/watch?v=wBIydqBHFes
10. What are some other ways in which you can find the value of ‘g’?
11. Would the results be different if the picket fence were made of a denser material?
12. How can the accuracy of this experiment be improved?
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6.13
SAMPLE DATA
Trial 1
Trial 2
Trial 3
Trial 4
Mean
Value
along
row Percent
error
‘g’ from velocity versus time graph
9.72 m/s
2
0.8
‘g’ from the position versus time graph
9.72 m/s
2
0.8
‘g’ from acceleration
versus time graph
9.71 m/s
2
0.8
Sample Calculation:
Percent error in g = 100 x |9.8 – 9.72| / 9.8 = 0.82 = 0.8%