LabQuest
1-2
Graph Matching
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.
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 round-trip time and the speed of sound, the
interface can determine the distance to the object; that is, its position. It can then use the change
in position to calculate the object’s velocity and acceleration. All of this information can be
displayed in a graph. A qualitative analysis of the graphs of your motion will help you
understand the concepts of kinematics.
walk back and forth
in front of
Motion Detector
OBJECTIVES
 Analyze the motion of a student walking across the room.
 Predict, sketch, and test position vs. time kinematics graphs.
 Predict, sketch, and test velocity vs. time kinematics graphs.
MATERIALS
LabQuest
LabQuest App
Motion Detector
Physics with Vernier
meter stick
masking tape
1
LabQuest
PRELIMINARY QUESTIONS
1. Sketch the position vs. time graph for each of the following situations. Use a coordinate
system with the origin at far left and positive distances increasing to the right.
a.
b.
c.
d.
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
2. Sketch the velocity vs. time graph for each of the situations described above.
PROCEDURE
1. Find an open area at least 4 m long in front of a wall. Use short strips of masking tape on the
floor to mark distances of 1 m, 2 m, and 3 m from the wall. You will be measuring distances
from the Motion Detector in your hands to the wall.
2. If your Motion Detector has a switch, set it to Normal. Connect the
Motion Detector to DIG 1 of LabQuest and choose New from the File
menu. If you have an older sensor that does not auto-ID, manually set up
the sensor.
3. On the Meter screen, tap Length, then change the data-collection length to 10 seconds. Select
OK.
Part l Preliminary Experiments
4. Open the hinge on the Motion Detector. When you collect data,
hold the Motion Detector so the round, metal detector is always
pointed directly at the wall. Sometimes you will have to walk
backwards.
5. Monitor the position readings. Move back and forth and confirm
that the values make sense.
6. Make a graph of your motion when you walk away from the wall with constant velocity. To
do this, stand about 1 m from the wall and start data collection. Walk backward, slowly away
from the wall after data collection begins.
7. Sketch what the distance vs. time graph will look like if you walk faster. Check your
prediction with the Motion Detector. Start data collection when you are ready to begin
walking.
6. Try to match the shape of the distance vs. time graphs that you sketched in the Preliminary
Questions section by walking in back and forth in front of the wall.
Part Il Position vs. Time Graph Matching
7. Choose Motion Match ► New Position Match from the Analyze menu to set up LabQuest
for graph matching. A target graph will be displayed for you to match.
8. Write down how you would walk to reproduce the target graph. Sketch or print a copy of the
graph.
2
Physics with Vernier
Graph Matching
9. To test your prediction, choose a starting position. Have your partner start data collection,
then walk in such a way that the graph of your motion matches the target graph on the screen.
10. If you were not successful, have your partner start data collection when you are ready to
begin walking. Repeat this process until your motion closely matches the graph on the
screen. Print or sketch the graph with your best attempt.
11. Perform a second graph match by again choosing Motion Match ► New Position Match
from the Analyze menu. This will generate a new target graph for you to match.
12. Answer the Analysis questions for Part II before proceeding to Part III.
Part IIl Velocity vs. Time Graph Matching
13. LabQuest can also generate random target velocity graphs for you to match. Choose Motion
Match ► New Velocity Match from the Analyze menu to view a velocity target graph.
14. Write down how you would walk to produce this target graph. Sketch or print a copy of the
graph.
15. To test your prediction, choose a starting position and stand at that point. Have your partner
start data collection, then walk in such a way that the graph of your 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.
16. If you were not successful, have your partner start data collection when you are ready to start
walking. Repeat this process until your motion closely matches the graph on the screen. Print
or sketch the graph with your best attempt.
17. Perform a second velocity graph match by choosing Motion Match ► New Velocity Match
from the Analyze menu. This will generate a new target velocity graph for you to match.
18. Remove the masking tape strips from the floor.
ANALYSIS
Part II Position vs. Time Graph Matching
1. Describe how you walked for each of the graphs that you matched.
2. Explain the significance of the slope of a position vs. time graph. Include a discussion of
positive and negative slope.
3. What type of motion is occurring when the slope of a position vs. time graph is zero?
4. What type of motion is occurring when the slope of a position vs. time graph is constant?
5. What type of motion is occurring when the slope of a position vs. time graph is changing?
Test your answer to this question using the Motion Detector.
6. Return to the procedure and complete Part III.
Part III Velocity vs. Time Graph Matching
7. Describe how you walked for each of the graphs that you matched.
8. What type of motion is occurring when the slope of a velocity vs. time graph is zero?
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LabQuest
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.
EXTENSIONS
1. Create a graph-matching challenge. Sketch a position vs. time graph on a piece of paper and
challenge another student in the class to match your graph. Have the other student challenge
you in the same way.
