Lab 3 – Computerized version of “Lab 8"
Newton’s Second Law on an Air Track
Purpose
The purpose of this experiment is the same as that of “Lab 8 ” in the lab manual, to test Newton’s
Second Law for a simple 2-body system, but with the additional objective of gaining some
experience with a computerized data acquisition system that automates some of our work.
Overview
We will make several significant changes in the apparatus and procedure from what you will read
about in “Lab 8” but there will be no change in what we are trying to measure or the physics we
are trying to test. The Air Table will be replaced with an Air Track that limits motion to one
dimension and makes it possible to use a sonar Motion Sensor to measure the position of a
conical reflector attached to a glider on the track. The motion sensor sends digital data on the
position of the reflector to a program in the computer, and the computer calculates the average
velocity over each time interval and fits those data to give us the acceleration. That is, the
computer does everything we did with the spark timer marks, a ruler, and the Graphical Analysis
fitting program in the previous lab.
Prelab
Read the theory section below and in the lab manual (pp. 85-86). The lab manual
describes the same two-body problem we will solve, one that is identical to one that
is in the PHY2048 homework and that is demonstrated in lecture.
Do the prelab assignment on LON-CAPA . (This comes from pp. 89-90 in the manual.)
If requested by your instructor, turn in the graph from the least-squares fit.
Review the information about the data acquisition program in this handout before class.
How the theory relates to the fit we will do
The main result of the derivation is equation (4) in the manual:
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This equation looks like
if we associate the acceleration (a) with the abscissa (x)
and the weight of the small mass (m2g) with the ordinate (y). The intercept is the friction in N
and the slope is the total mass of the system in kg. Notice that this will only work if we cleverly
keep the total mass of the system constant (even as we vary m2 ) by attaching the unused 10g
masses to the glider. Pay attention to this step in the procedure you will get next week.
Lab 3 – Computerized version of “Lab 8" – Procedure
Equipment required
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PASCO Science WorkshopTM 700 interface connected via a SCSI interface to a ...
computer running the PASCO DataStudio software. The computer must be booted up
with the interface turned on for the operating system to identify it properly.
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Motion Sensor.
CENCO Air Track with blower.
Aluminum glider with reflector, which should have a string attached.
A set of five masses, each about 10 g.
Lightweight string or thread, if needed.
Triple beam balance.
Setup the apparatus
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The track should be ready to use (see below) with motion
sensor held in place on one end with a heavy rubber band
(see closeup picture to the right). Turn the air-blower off
except when taking data because it is very noisy.
Set up the “DataStudio” program
1.
Double-click on the DataStudio icon.
2.
If the “How would you like to use DataStudio?” window
comes up, click on the red X to close it.
3.
Use the pull-down menu under “Experiment” to select the
“Change Interface...” option. This will bring up the box
shown below. Select the “SW700” and click OK.
4.
The “Experiment Setup” window will appear. There is an
alphabetical list of sensors in the left-hand column. Click on the
“Motion Sensor”. After you do this, an icon of the sensor will
appear, showing how it is supposed to be plugged into the SW700
interface. See picture below. The yellow connector should be
plugged into the left-most socket.
5.
Double-click on the icon for the Motion Sensor to bring
up the “Sensor Properties” box shown at right. The
“Measurement” tab should show it is set to measure
position (to 0.001 m) every 0.100 s (a sample rate of
10.0 Hz) and calculate velocity and acceleration.
6.
We will get better data if we calibrate the sensor for the
speed of sound in the laboratory and/or correct for any
timing error in its pulse rate. First, use the meter stick to
position the glider so there is 1.00 m between the face of
the motion detector and the tip of the conical reflector.
Important: Do not touch the face of the motion detector
with the meter stick! It is fragile and expensive. Eyeball it
from above. Once you have it in the correct place, select
the motion sensor tab shown at right. The motion detector
will start clicking and the display will show the estimated
distance to the reflector. Push the “Calibrate” button and will correct that distance to 1 m.
(This is done with the air blower off.) Close this window when done.
7.
There is a list of display options at the bottom of the left
column of the Setup window. Double-click on the one that
says “Graph”, and a display called “Graph 1” will open up.
This is where our data will appear.
8.
A window will pop open. Choose the Velocity as your Data
Source. The computer will measure position, calculate the
average velocity over each 0.100 s time interval, and display
the velocity so we can fit a line to those data.
9.
Resize the “Graph 1” window so it fills most of the screen.
We are now ready to take data.
Collect and analyze the data
1.
We will now follow a procedure similar to that described on pages 86 and 87 of the lab
manual. The first step is to level the track. Put the glider near the center of the track and
turn on the air blower. There is a single nylon screw on the computer end of the track.
Adjust it until the glider stays where you put it on the track. Turn off the air blower when
you are done.
2.
Remove the glider from the track and measure its mass using the large balance at the
front of the room. (We only have one of these high-capacity balances, so you might do
this step later if it is too busy.) Convert its mass to kg and record the glider mass, M, in
Data Table 1. Now add the five “10 g” masses to the balance and measure the total mass
m1 + m2. Convert it to kg and record in Data Table 1.
