Lab #2
Linear Motion Using Sonic Ranger
page 1
Prof. Susanne M. Lee
University at Albany, SUNY
Linear Motion Using Sonic Ranger
Reading: Giambatista, Richardson, and Richardson – Chapter 3 (3.1 – 3.2).
Summary: Being able to measure linear motion is extremely important not only in the
sciences but also in regular police work. To catch speeding motorists, policemen need to
accurately measure the speed of a car moving in a straight line. In this lab on person in
your lab group will be the speeding motorist while the others will be the policemen, who
will use a detector that operates on a similar principle to police radar guns. The
“motorist” will move around in front of the detector on foot and a skateboard, while the
“policemen” record the “motorist’s” motion. Then using the equations of linear motion,
you will all analyze the data to determine if the “motorist’s” speed and acceleration
warrant a ticket. You will also learn how to program these equations and plot your data
in Excel.
Note #1: All questions are to be answered in full sentences. If they are not, you will lose
10 points from your overall lab score.
Note #2: In this lab all the grading information is present, so you understand the sorts of
things expected in your lab report. Future labs will only show the number of points each
section is worth, not the breakdown within each section.
Pre-Lab Analysis
1.) Write the equations for linear motion (without acceleration) that describe each of the
following quantities: (you can find these in your textbook)
a) displacement and distance of an object's position (4 pts)1
b) average speed and average velocity in terms of displacement and time. (4 pts)2
c) What is the difference between distance and displacement? (3 pts)3
d) What is the difference between speed and velocity? (3 pts)4
In this lab the “motorist” will walk back and forth in front of a motion detector
(sonic ranger), which uses sound to determine the “motorist’s” distance from the detector.
This data is processed by the LoggerPro motion software and will appear on the computer
screen in the form of graphs, from which the some of the above four quantities can be
determined. All lab group members then will record the measurable values in his or her
own lab notebook and use Excel to calculate the quantities not measured.
How the Sonic Ranger (motion detector) works:
The motion detector emits short bursts of ultrasonic sound waves; each burst is
accompanied by a clicking sound from the detector. The computer times how long it takes
for the sound pulse to hit an object in the path of the sound wave, bounce off the object,
and come back to the detector. Using this time and the speed of sound in air, the computer
determines how far away the object is from the detector. The sound waves emitted from
the detector fill a cone of about 20°. Stationary or moving objects (stools, tables, lab
partners) within that 20º cone will confuse the sound waves and produce incorrect
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
readings. The range of the detector is 0.5!m - ~5!m. Anything closer than 0.5!m or farther
than ~5!m away will not be detected.
2.) Section 6 of the lab (below) shows two different graphs of sonic ranger data. In your
lab notebook, predict how you would have to move to match each figure. [6 pts]5
3.) Outline the lab following the format of “Outline Format” posted on the Electronic
Reserves web page. [20 pts]6
Equipment to be used in this lab:
r
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ULI interface.
1 motion sensor (Sonic Ranger)
2 skateboards
1 wooden board for use with skateboards
Masking tape (for marking min/max sonic ranger detection limits)
3 people to a lab group – for this experiment oonnllyy
1.) Equipment Set-up
r Check that the motion sensor is connected to Port 2 of the ULI box.
r Put the motion detector on the edge of the lab table pointing towards the
center of the room (see Figure 1).
Figure 1: Sonic ranger is on the table to the right – the blue box with a silver cable coming
out of its side. The skateboard on the board will be used in Section 6 of the lab.
2.) Computer Set-up
r On the computer desktop, double click on the “Experiments” folder; then
double click on the "Linear Motion" icon. Make sure the graph that comes up
displays Distance vs Time.
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
r Click on the "Experiment" menu, then "Sampling…".
Check that the
"Experiment Length" is set to 5 seconds and the "Sampling Speed" to
3!samples/second. Click "OK".
3.) Determining range of Motion Detector
r Click on “Collect” and move around in front of the detector until you find the
closest and farthest positions that the sonic ranger detects. Mark these spots on
the floor with some tape.
r Notice “Collect” changes to “Stop” right after you begin to hear the clicks from
the detector. Once you have determined the detector’s min/max positions, click
“Stop” to stop the data collection process.
4.) Position versus Time Graphs – law-abiding “motorist”
r Create a table in your lab notebook; label it "Slow and Away". (2 pts)7 The
columns should be labeled (starting with the first column label): trial #, name (of
“motorist”), starting position, starting time, ending position, ending time. (12 pts)8
r Have the “motorist” stand at the 0.5 m mark, while one “police-person” clicks
on “Collect”.
r The “motorist” should now walk slowly away from the detector and with as
constant a speed as possible. When the farthest tape mark is crossed, the
“policeperson” should click on “Stop”.
r The graph that appears on the screen displays the “motorist’s” position versus
time. Record the starting and ending positions and times in your notebook
table in the appropriate columns associated with trial #1.
• Determining plot coordinates in LoggerPro:
® Click on the “X=?” icon. A little box should appear at the upper left
corner of the graph.
® Move the cursor to a point on the graph without clicking. A vertical line
should appear that intersects the graph, giving the position and time of
the intersection point. These values should appear in a box on the screen.
r In order for a speeding ticket to hold up in a court of law, the radar gun has to
have been calibrated within the 20 minutes prior to the speeding ticket. In the
lab, the “policepersons” will now “calibrate” the motion sensor by repeating
the same motion as the “motorist”. (This is not how the real radar guns are
calibrated.)
