LPC Physics
Gravitational Acceleration and the Picket Fence
Gravitational Acceleration and the Picket Fence
Purpose:
In this two-part experiment you will study accelerated motion and gain experience using
the Lab Pro interface to gather, record, and analyze experimental data. In the first part of
the lab you will use a “picket fence” made from Plexiglas, drop it through a photogate
connected through the LabPro to a computer. Using the Logger Pro software, you will
then be able to generate graphs of the object’s motion, and determine values for its
acceleration. Finally, you will compare the experimental values of acceleration to
accepted value for the acceleration of gravity at the surface of the Earth (see your text).
Plexiglas
“picket fence”
5 cm from
leading edge to
leading edge
Red LED lights
up when
photogate beam
is broken
Photogate
Figure 1 Basic Equipment Set-up
In the second part of the lab, you will use a “rotational picket fence” also known as a
smart pulley to measure the acceleration of a pair of suspended masses (see figure 2
below). In particular, the masses are designed to mimic the acceleration of gravity on the
Moon, and Mars respectively. In addition to determining the acceleration of the two
mass system, you will also measure the time of fall and verify the “free fall” formula by
measuring the height and the time it takes for upper mass to reach the ground.
smart pulley-photogate
m1
LabPro
m2
Figure 2 Basic Equipment Set-up
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LPC Physics
Gravitational Acceleration and the Picket Fence
Equipment: part I
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LabPro and Computer
Photogate
Plexiglas and Blue Masking Tape
Logger Pro Software
Experiment and Analysis: part I
1. Create a “picket fence” from Plexiglas and electrical tape as shown above. The strips
of tape should be carefully placed so that the leading edges are 5 cm apart (i.e. from
bottom of one strip to the bottom of the next). Try to make your picket fence as
precise and neat as possible. Or, if your instructor prefers, use a screen-printed picket
fence.
2. Set up a photogate so that the picket fence can be dropped vertically through it as
shown. For best results, the photogate should be attached to something rather than
simply held.
3. Connect the AC adapter to the LabPro by inserting the round plug on the 6-volt
power supply into the side of the interface. Shortly after plugging the power supply
into the outlet, the interface will run through a self-test. You will hear a series of
beeps and blinking lights (red, yellow, then green) indicating a successful startup.
4. Attach the LabPro to the computer using the USB cable. The LabPro computer
connection is located on the right side of the interface. Slide the door on the
computer connection to the right and plug the square end of the USB cable into the
LabPro USB connection.
5. Connect a photogate to a digital port (DIG/SONIC1) on the LabPro. The digital
ports, which accept British Telecom-style plugs with a left-hand connector, are
located on the same side as the computer connections. If you are using an older
Vernier photogate, you may need to remove the cable with a phono plug on one end,
and replace it with the cable labeled “Photogate Cable”, with British Telecom-style
plugs on each end. If you are using a very old Vernier or Pasco photogate, you will
need to use the Digital Adapter.
6. Open the Experiments folder on the desktop and open the file picket_fence.xmbl (or
.cmbl) This will start the program Logger Pro3.3 and bring up the appropriate data
file. If you do not have an auto-ID sensor (which is the likely case), a dialog box will
pop up asking you to confirm the sensors being used. If you have the suggested
sensor attached to the LabPro in the suggested port, click “OK”. If the “OK” button
is not active, ask your instructor for help.
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Gravitational Acceleration and the Picket Fence
7. When the program opens, you will see three graphs: distance vs. time, velocity vs.
time (called “accelerations”), and acceleration vs. time. Choose Experiment > Set
Up Sensors > LabPro 1. In the dialog box that appears, click on the photogate icon
in the DIG/SONIC1 box, and verify that “Motion Timing” is selected as the current
calibration.
8. Click on the photogate icon again. If you are using the screen-printed picket fences,
make sure that the “Vernier Picket Fence” option is selected. If you are using a tapeand-Plexiglas picket fence, select User defined button and enter "0.05" meters for
your distance.
9. Run the program by clicking on the Collect button at upper right, and drop your
picket fence through the photogate. If all is working properly, your graphs will
display points, and data will appear in the data tables. Save your graphs in the
Physics 8A folder on the desktop.
10. Click on the velocity vs. time graph to make it active, and drag the cursor over the
data points so that they are highlighted. Select Analyze > Linear Fit. A straight line
will now pass through your points, and the equation for the line will appear. The
slope of this line is your experimental value for g (Why?) Record this value in your
lab notebook for later inclusion in the data table—see the analysis section below.