2. Create a velocity vs. time challenge in a similar manner.
Back and Forth Motion
Lots of objects go back and forth; that is, they move along a line first in one direction, then move
back the other way. An oscillating pendulum or a ball tossed vertically into the air is an example
of a thing that go back and forth. Graphs of the position vs. time and velocity vs. time for such
objects share a number of features. In this experiment, you will observe a number of objects that
change speed and direction as they go back and forth. Analyzing and comparing graphs of their
motion will help you to apply ideas of kinematics more clearly.
In this experiment you will use a Motion Detector to observe the back and forth motion of the
following five objects:





Oscillating pendulum
Dynamics cart rolling up and down an incline
Student jumping into the air
Mass oscillating at the end of a spring
Ball tossed into the air
OBJECTIVES

Qualitatively analyze the motion of objects that move back and forth.
 Analyze and interpret back and forth motion in kinematics graphs.
 Use kinematic graphs to catalog objects that exhibit similar motion.
MATERIALS
LabQuest
LabQuest App
Motion Detector
pendulum with large bob
spring with hanging mass
meter stick
incline with dynamics cart
rubber ball (15 cm diameter or more)
protective wire basket for Motion Detector
protractor
PRELIMINARY QUESTIONS
1. Do any of the five objects listed above move in similar ways? If so, which ones? What do
they have in common?
2. What is the shape of a velocity vs. time graph for any object that has a constant acceleration?
4
Physics with Vernier
Back and Forth Motion
3. Do you think that any of the five objects has a constant acceleration? If so, which one(s)?
4. Consider a ball thrown straight upward. It moves up, changes direction, and falls back down.
What is the acceleration of a ball on the way up? What is the acceleration when it reaches its
top point? What is the acceleration on the way down?
PROCEDURE
These five activities will ask you to predict the appearance of graphs of position vs. time and
velocity vs. time for various motions, and then collect the corresponding data. The Motion
Detector defines the origin of a coordinate system extending perpendicularly from the front of
the Motion Detector. Use this coordinate system in making your sketches. After collecting data
with the Motion Detector, you may want to print or sketch the graphs for use later in the analysis.
For each part LabQuest must be prepared with these two steps:
1. If your Motion Detector has a switch, set it to Normal. Connect the
Motion Detector to DIG 1 on LabQuest and choose New from the File
menu. If you have an older sensor that does not auto-ID, manually set up
the sensor.
Part I Oscillating Pendulum
Motion Detector
Figure 1
2. Place the Motion Detector near a pendulum with a length of 1 to 2 m. The Motion Detector
should be level with the pendulum bob and about 1 m away when the pendulum hangs at rest.
The bob must never be closer to the detector than 0.4 m.
3. Sketch your prediction of the position vs. time and velocity vs. time graphs of a pendulum
bob swinging back and forth. Ignore the small vertical motion of the bob and measure
distance along a horizontal line in the plane of the bob’s motion. Based on the shape of your
velocity graph, do you expect the acceleration to be constant or changing? Why? Will it
change direction? Will there be a point where the acceleration is zero?
4. Pull the pendulum about 15 cm toward the Motion Detector and release it to start the
pendulum swinging.
5. Start data collection.
6. When data collection is complete, a graph of position vs. time will be displayed. If you do not
see a smooth graph, the pendulum was most likely not in the beam of the Motion Detector.
Adjust the aim and try again.
a. To take more data, start data collection after you have released the pendulum.
b. Continue to repeat this process until you get a smooth graph.
7. Examine the velocity graph.
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LabQuest
8. Answer the Analysis questions for this Part I before proceeding to Part II.
Part II Dynamics Cart on an Incline
9. If your Motion Detector has a switch, set it to the Track position. Place
the Motion Detector at the top of an incline that is between 1 and 2 m
long. The angle of the incline should be about 5°, or a rise of 9 to 18 cm.
10. 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?
11. Hold the dynamics cart at the base of the incline. Start data collection then give the cart a
push up the incline. Make sure that the cart does not get closer to the Motion Detector than
0.15 m for Motion Detectors with a switch or 0.4 m for those without a switch. Keep your
hands away from the track as the cart rolls.
12. If you do not see a smooth graph, the cart was most likely not in the beam of the Motion
Detector. Adjust the aim and try again.
a. To take more data, start data collection when you are ready to release the cart.
b. Repeat this process until you get a smooth graph.
13. Examine the velocity graph.
14. Answer the Analysis questions for Part II before proceeding to Part III.
Part III Student Jumping in the Air
15. If your Motion Detector has a switch, set it to Normal. Secure the Motion Detector about 3 m
above the floor, pointing down.
16. Sketch your predictions for the position vs. time and velocity vs. time graphs for a student
jumping straight up and falling back down. Will the acceleration be constant? Will it change
direction? Will there be a point where the acceleration is zero?
17. Stand directly under the Motion Detector.
18. Start data collection, then bend your knees and jump. Keep your arms still while in the air.
19. If you do not see a smooth graph, you were most likely not in the beam of the Motion
Detector. Adjust the aim and try again.
a. To take more data, start data collection when you are ready to jump.
b. Repeat this process until you get a smooth graph.