3.
Place the glider back on the track. Use your balance to determine
the mass of one of the “10 g” masses and enter the value in DataCalculations Table 2. Run the string over the pulley as shown in
Figure 8-1 in the lab manual (pg. 86) and hang the mass from the
string.
4.
Hang the other four masses on the glider as shown in the picture shown here, balancing
them on both sides of the glider. Position the glider on the track so that the “10 g” mass
is as high as possible, close to the pulley.
5.
One lab partner should hold the glider in place and turn
on the air blower. After it has settled down, tell the
other lab partner you are ready to start recording the
data. When ready, the partner on the computer should
click on the “Start” button (see picture at right) and say
‘go’. Wait a second, steady the glider, and then release
it. The partner on the computer should click the
“Stop” button after the cart bounces off the far end of the track. You will have data
displayed in the “Graph 1" window that should resemble the left-most picture below.
6.
Turn off the air blower as soon as you are done collecting each data set. If you mess up,
you can go up to the “Experiment” menu and select the option that will delete all of the
data being displayed and try again.
7.
The buttons across the top of this window (see the
enlarged version below) are used to analyze the
data. If you position the mouse cursor over a
button, a window will tell you what it does. We
will mainly use the leftmost button (to select part
of the data to view or fit), the menu under the
“Fit” button, and the menu under the “Data”
button.
8.
The first step is to enlarge the graph and select the region we want to fit. Click the
leftmost button, and the scale of the graph will be changed so the data fill the entire
window. We can now identify the region where the glider was freely accelerating,
between the time it was completely released and the time the mass hit the floor. See
example on the next page.
9.
There will be a region near the start where the
velocity has a slight curve for a few tenths of a
second. This is where the glider was still touching a
finger as it was released. There is also a “flat top”
region where the velocity became constant after the
mass hit the floor but before it bounced. Use the
mouse to select a region between those two places,
like is shown at right. You just click and drag to put
a box around the part you want, and the selected part
will be highlighted in yellow.
10.
Use the pull-down menu under “Fit” to select a “Linear Fit”.
11.
The fitted line will be shown along with a box containing the
fit parameters. The fit parameters are the same ones we get
from “Graphical Analysis”. We get uncertainties as well as
the correlation coefficient “r”. Notice that the data being fit
are still highlighted in yellow. Changing the selection region
will change the fit, if you need to do that.
12.
Record the slope (the acceleration), the intercept (the initial velocity), and the correlation
coefficient “r” in Data-Calculations Table 2. Also make a mental note of how linear the
fit looked so you can answer question 1 on pg. 93 qualitatively as well as by comparing
the value of “r” to 1.000.
13.
Repeat this process with two of the “10 g” masses on
the end of the string. Use the balance to determine
their mass, record it, make sure the other three masses
are still on the glider, and make a run as described
starting at step 5 above. However, because the new
data set appears on top of the old one, it can get messy
if you don’t remove or hide the previous run. What
you need to do is use the pull-down menu under
“Data” to un-check the run(s) you don’t want to see.
You can also just delete an old data set by using the options under the “Experiment”
menu for the program itself.
14.
Continue until you have five sets of data using 10, 20, 30, 40, and 50 grams to accelerate
the glider.
15.
Double check that you have recorded
everything you need, and then exit the
program. Answer “No” when it asks if you
want to save the data from this experiment.
Calculations
1.
Calculate the applied force in Data-Calculations Table 2 for each run. Remember to
convert g to kg, then multiply by g = 9.80 m/s2 to get the force.
2.
According to Equation (4) on pg. 86 of the lab manual, the acceleration “a” should be
proportional to the applied force, with the total mass as the slope and any friction as the
intercept. Use “Graphical Analysis” to perform a linear least-squares fit with the
acceleration “a” from Table 2 as the abscissa and the applied force “m2 g” as the ordinate.
3.
Record the intercept (friction) and its uncertainty, the slope (total mass) and its
uncertainty, and “r” in Calculation Table 3. Print a copy of this fit and include it in your
lab report.
4.
Calculate the % error for the total mass. (Here we assume that the total mass that we
measured with the large balance and recorded in Data Table 1 is “exact” enough to treat it
as a known value when comparing to the fitted value for the slope.)
Other details
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The DataStudio program can produce printouts of your fits, but we don’t really need to use
all of that paper. Make a mental note of how linear they looked, or make a note here.
Lab report
Answer the 4 questions on pg. 93 and include them in your lab report along with the other things
required by your lab instructor. Be sure your answers are supported by quantitative statements
using “r” and the uncertainties in your fitted values, not just vague claims or a short answer such
as “yes” or “no”.
Question 3 cannot be answered in the space available in the lab manual. You should set up a table
on a separate sheet of paper and show the formula you used (there are two choices) and a sample
calculation using that formula. Put that sheet right after question 3.