® However first, each “policeperson” should practise walking the same
distance in the same time as the motorist, then record it with the detector
and LoggerPro. Try to make the policeperson’s and motorist’s motions as
similar as possible. (You will get extra credit for data that is within 10%
of each other.)
® Record the starting/ending positions and times in your lab notebooks.
(12 pts)9
r Print the graphs both of you produced and label them with the appropriate trial
# and name. Label the graph axes with the appropriate variables and units on
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
each variable. Attach this graph to a blank page in your lab notebook after
your data table recording starting/ending times and positions. [18 pts]10 (4 pts
extra credit: for really constant velocities)11
5.) Data Analysis – Displacement, Distance, Speed, and Velocity Calculations
r Minimize LoggerPro and Open Excel by double clicking on the Excel icon on
the computer desktop.
r Enter the data from your lab notebook into the Excel worksheet that appears
when you open Excel. Start with trial # in column A.
r You will now use Excel to calculate your displacement, distance, average
speed, and average velocity, so make columns for these in your Excel
worksheet by labeling each column appropriately (with units).
r To enter an equation in a cell, start by clicking on the cell where you want the
result of the calculation to appear, then type an “=” sign and proceed with
entering the appropriate formula. If you have not used Excel before, more detailed
instructions for entering formulas are given at the end of this lab.
r Enter the calculations for the displacement, distance, average speed, and
average velocity. Make sure you enter the appropriate formula that will
calculate the requested quantity. For each column choose one cell and do the
same calculation on your calculator to make sure the computer is calculating
the formula correctly.
r Once you have calculated everything, print your table with all the values.
Underneath each column, give the general formula (e.g. for displacement:
G2!=!C2!–!E2) you used in your calculation. (29 pts)12
r Are any of your calculated values negative? If so, comment on their meaning.
(2 pts)13
6.) The Speeding “Motorist” - on a Skateboard (Matching the Plot)
r Minimize Excel and maximize the LoggerPro software (click on the LoggerPro
box at the very bottom of the computer screen).
r Click on the "Experiment" menu, then "Sampling…". Change the "Sampling
Speed" to 20 samples/second (from 3 samples/sec). Click "OK".
r Place the skateboard on the wooden board in the middle of the room. The
“motorist” should stand on the skateboard, while one of the policepersons will
become an accomplice and push the skateboard. Duplicate the figure below
assigned by your TA.
® To get the best results, the person standing on the skateboard must stand
very still – any body motion like moving arms will be detected by the
motion sensor instead of the actual motion wanted.
® The person pushing the skateboard should not try to make it go fast
immediately or the “motorist” will fall off the skateboard. That is,
instead of giving the person a large acceleration right away, make it
smaller, but push them for longer to get the “motorist” up to speed
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
before the “policeperson” begins to collect data.
r Print your best effort. (5 pts)14
r Were your predictions from Question 2 in the Pre-Lab Analysis correct? If not,
what changes did you need to make in order to reproduce the curves? (1 pt)15
(10 pts)16
r Now find (using LoggerPro) the “motorist’s” instantaneous velocity
everywhere during the motion. If the “motorist’s” speed was greater than
4!m/s, he or she should get a speeding ticket (for the purposes of this lab).
r Do the “motorist” and “accomplice” in your group deserve a ticket? Why?
Support your answer with a plot of the “motorist’s” velocity versus time and
indicate on the graph where the “motorist” was speeding. (10 pts)17
4.5
4.0
3.5
3.0
Distance (m)
2.5
2.0
1.5
1.0
0.5
0.0
0
1
2
Time (sec)
Figure 2. Distance plot to be matched by lab groups 1-5.
3
4
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
4.5
4.0
3.5
3.0
Distance (m)
2.5
2.0
1.5
1.0
0.5
0.0
0
1
2
Time (sec)
Figure 3. Distance plot to be matched by lab groups 6-10.
3
4
Lab #2
Linear Motion Using Sonic Ranger
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Prof. Susanne M. Lee
University at Albany, SUNY
Excel Instructions for Formula Entering
The following instructions will lead you through entering a formula to calculate the
displacement.
1.) In cell G2 (where the first displacement calculation is to appear), type the following
(without the quote marks): "= C2-E2". (Make sure you entered the columns in the order
in which they are listed in the instructions above under Section 4, or this formula will
not give you the correct answer.)
2.) Next click either on the check mark to the left of the formula you just typed (at the top
of the worksheet) or press enter on the numberpad. The formula should disappear and
the result of the calculation should be displayed. Check with your calculator that this
number is correct.
3.) Move the mouse to the lower right hand corner of cell G2 (make sure G2 is still
selected) and the big fat cross will turn to a solid black skinnier cross. When this
happens, click and hold the left mouse button down while you drag the cross down to
the bottom-most cell of your table. This will fill each cell with the formula you just
typed, while at the same time changing the row number to the appropriate row. For
example in the third row, the formula should read “=C3-E3”. Click on cell G3 and
make sure the formula reads correctly.
4.) If you need to take the absolute value of a number that is in cell X1, type “=ABS(X1)”
in the cell in which you want the absolute value of X1 to appear.
5.) In Excel, you need to use “!*!” to multiply two numbers together. Writing (2)(3) will
produce an error message.
6.) Similarly, to divide two numbers in Excel use the “/” sign.
7.) If any of your formulas require mixing addition or subtraction with multiplication or
division, use parantheses around the quantities to be added or subtracted. For
example: suppose you wanted to add 2 to 3 and then multiply the sum by 6. You
would write this as (2+3)*6. If you leave out the parentheses and write 2+3*6, the
computer will assume you meant 2+(3*6).