20. Examine the velocity graph.
21. Answer the Analysis questions for Part III before proceeding to Part IV.
Part IV A Mass Oscillating at the End of a Spring
22. Place the Motion Detector so it is facing upward, about 1 m below a mass suspended from a
spring. Place a wire basket over the Motion Detector to protect it.
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Back and Forth Motion
23. Sketch your prediction for the position vs. time and velocity vs. time graphs of a mass
hanging from a spring as the mass moves up and down. Will the acceleration be constant?
Will it change direction? Will there be a point where the acceleration is zero?
24. Lift the mass about 10 cm (and no more) and let it fall so that it moves up and down.
25. Start data collection.
26. If you do not see a smooth graph, the mass was most likely not in the beam of the Motion
Detector. Adjust the aim and try again.
a. To take more data, start data collection when you are ready to release the mass.
b. Repeat this process until you get a smooth graph.
27. Examine the velocity graph.
28. Answer the Analysis questions for Part IV before proceeding to Part V.
Part V Ball Tossed into the Air
29. Sketch your predictions for the position vs. time and
velocity vs. time graphs of a ball thrown straight up
into the air. Will the acceleration be constant? Will it
change direction? Will there be a point where the
acceleration is zero?
30. Place the Motion Detector on the floor pointing
toward the ceiling as shown in Figure 2. Place a
protective wire basket over the Motion Detector.
31. Hold the rubber ball with your hands on either side,
about 0.5 m above the Motion Detector.
Motion Detector
Figure 2
32. Start data collection, then gently toss the ball straight
up over the Motion Detector. Move your hands quickly out of the way so that the Motion
Detector tracks the ball rather than your hand. Catch the ball just before it reaches the wire
basket.
33. If you do not see a smooth graph, the ball was most likely not in the beam of the Motion
Detector. Adjust the aim and try again.
a. To take more data, start data collection when you are ready to toss the ball.
b. Repeat this process until you get a smooth graph.
34. Examine the velocity graph.
ANALYSIS
Part I Oscillating Pendulum
1. Print or sketch the position and velocity graphs for one oscillation of the pendulum. Compare
these to your predicted graphs and comment on any differences.
2. Was the acceleration constant or changing? How can you tell?
3. Was there any point in the motion where the velocity was zero? Explain.
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LabQuest
4. Was there any point in the motion where the acceleration was zero? Explain.
5. Where was the pendulum bob when the acceleration was greatest?
6. Return to the procedure and complete the next part.
Part II Dynamics Cart on an Incline
7. Print or sketch the portions of the position and velocity graphs that represent the time that the
cart was going up and down the incline. Compare these to your predicted graphs and
comment on any differences.
8. Was the acceleration constant or changing? How can you tell?
9. By hand, add tangent lines to a sketch of the velocity graph to determine the sign of the
acceleration of the cart when it was on the way up, at the top, and on the way down the
incline. What did you discover?
10. Was there any point in the motion where the velocity was zero? Explain.
11. Was there any point in the motion where the acceleration was zero? Explain.
12. Return to the procedure and complete the next part.
Part III Student Jumping in the Air
13. Print or sketch the portion of the position and velocity graphs that represent the time from the
first bend of the knees through the landing. Compare these to your predicted graphs and
comment on any differences.
14. By hand, add tangent lines to the velocity graph to determine where the acceleration was
greatest. Was it when the student was pushing off the floor, in the air, or during the landing?
15. When the student was airborne, was the acceleration constant or changing? How can you
tell?
16. Was there any point in the motion where the velocity was zero? Explain.
17. Was there any point in the motion where the acceleration was zero? Explain.
18. Return to the procedure and complete the next part.
Part IV Mass Oscillating on a Spring
19. Print or sketch the position and velocity graphs for one vibration of the mass. Compare these
to your predicted graphs and comment on any differences.
20. Was the acceleration constant or changing? How can you tell?
21. Was there any point in the motion where the velocity was zero? Explain.
22. Was there any point in the motion where the acceleration was zero? Explain.
23. Where was the mass when the acceleration was greatest?
24. How does the motion of the oscillating spring compare to that of the pendulum?
25. Return to the procedure and complete the next part.
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Back and Forth Motion
Part V Ball Tossed into the Air
26. Print or sketch the portions of the position and velocity graphs that represent the time the ball
was in the air. Compare these to your predicted graphs and comment on any differences.
27. Was the acceleration constant or changing? How can you tell?
28. By hand, add tangent lines to a sketch of the velocity graph to determine the sign of the
acceleration of the ball when it was on the way up, at the top, and on the way down. What
did you discover?
29. Was there any point in the motion where the velocity was zero? Explain.
30. Was there any point in the motion where the acceleration was zero? Explain.
Analysis of All Parts
31. State two features that the five position graphs had in common. State two ways that the five
position graphs were different from one another.
32. State two features that the five velocity graphs had in common.
33. State two ways that the five velocity graphs were different from one another.
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