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PHY 133 Lab 2 ­ Acceleration [Stony Brook Physics Laboratory Manuals]
Stony Brook Physics Laboratory Manuals
PHY 133 Lab 2 - Acceleration
The purpose of this lab is to measure the gravitational acceleration constant g by measuring the rate at which a falling object
increases its speed. You will also learn how to use the computerized lab equipment and motion-tracking program called LoggerPro,
which you will use for future labs in this course.
Equipment
computer for taking and recording data
photo gate (combined light source and detector assembly)
interface box
clear plastic ruler with periodic opaque regions made with masking tape
Measurement of the gravitational acceleration g by measuring velocity vs. time
In this lab, you will drop a ruler through a photo gate. From this we can infer the rate at which the ruler will accelerate due to the
earth’s gravitational force. The clear plastic ruler is covered at regular intervals with pieces of masking tape that block the light beam
of the photo gate. The detector in the photogate creates light “on” and light “off” signals that turn on and off a timer run by
computer software. The times are recorded by the computer and displayed on the monitor. Using the distance between successive
pieces of masking tape and these times, the computer will perform the calculation of the average velocity of the ruler in these time
intervals during its fall. The results can be displayed graphically on the monitor in various instructive ways.
Using the photogate and computer
We need to determine the length d between the leading edges of two successive pieces of tape, i.e., the length of one piece of tape
and the clear space following it.
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To be more accurate, you can take an average of many of these distances. To do this, measure the distance D from the leading edge
of the first piece of tape to the leading edge of the last piece of tape on the ruler. If there are N such “picket pairs” (tape + clear
space) on your ruler, you find the average value of d by diving the total distance D by the number N of “picket pairs”: d
=
D
N
.
After measuring D and calculating your average d value, you need to estimate their uncertainties. Things you should take into
account are the accuracy of your measurement tool, and how straight your masking tape is. Having estimated your uncertainty in the
measured value of D, you can find the uncertainty in your calculated value of d by noting that because d = D , the uncertainty in d
N
is Δd
= Δ(
D
N
) =
ΔD
N
, since N is a constant.
To prepare your setup for data collection, connect the photogate output wire to the interface box by plugging the cable from the
photogate into the top socket (labeled “DIG/SONIC 1”) of the interface box (called “LabPro”). Test the photogate: block/unblock
the photogate light beam with your finger, and you should see the red light on the cross bar of the photogate turn on/off.
Now, prepare the computer for data taking:
Turn on the computer and check the system by doing the following. On the Desktop, double-click the icon labeled
“Exp2_xva_t,” which should open the LoggerPro file for this lab. The file should open in a new window, with a spreadsheet
on the left (having columns for “Time,” “State,” “Distance,” “Velocity,” “Acceleration”) and 3 blank graphs on the right (one
for distance vs. time, velocity vs. time, and acceleration vs. time). A “Sensor Confirmation” window should appear, and you
should select “DIG1 on LabPro: 1” and “Photogate,” then click “Connect.”
To ensure that the photogate is connected properly, do the following. Under the “Experiment” tab at the top of the
LoggerPro window, go to “Set Up Sensors,” then click “Show All Interfaces.” A window should appear with a picture of the
interface box. On the top-right, under “DIG/SONIC 1,” check that an icon of a photogate appears, reading
“Blocked/Unblocked” when you pass your finger through the photogate. If this happens, then the photogate is connected
properly.
To input your value of d (the distance that LoggerPro associates with the photogate times to calculate velocity and
acceleration of the falling ruler), under the “Data” tab in LoggerPro, click “User Parameters.” A window should appear with a
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row labeled “PhotogateDistance1.” Enter your value of d (with units in meters “m”), and click “OK.” Not inputting your
value of d will cause the LoggerPro calculations to yield incorrect velocity and acceleration values!
Now you should begin collecting your data.
1. For each trial, hold the ruler steady slightly above the photogate beam, and perpendicular to the beam, then click the green
“Collect” button at the top of the LoggerPro window.
2. Once the “Waiting for data” text appears, release the ruler so that it falls straight downward, perpendicularly through the
beam, without twisting in the air. If you do this well, each piece of tape on the ruler will block the photogate beam, and each
clear space will allow the beam to pass through. (In the “State” column on the LoggerPro spreadsheet, a value of “1”
indicates that the photogate is blocked, and the following value of “0” indicates that the beam is no longer blocked.) Make
sure that the ruler is oriented perpendicular to the photogate beam during its entire fall, without twisting; otherwise, you
should repeat the trial.
3. After the ruler has fallen through the photogate, you should see the collected data on the screen: the Time, State, Distance,
Velocity, and Acceleration columns will fill with values. Push the red “STOP” button at the top of the LoggerPro window to
stop collecting data.
4. Make sure that there are at least 6 pairs of State “1” and State “0” values, corresponding to the pairs of tape and spaces on
your ruler. If there are too few measurements for this trial, then repeat dropping the ruler until a “good” data set is taken. (A
“good” data set should show an exponentially increasing distance plot, a linear velocity plot, and a roughly constant
acceleration plot.)
5. Copy the spreadsheet values for this trial into your lab notebook, and sketch the graphs of distance vs. time, velocity vs. time,
and acceleration vs. time into your notebook as well. In your lab report, you should show these sketches, and explain why
each indicates the motion of a dropped object freely falling to the ground.
