Otterbein University Department of Physics
Physics Laboratory 1500-2
EXPERIMENT 1500-2
MOTION DIAGRAMS
APPARATUS
Track and cart, motion detector, LabPro interface. Software: Logger Pro 3.4
INTRODUCTION
In this lab we will explore the motion of objects, and how to efficiently describe this
motion. Namely, we will learn how to create motion diagrams (position, velocity or
acceleration as a function of time), and how to extract kinematical information from these
diagrams. In short, we want to be able to cast the motion of any object in the real,
physical world into a two-dimensional plot that captures the essential parameters of the
motion. Of course, we can and will also do the opposite: translate the plot into a real,
physical motion of an object.
To display the motion diagrams quickly, we will use a motion detector connected to a
computer. The motion detector will measure the position of moving objects as a function
of time. From the position data, the computer will derive the values of the object’s
velocity and acceleration as a function of time. The motion detector uses sonar to
measure the distance to an object. It emits a short burst of ultrasound and measures the
time for echoes to return to it. Since the velocity of sound is known, the distance can be
determined from the echo delay.
The average velocity of the object as a function of time can be determined from the
position data using the definition,
x x(t i 1 )  x(t i )

t
t i 1  t i
This is the average velocity of the ball in the time interval from ti to ti+1. Similarly, once
the velocity as a function of time is known, the average acceleration of the ball in the
time interval from ti to ti+1 is defined to be
vaverage 
v v(t i 1 )  v(t i )

t
t i 1  t i
The computer will perform these calculations for you. In practice, the computer also
does some averaging of the data as well, to reduce the noise.
aaverage 
SETUP
1. Plug in the LabPro interface, and connect the motion detector to the port Dig/Sonic 1.
The LabPro translates the electrical signals from a variety of measuring devices into
the digital language of the computer. Put the motion detector on the lab table with
the sensor facing the room.
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Otterbein University Department of Physics
Physics Laboratory 1500-2
2. Launch Logger Pro by clicking the icon on the desktop that shows a picture of a
vernier caliper. Logger Pro collects, displays and analyzes data from the LabPro
interface. Let’s adjust some of the settings, to get a feeling for how Logger Pro
works.
a. Use a thermometer to determine the room temperature in centigrade. Then under
“Experiment” go into “Set up sensors” and click on the motion detector. Enter the
temperature in the appropriate field. Logger Pro needs to know this, since the
speed of sound in air depends on temperature. Finally, click OK.
b. Click on the button that looks like a clock. Make sure that the mode is set to Real
time collect. That tells Logger Pro that time is one of the variables in your
experiment. Click on the tab marked Sampling. Set the experiment length to 5
seconds, and the sampling speed to 20 samples/second. Click on the Averaging
tab and set the averaging mode to 3 pts. Now Logger Pro will average three data
points together when it analyzes your data, in order to reduce the noise.
In the future, you will use pre-programmed setup files, so you won’t always have to
go through this procedure; but now you should have a better idea of how Logger Pro
works.
3. Check out the motion detector. Click the Collect button. When the motion detector
starts to click, place an object (such as your hand) in the ultrasound beam to see if it
gives sensible readings. The floor should give a reading of zero, and you should get
correct position readings for any object more than 40 cm away from the detector.
The beam of ultrasound makes a cone of about 15; make sure the object whose
position you are measuring is within this cone, and that there are no other objects in
the cone that are closer to detector. The motion detector may also be confused by
multiple echoes from hard surfaces such as the ceiling and floor. If you get
nonsensical distance readings, make sure the motion detector is aimed in the right
direction, and that there are no other objects in the way. The problem of echoes can
be reduced by reducing the sampling speed, but you don’t want to do that if you don’t
have to. Ask the lab instructor or assistant for help if you are unable to get sensible
readings from the motion detector.
PART I – MOTION DIAGRAMS
Motion diagrams are plots of position, velocity or acceleration as a function of time. They
display the essential parameters of the motion of an object. In this lab, a motion detector
plugged into a computer will create these two-dimensional plots for you. The horizontal
axis exhibits the independent variable as usual, in this case time. The origin of the time
axis, i.e. the moment when t = 0 s, corresponds to the moment when you pressed the
“Collect” button to begin taking data. The vertical axis will represent either position or
velocity of an object. Note that both quantities change in time, i.e. are functions of time,
and therefore dependent variables.
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Otterbein University Department of Physics
Physics Laboratory 1500-2
A. Position versus time
Let’s first explore position versus time motion diagrams. What does the computer display
on the vertical axis? Position is spatial, i.e. somehow in the room. Where is the position
coordinate axis in the space of the physics lab? We have to measure position relative to
something; there has to be an origin and a notion both positive and negative directions.
Record all answers to the questions. Of course, you are expected to go beyond a simple
"yes" or "no" response and provide justification for your answers.
