Graphical Analysis of Motion
2012
Graphical Analysis of Motion
One of the most effective methods of describing motion is to plot graphs of position, velocity, and
acceleration vs. time. From such a graphical representation, it is possible to determine in what direction an
object is going, how fast it is moving, how far it traveled, and whether it is speeding up or slowing down. In
this experiment, you will use a Motion Detector to determine this information by plotting a real time graph
of your motion as you move across the classroom and the motion of other objects.
The Motion Detector measures the time it takes for a high frequency sound pulse to travel from the
detector to an object and back. Using this round­trip time and the speed of sound, you can determine the
position to the object. Logger Pro will perform this calculation for you. It can then use the change in
position to calculate the object’s velocity and acceleration. All of this information can be displayed either as
a table or a graph. A qualitative analysis of the graphs of your motion will help you develop an
understanding of the concepts of kinematics.
Materials
computer
Vernier Motion Detector
Vernier computer interface
meter stick
Logger Pro
masking tape
Constant v cart
Low friction cart/incline
Note: When not using the low friction cart place it upside down so it won’t roll off the table
Adapted from Physics with Computers
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Graphical Analysis of Motion
Preliminary questions
1. The Problem Statement section of a lab includes both an overall problem/ goal for the lab and
hypotheses. So first write a problem/ goal for the lab. You should then make hypotheses to address
each of the items below
About Position versus time graphs:
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How does a position versus time graph show the speed (how fast or slow) an object is moving?
How does a position versus time graph show the direction of an object’s motion?
What shape shows motion with constant velocity on a position versus time graph?
What shape shows accelerated motion on a position versus time graph?
About Velocity versus time graphs:
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How does a velocity versus time graph show the speed (how fast or slow) an object is moving?
How does a velocity versus time graph show the direction of an object’s motion?
What shape shows motion with constant velocity on a velocity versus time graph?
What shape shows constant acceleration on a velocity versus time graph?
About Acceleration versus time graphs
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Does an acceleration versus time graph tell you the object’s position? If so how?
Does an acceleration versus time graph tell you the object’s velocity? If so how?
Can an object have zero velocity and still have an acceleration (non zero acceleration)?
What shape shows motion with constant acceleration on an acceleration versus time graph?
2. Using the hypotheses you have just made, sketch the position vs. time graph for each of the following
situations:
● An object at rest
● An object moving in the positive direction with a constant speed
● An object moving in the negative direction with a constant speed
● An object that is accelerating in the positive direction, starting from rest
3. Using the hypotheses you have just made, sketch the velocity vs. time graph for each of the following
situations:
● An object at rest
● An object moving in the positive direction with a constant speed
● An object moving in the negative direction with a constant speed
● An object that is accelerating in the positive direction, starting from rest
Adapted from Physics with Computers
1 ­
Graphical Analysis of Motion
Procedure
Part l Preliminary Position Experiments
1.
2.
3.
4.
5.
Connect the Motion Detector to the DIG/SONIC 1 channel of the interface.
Place the Motion Detector so that it points toward an open space at least 4 m long. Use short strips of
masking tape on the floor to mark the 1 m, 2 m, 3 m, and 4 m positions from the Motion Detector.
Open the file “01a Graph Matching” from the Physics with Vernier folder.
Using Logger Pro, produce a graph of your motion when you walk away from the detector with
constant velocity. To do this, stand about 1 m from the Motion Detector and have your lab partner
click . Walk slowly away from the Motion Detector when you hear it begin to click. SAVE
AND PRINT THIS GRAPH USING PRINT GRAPH AND PRINTING TO RM 75(one copy per
person) Sketch on the graph you printed what the position vs. time graph will look like if you walk
faster. Check your prediction with the Motion Detector.
Try to match the shape of the position vs. time graphs that you sketched in the Preliminary Questions
section by walking in front of the Motion Detector. Save each graph by copying it into a document on
google docs. Share this document with your lab partners.
Part Il Position vs. Time Graph Matching
Open the experiment file “01b Graph Matching.” A position vs. time graph will appear.