Using a graph to find the value of g
We are now going to make a plot of velocity vs. time (v vs. t ) to determine the value of acceleration due to gravity g. In this plot, we
need to have estimates for our uncertainty in v. The uncertainty in v comes from the uncertainty in your measurement of the
d
distance d on the ruler. Given that v = t , and assuming that the photogate is extremely precise so that there is no uncertainty in
time t , you should be able to calculate the uncertainty in v using the multiplication/division rule from the uncertainty guide. Doing
this, you should find that the uncertainty in each value of velocity is Δv
= v(
Δd
d
. So, when plotting v vs. t , you should have
)
error bars on your data points along the vertical axis (v) , but no error bars along the horizontal axis (t). Using the Plotting Tool to
plot your data, then, you do not need to enter anything into the x error boxes and you should select the option that there are errors
only in y. Do you think this graph should go through the origin at (0,0) (or, in other words, at t = 0 , should we have v = 0 )? If
so, you can check the box to constrain your linear fit to pass through the origin as well.
Make your plot of v vs. t using the Plotting Tool. The slope of the graph should be equal to the acceleration of your ruler, or the
acceleration due to gravity, g. The Plotting Tool linear fit should also give the uncertainty in the slope, which is your uncertainty
2
(Δg) in your estimate of g . How does the value you obtain compare to the accepted value of 9.81 m/s ? Is your estimate and its
uncertainty consistent with this value?
A different approach to getting g and its error
In the approach taken above, you estimated the uncertainty in a single estimate of g based upon the propagation of what we
expected to be the most significant source of experimental error. Another approach you can take is to make several measurements,
collect many estimates, find their mean value, and then find the standard deviation (uncertainty) in that mean value. You can collect
several estimates of g quickly by using the built-in fitting tool in the LoggerPro program. This tool, unlike the one you just used, will
not take into account the uncertainties in your input values (v and t ). Instead, you must estimate the uncertainty in your
measurement using the statistical approach used in Lab 1 (equation E.5b in the uncertainty guide) to estimate the uncertainty in an
average value of a measured quantity.
Following steps 1 through 4 above, you will repeat the same procedure to obtain at least 4 more estimates of g. However, rather than
plotting v vs. t for each dataset and finding the slope, you will use a linear fitting tool on LoggerPro to get the slope of the velocity
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vs. time plot generated automatically for each trial.
After each of your additional drops of the ruler through the photogate, click on the velocity vs. time plot generated for that trial that
appears on the right side of the LoggerPro window. Then, under the “Analyze” tab at the top of the screen, click “Linear Fit.” A
small box should appear over the velocity vs. time plot, listing the information for the linear fit to the data. You can click and drag
the endpoints to only fit the portion of your data that show a constant slope. Since the linear fit is of the form v = mt + b, the
slope (m) should display a value close to the expected value of 9.81 m/s2. Record this value, then repeat this process with more
trials until you have at least 5 estimates for g.
Find the average (ḡ ) and the uncertainty in the average (Δḡ ) by applying equations E.5 and E.5b of the uncertainty guide,
respectively. Compare this average estimate and its uncertainty (ḡ ± Δḡ ) to the single estimate and its uncertainty (g ± Δg)
obtained from the previous method, and compare both to the accepted value of g. Which is more accurate? Which is more precise?
Is this expected? Why or why not? Discuss this in your lab report!
Demonstration of non-zero initial velocity
In this last part, see what happens to the initial (“initial” being the first time at which the photogate is blocked by the tape on your
ruler) velocity v0 - or, the velocity of your first time interval - if the ruler is dropped from a height far above the photogate beam.
Hold the ruler a few inches above the photogate, and drop it through the beam in the same manner as before. Compare the first
value of velocity on your LoggerPro spreadsheet to the first value that appeared for the previous trials where you dropped the ruler
just above the photogate. Is this initial velocity v0 greater or less than the initial velocity for the previous trials? What would you
expect, and why? How does this change the plot of velocity vs. time?
Something Extra
Although you have now completed the required part of the lab, you may be interested in using another approach to measure the
acceleration due to gravity of a freely falling object.
In this experiment, we produced a specialized object (a periodically-marked ruler) to measure its acceleration using a photogate. It is
also possible to use sound to measure the drop time of a falling object by having weights tied at a set distance on a string. This
approach is nicely illustrated at Physclips [http://www.animations.physics.unsw.edu.au/mechanics/chapter2_projectiles.html] (Section 2.2).
However, if we want to measure the acceleration of an arbitrary object, we can record a video of its motion, import it into a
computer program (such as LoggerPro), and analyze the motion frame by frame through time. (A video recording at 30 frames per
second is one frame every 0.033 seconds!) One tool to do this is here
[https://www.ic.sunysb.edu/class/phy141md/videoanalysis/verticaldrop.html]. If you use the plotting program on that page with the given
video of a falling object, it will automatically fit the data to a quadratic relationship. Recalling that, for a freely falling object,
1
1
2
y − y0 = v0 t −
gt , the coefficient (a) of the squared term of this fit should equal − g. You can also propagate the given
2
2
uncertainty in this coefficient into the uncertainty in the estimate of g, using Δa
= Δ(
1
2
g) =
1
2
Δg → Δg = 2Δa
.
How does this estimate for g compare to the value you got from the ruler drop experiment? (If you do this part of the lab, don't
forget to paste your plot into your lab report and notebook!)
Note: This tool can be used with a variety of videos. The main restrictions are that the background should not be moving, there must
be a reference length (like the 1 m line in the video above), and the video must be taken in good light. If you have a video of
something moving that you think would be interesting to analyze, please share it with your TA!
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