1. Put the motion detector down on a table or counter so that you are not moving it.
While recording data, have a member of your group walk toward and away from
the detector. Do this multiple times if you need to do so, but ultimately figure out
where the position axis origin is located as well as where the positive and negative
values of position are located.
2. Next figure out how the graph tells you which way the person was moving and
whether they were moving slowly or quickly.
3. Do your answers change if the person stands still and you move the motion
detector back and forth? If so, in what way or ways do you they change? Feel
free to explore this question by playing with the detector.
4. Using the apparatus you have and just one person moving, can you create a
position versus time graph that has the shape of a circle?
Matching a position versus time plot with actual motion
You should now be able to analyze a plot and write a description of motion that might
have created the plot. Also, you should be able to move in such a way that you create the
plot, which is what we’ll do next.
5. Keeping the motion detector stationary, walk so that you match the graph below.
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Position (m)
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
t (s)
Write a description of how you had to move to create this graph. Include qualitative
descriptions using words such as: toward, away, slowly, quickly, gradually, etc.
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Otterbein University Department of Physics
Physics Laboratory 1500-2
6. Keeping the motion detector stationary, walk so that you match the graph below.
3
Position (m)
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
t (s)
Write a description of how you had to move to create this graph. Include qualitative
descriptions using words such as: toward, away, slowly, quickly, gradually, etc.
B. Velocity versus time
Let’s now explore velocity-versus-time motion diagrams. Velocity implies a vector
quantity so it must convey both speed (magnitude) and direction. In one-dimensional
motion the direction is indicated by assigning a positive or negative sign to the speed.
This changes the scalar speed into a velocity vector. Keep this in mind as you work
through the exercises that follow.
Matching a velocity versus time plot with actual motion
7. Walk so that you match the graph below. Write down a description of how you
had to move to create this graph. Include qualitative descriptions.
1
0.8
0.6
Velocity (m/s)
0.4
0.2
0
-0.2 0
1
2
3
-0.4
-0.6
-0.8
-1
t (s)
4
4
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Otterbein University Department of Physics
Physics Laboratory 1500-2
8. Walk so that you match the graph below. Write down a description of how you
had to move to create this graph. Include qualitative descriptions using words
such as: toward, away, slowly, quickly, gradually, etc.
1
0.8
0.6
Velocity (m/s)
0.4
0.2
0
-0.2 0
1
2
3
4
5
-0.4
-0.6
-0.8
-1
t (s)
Connecting position and velocity graphs
By now you should have a good understanding of how a person's motion in front of the
motion detector translates into a velocity versus time graph on the computer. We will
now connect the position-time graph to its corresponding velocity-time graph.
9. Go back to the position-time graph of question 5. On a sheet of graph paper, draw
a velocity-versus-time graph that matches this motion.
PART II – CART ON TRACK AT CONSTANT ACCELERATION
Now on to some actual physics, namely the motion of objects under the influence of
gravity. We are still only describing motion, i.e. asking how something is moving, and
not asking why it moves. That is, we are dealing with kinematics, not dynamics. Since we
are not allowed to talk about forces yet, we can cast the influence of gravity entirely into
a single, simple statement: objects under the influence of gravity move at constant
acceleration. In free fall nothing is holding the objects back, so they are subject to the
maximal acceleration, which is a=g=9.8 m/s2. This is a large acceleration, and
accordingly, objects move very fast – typically too fast for humans to pay attention to
precisely how they fall. (Do they speed up? How?) Back in the days, Galileo didn’t even
have a watch at his disposal, so he slowed things down in an ingeniously simple way: he
put objects on a very slightly inclined plane. This is basically what we did in the last lab,
and we shall use the same setup again. However, we will speed things up by putting two
big books under the higher end of the track to be able to safely ignore friction.
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Otterbein University Department of Physics
Physics Laboratory 1500-2
This part of the lab is transitional, in that we will qualitatively explore the motion of a
cart at constant acceleration, before diving into a full quantitative analysis of an object in
free fall.
1. Set up the motion detector at the high end of the track, and load the configuration
file which will display position, velocity and acceleration as a function of time.
2. Starting from the low end of the track, push the cart uphill so that it turns around
roughly in the middle of the track.
3. Print out the three motion diagrams and describe how they look, focusing on the
interesting part, i.e. the time when the cart was actively moving.
4. Determine the slope of the velocity plot with the method we learned in the
previous lab. What is its connection to the intercept of the (constant) acceleration
plot?
5. Make the incline steeper by putting more books under the high end, i.e. increase
the angle of inclination. Push the cart so it goes half-way up again and produce a
new set of motion diagrams. Describe what changes and what not (shapes,
maxima, slopes, intercepts, etc.)
6. Predict what is going to happen if we increase the incline indefinitely, i.e. the
inclination angle become 90 degrees.
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