11. Now make the distance vs. time window active. Select Analyze > Curve Fit >
Quadratic, and then “Try Fit.” Now an equation of the form y = a + bt + ct 2
appears. The acceleration of gravity can be easily determined from this relation. If
you don’t know how, then consult Chapter 2 of your text, and discuss it with your lab
partners. Determine the value of g from this curve fit and record it in the data table.
Be sure to record your work as well.
12. Now make the third window, acceleration vs. time, active. Highlight the data points,
and select Analyze > Integral. Record the result. What does this number
represent? Is the value close to the number you would expect? Explain.
13. With the same set of points highlighted, select Analyze > Statistics. You should see
an average value of the acceleration, and a standard deviation. Record these values.
How does the average value compare with the value you determined in Step 10?
Discuss your comparison. Does the average value agree with the accepted value for
“g” within the standard deviation? If not, propose a hypothesis about the source of
error.
14. Create a data table for your results. Be sure all rows and columns are properly
labeled and that units are included (see the accelerated motion lab for help). Make
sure that the table summarizes the results from parts I – 12 above. See the Results
section and end of part II below and see the lab guide before summarizing your
results for the lab.
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LPC Physics
Gravitational Acceleration and the Picket Fence
Experiment: Part II
1. Set up the smart Pulley system as shown in figure 2 (this is also known as Atwood's
machine). Some of the smart pulley-photogates come as one piece, others you may
have to put together yourself. For the two masses, let m1 = 70 g and m2 = 50 g. This
will simulate free fall on the moon.
2. Connect the AC adapter to the LabPro by inserting the round plug on the 6-volt
power supply into the side of the interface. Shortly after plugging the power supply
into the outlet, the interface will run through a self-test. You will hear a series of
beeps and blinking lights (red, yellow, then green) indicating a successful startup.
3. Connect the Smart Pulley/Photogate to the DIG/SONIC1 port of the LabPro. If you
are using a one-piece Smart Pulley/Photogate, a PASCO or very old Vernier
Photogate, you will need to use the digital adapter. If you are using a newer Vernier
(with removable cable), simply remove the cable with the Phono plug, and connect
the Photogate Cable with a British-Telecom plug on one end.
4. Measure the height of m1 above the floor.
5. Release m2 and use the stopwatch to determine the time for m1 to fall from its original
position to the floor. Calculate the acceleration using the equation h = ½ at2, where h
is the height of m1 above the floor. Switch with your lab partners and repeat.
6. Open the file atwood.xmbl (or .cmbl) in the Experiments folder on the desktop.
This will start the program Logger Pro3.3 and bring up the appropriate data file. If
you do not have an auto-ID sensor (which is the likely case), a dialog box will pop up
asking you to confirm the sensors being used. If you have the suggested sensor
attached to the LabPro in the suggested port, click “OK”. If the “OK” button is not
active, ask your instructor for help.
7. Once Logger Pro 3 is open, click on Experiment > Set Up Sensors > LabPro 1.
Click on the photogate icons, and verify that “Motion Timing” is selected under
“Current Calibrations”. In the same menu, choose “Set Distance or Length…”, make
sure that “Smart Pulley (10 Spoke) in Groove” is selected. The program calculates
the acceleration and velocity of the falling mass by treating the pulley as a picket
fence with the proper spacing.
8. Now press Collect and release the mass. If the acceleration nearly matches the value
you measured in Step 5, repeat this procedure twice more. If not, see if you can find
out what is wrong before asking for help (but do ask if necessary!).
9. Now simulate gravity of Mars by changing m1 to 100 g. If this mass pair proves a bit
cumbersome, you can use any smaller pair of masses as long as m1 is twice as large as m2.
Repeat steps 5 – 8.
Acceleration with Air Resistance
10. Repeat one or both (its up to you) of the two masses trials with a 3X5 index card
taped to the bottom of the falling mass.
11.Discuss the effect that air resistance has on the system’s theoretical acceleration.
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LPC Physics
Gravitational Acceleration and the Picket Fence
Analysis, Part II
1. For each run, examine the acceleration vs. time graph. Highlight a relatively constant
portion (including at least 10 data points), and click on the Statistics button. Record
(in your own table) the average acceleration and standard deviation.