2. Discuss with your group how you would walk to produce this target graph, write out a procedure for
how to walk to make the graph.
1.
Adapted from Physics with Computers
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Graphical Analysis of Motion
To test your prediction, choose a starting position and stand at that point. Start data collection by
clicking . When you hear the Motion Detector begin to click, walk in such a way that the graph
of your motion matches the target graph on the computer screen.
4. If you were not successful, repeat the process until your motion closely matches the graph on the
screen. SAVE AND PRINT THIS GRAPH USING PRINT GRAPH AND PRINTING TO RM
75(one copy per person) Save each graph by copying it into a document on google docs. Share this
document with your lab partners.
3.
Results: (part II)
The results section of a lab report contains Data, Observations, and Calculations (including graphs)
Data
Collect DATA to determine the average velocity for when you were walking away at a constant speed.
Click the examine button and record the initial and final positions and times in the table below.
Position (m)
Time (s)
Initial
Final
Calculations
Use the data you collected to determine your average velocity for that time interval by computing the slope
(in this case):
v=Δd/Δt or (v = ∆x/∆t)
Part lII Preliminary Velocity Experiments
Open the file “01a Graph Matching” from the Physics with Vernier folder. Click on the y axis label that
says position and change it to read velocity.
2. Try to match the shape of the velocity vs. time graphs that you sketched in the Preliminary Questions
section by using the constant velocity car in front of the Motion Detector or by walking. You may also
attempt to match the graphs using the low friction cart on a level track. Save each graph by copying it
into a document on google docs. Share this document with your lab partners.
1.
Adapted from Physics with Computers
1 ­
Graphical Analysis of Motion
Part IV Velocity vs. Time Graph Matching
1. Open the experiment file “01d Graph Matching.” A velocity vs. time graph will appear.
2. Discuss with your group how you would move the low friction cart on the level track to produce
this target graph and write out your procedure for how to move the cart.
3. To test your prediction, choose a starting position and place the cart at that point. Start by clicking
. When you hear the Motion Detector begin to click, move the cart as needed so that that
the graph of the motion matches the target graph on the screen. It will be more difficult to match the
velocity graph than it was for the position graph. You may find you get some interference with your
hand as you work.
4. If you were not successful, repeat the process until your motion closely matches the graph on the
screen. SAVE AND PRINT THIS GRAPH USING PRINT GRAPH AND PRINTING TO
RM 75(one copy per person)Save each graph by copying it into a document on google docs.
Share this document with your lab partners.
Results (part IV)
Data
1.
Collect data on the displacement of your car for the first section of the motion. Click and drag your
mouse to highlight the graph covering the same initial to final time you will use from the position
graph. Then click on the Statistics button. and record the average velocity for that time interval.
Then change the y axis label to Position and record the initial and final position of the car for the same
initial and final times.
Time (s)
Average Velocity
(m/s)
Initial
Final
(only one average velocity is recorded)
Calculations
Adapted from Physics with Computers
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Position (m)
Graphical Analysis of Motion
1.
Use the data from part IV to determine the displacement of the car using two different calculations:
a. First compute the displacement from or ∆x = xf – xi
b. Then compute it from the velocity and the time, by computing the area under the graph:
Δx=vavΔt
c.
Compare the two displacements using a percent error calculation. Use the first
computation as the accepted value and the second (from the velocity and time) as the
experimental.
Part V Accelerated motion:
Open the experiment file “02 Cart.” Two graphs will appear on the screen.
Place the Motion Detector at the top of an incline that is between 1 and 2 m long. Be very careful not to
let the cart roll off the incline or the table. When you are not using the cart place it upside down.
3. Sketch your prediction of the position vs. time and velocity vs. time graphs for a cart rolling freely up an
incline and then back down. The cart will be rolling up the incline and toward the Motion Detector
initially. Will the acceleration be constant? Will it change direction? Will there be a point where the
acceleration is zero?
1.
2.
Hold the dynamics cart at the base of the incline. Click to begin taking data. When you hear the
clicking, give the cart a push up the incline. Make sure that the cart does not get closer than 0.4 m to the
Motion Detector and keep your hands away from the track as the cart rolls. (you may need a little
practice with this.)