2. For each pair of masses, average the acceleration values obtained from the separate
trials (average the average values!). Calculate the uncertainty from the half range
relationship (amax- amin)/2.
3. Compare your results with the theoretical values of gmars = g/3 gmoon = g/6. Note
that while these are not the exact values on Mars and the Moon, respectively, they are
the values used to determine the values of the masses used the experiment. You will
see how this is calculated later when you study Newton’s second law.
Results:
Write at least one paragraph describing:
• what you expected to learn about the lab (i.e. what was the reason for conducting
the experiment?)
• your results and what you learned from them
• answers to questions in the lab report (in bold italics)
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in
this laboratory
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Gravitational Acceleration and the Picket Fence
Theory:
When Aristotle studied motion, he concentrated on what he was able to observe, and
formulated his theories based on his observations. Noting that an object rolling on the
ground will eventually come to a stop, he divided motion into two distinct areas: Natural
Motion and Violent Motion.
Natural Motion is like that of a stone falling to the Earth, or smoke rising into the
sky; a stone, being of the Earth, will “strive” to regain its “natural place” on the surface
of the earth. Smoke, being primarily of the air, will “strive” to take its “natural place” in
the air. A feather, obviously not as solid as a rock, is a mixture of more Earth than air,
and thus falls to the ground though not as fast as the earthen rock. Heavier objects will
“strive” harder, and thus fall to the ground more quickly.
Violent Motion, according to Aristotle, occurs as the result of sustained force. An
arrow shot from a bow is an example of Violent Motion. It is also a good example of
how Aristotle ran into trouble matching his theories to his observations, for it is not
obvious what is sustaining the force on the arrow. Aristotle explained that as the arrow
“breaks through” the air, pushing it out of the way, the air must then rush back together at
the tail of the arrow, to avoid the creation of a vacuum. This rush of air at the backside of
the arrow is what propels the arrow forward, much as a watermelon seed may be
launched across the room by pinching one end between your fingers.
While Aristotle did the best he could, creating theories to explain his
observations, the genius of Galileo is that he was able to extend his understanding of the
phenomena he observed to situations that were not physically attainable. Galileo studied
motion with the assistance of meticulously polished inclined planes. By rolling polished
balls on successively smoother surfaces, he found that the smoother the surface, the
farther the ball would roll. This led Galileo to believe that rather than needing a force to
continue constant motion there was force (friction) acting on the object, arising from
contact between the surfaces, that slowed the rolling object. In the absence of this force
the object would continue to maintain its constant motion forever. By placing two
inclined planes facing each other Galileo found that, except for the effects of friction, the
ball rolled up the far plane to the same height at which it had started.
Initial position
Final position
Figure 2 Inclined planes of equal pitch
If the far plane was replaced by one of a shallower angle the ball traveled a greater
distance, but still returned to its initial height.
Initial position
Final position
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Gravitational Acceleration and the Picket Fence
Figure 3 Inclined planes of unequal pitch
It seemed obvious, then, that if the far inclined plane were removed the ball, having no
way to return to its original height, would continue to roll with constant velocity forever.
Initial position
Final position?
Figure 4 Inclined planes…second plane has zero pitch
Galileo also used inclined planes to investigate the acceleration of falling bodies.
By rolling or sliding objects down inclined planes, he was able to slow the motion to a
point where it could be analyzed. He found that balls rolling down the incline increased
their velocities by equal increments in equal time intervals. That is, they underwent a
constant acceleration. By increasing the angle of the plane, the acceleration increased,
until the plane was completely vertical and the motion of the ball was that of free fall. By
studying the accelerations at smaller angles, Galileo was able to extrapolate and
determine the acceleration of a freely falling body.
a.
b.
c.
d.
Figure 5 from a. to d. , the least to most acceleration
Galileo’s use of inclined planes was due largely to a lack of suitable timing devices.
While his methods and ability to extrapolate from the observable to the theoretical prove
his genius, I am sure that if he’d had the equipment we have today, he would have used
it. Lacking Galileo’s time and patience, but possessing computerized timing devices we
will skip straight to the part of the experiment that Galileo could not do. We will
measure the acceleration of a freely falling extended body. The use of an extended object
will allow us to keep the measuring device stationary and record the time it takes to fall a
sequence of previously determined distances.1
1
The theory for this experiment was written by Jennifer LK Whalen
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