5. Zoom in (if necessary) on the portion of each graph that represents the time that the cart was freely
rolling. To do this, use the mouse to drag a rectangle around the useful portion of the data, then click the
Zoom In button, .Check your graph with the teacher. SAVE AND PRINT USING PRINT, BUT
PRINT PAGE ONE ONLY, PRINT TO THE ROOM 75 PRINTER (one copy per person).Save
each graph by copying it into a document on google docs. Share this document with your lab partners.
4.
Results (part V)
1. Collect data on the acceleration of the cart as it went up the incline. From the velocity graph collect
the initial and final velocities and times by using the examine button and record. Then change
the y axis of the velocity graph to give acceleration. PRINT THIS GRAPH, CLICK ON GRAPH
TO BE SURE IT IS SELECTED, USE PRINT GRAPH, PRINT TO THE ROOM 75
PRINTER(one copy per person). Click and drag your mouse to highlight the graph covering the
same initial to final time you used from the velocity graph. Then click on the Statistics button.
and record the average acceleration.
Adapted from Physics with Computers
1 ­
Graphical Analysis of Motion
Adapted from Physics with Computers
1 ­
Graphical Analysis of Motion
Data
Velocity (m/s)
Time (s)
Average Acceleration
(m/s2)
Initial
Final
Calculations:
Use the data from part V Accelerated Motion
a.
Determine the average acceleration from the Velocity vs. Time graph using the slope
formula (in this case):
rise
run
b.
=
Δv
Δt
= aav
Compare this to the average acceleration determined from the Acceleration vs. time graph
by using a percent error calculation. Use the average acceleration from the acceleration
versus time graph as the accepted value and the slope calculation as the experimental value.
Conclusion questions
Part II Position vs. Time Graph Matching
1.
2.
3.
4.
5.
Describe how you walked to match the position vs. time graph that you matched. Be complete and
detailed.
Explain the significance of the slope of a position vs. time graph. Include a discussion of positive and
negative slope and what the amount (or magnitude) of the slope tells you.
What type of motion is occurring when the slope of a position vs. time graph is zero?
What type of motion is occurring when the slope of a position vs. time graph is constant?
What type of motion is occurring when the slope of a position vs. time graph is changing?
Part IV Velocity vs. Time Graph Matching
Describe how the car moved for each of the velocity vs. time graph that you matched.
7. What does the area under a velocity vs. time graph represent?
8. What type of motion is occurring when the slope of a velocity vs. time graph is zero?
9. What type of motion is occurring when the slope of a velocity vs. time graph is not zero? Test your
answer using the Motion Detector.
6.
Adapted from Physics with Computers
1 ­
Graphical Analysis of Motion
Part V Accelerated Motion
How does the slope of the velocity versus time graph compare with the average acceleration from the
acceleration versus time graph? Refer to the percent difference you computed. Was this what you
expected? What could account for any differences?
11. Was the acceleration about constant or was it changing? How can you tell from each graph?
12. Was there any point in the motion where the velocity was zero? If so when did this occur (what was
the cart doing?). Explain your answers!
13. Was there any point in the motion where the acceleration was zero? If so when did this occur (what
was the cart doing?). Explain your answers!
10.
The Parts of the Lab Report to be Included in this Write Up Are:
Title Page
Problem
Statement
Results
Conclusion
Works Cited
and Format
and
Structure
5
5
25
25 (question format)
5
Total Points Possible for this Lab Write Up: 65 points
An optional rough draft will be edited by your instructor for this lab. The submission date will be
announced in class.
This lab report will be submitted via Google docs:
● You must use your school google docs account
● You must name your file using the following system:
(assignment type)­(course #)­(section)­(“year”)­(assignment title)­(Your Last Name)
For Example:
Lab­SC0341­1­1213­Motion Lab­Barker
●
The lab is due at 2 pm on ___________. Any changes made after this time will result in a
deduction and I will restore the document to the 2pm version. Late labs are a zero.
Adapted from Physics with Computers
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