Open a Microsoft Word document to keep a log of your
experimental procedures and your results. This log will form the basis of
your studio session report. Address the points highlighted in blue.
Answer all questions.
Use an on-line simulation from the University of Colorado PhET
group to explore vector addition.
HERE to open the simulation.
Explore the interface
- Clear All puts the vectors back in the bucket. Refresh your
browser to reset everything.
- The boxes on the top hold the magnitude, angle with the x-axis,
x-component and y-component of the last vector clicked. You may not enter values into these boxes.
You can change the magnitude and directions of the vectors by dragging them.
- The sum vector is the green vector.
- This simulation only allows integer values for the x- and
y-components of a red vector. Consequently, you cannot always exactly set the values of magnitude and
direction. Choose the closest values.
- The vectors can be easily translated, which is an important
learning goal for this simulation.
Use the simulation to solve the following problems:
(a) You walk 30 m in a direction 30o North of East.
Use the simulation to represent your displacement vector.
- How far did you move in the North direction?
- How far did you move in the East direction?
- How would you calculate the North and East
components of your displacement vector if you could not use the simulation?
Check that you get the same results.
(b) To get to a restaurant, you leave home and drive 6
miles South and then 10 miles West.
Use the simulation to represent your displacement vector.
- If a bird flew from your house to the
restaurant in a straight line, what distance would it cover?
- In what direction would it fly?
- How would you calculate the magnitude and
direction of the bird's displacement vector if you could not use the
simulation? Check that you get the same results.
(c) Suppose you and a friend are test driving a new car. You drive out of the car dealership and go 10 miles
East, and then 8 miles
South. Then, your friend drives 8 miles West, and 6 miles North.
- Use the simulation to find the magnitude and
direction of the car's displacement vector.
- Describe how you use the simulation to add
(d) An airplane is flying North with a velocity of 200 m/s. A strong wind is
blowing East at 50 m/s.
- What is the airplane's resultant velocity (magnitude and
Understanding Motion Distance and Time
Even a simple human motion such as walking is complicated.
Different parts of the human body change their position at different rates.
Their instantaneous velocities differ in magnitude as well as direction.
Today we will simplify. We will study walking while treating the
body as one rigid object. We will plot how its position changes when
it moves in front of a motion sensor.
You will use the motion sensor connected to the Pasco 850 interface to collect the data. You will
measure your distance from the sensor as a
function of time as you walk toward and away from the
sensor. The motion sensor is a sonar ranging device. It uses pulses of
ultrasound that reflect from an object to determine the position of the object.
Our motion sensor cannot accurately measure distances smaller than approximately
- Motion sensor
- Meter stick
How does the motion sensor work?
transducer in the face of the Motion Sensor transmits a
burst of 16 ultrasonic pulses with a frequency of about
49 kHz. The ultrasonic pulses reflect off a target
and return to the face of the sensor. The target
indicator flashes when the transducer detects an echo.
The sensor measures the time between the trigger
rising edge and the echo rising edge. It uses this time
and the speed of sound to calculate the distance to the
object. To determine velocity, it used consecutive
position measurements to calculate the rate of change of
position. Similarly, determines acceleration by
using consecutive velocity measurements.
Note: The motion sensor must face the target.
Setting up the motion sensor
- Make sure the Pasco 850 interface is turned on. Open the
Capstone program. The icon for this program is on the desktop.
- Plug the Pasco motion sensor into the interface. Put the yellow plug into Digital
Channel 1 and the black plug into Digital Channel 2. Switch the motion
sensor to long range (the stick man).
- In the Capstone program, click the Hardware setup button on the left, click digital channel 1 on the picture of the
Pasco 850 interface, and choose the motion
sensor II from the pull-down menu. Click the Hardware setup button again
to close the window.
- Drag a Graph icon onto the main display.
- Click "Recording Conditions" below the main display. Choose "Stop
Time Based, 20 Seconds". Click "OK".
- To test the motion sensor, lay it flat on the table facing upward and
move the piece of cardboard towards and away from the front of the motion
sensor. Start collecting data by pressing the Record button.
- Data collection stops after 20 s. You can also stop data
collection by clicking on the Stop button.
To become familiar with the Capstone tools, do the
following exercises, and summarize your result or conclusion
and your evidence for the conclusion for each
exercise in your log.
- Explore how to use the "Highlight range of points" button to zoom in and examine
a specific region of your data.
- Find out what you can do
with the "Show coordinates" button?
- Devise a way to measure the length
of one person's arm using the motion sensor.
Hint: A piece of cardboard may be useful.
- Compare the arm length you obtain with the motion
sensor equipment to what you measure using a meter stick.
- Turn the motion sensor so that it is facing you.
- Below the main window click the pull down arrow next to "Delete
Last Run", and then click "Delete all Runs".
- Click "Recording Conditions", "Start Condition,
Time Based, 4 Seconds".
- (a) Measure the distance from the sensor as a function of
time as you walk slowly and steadily away from the sensor.
Position yourself approximately 40 cm in front of the motion sensor
and click "Record". You have four seconds to adjust your
position. Then your distance from the motion sensor will be
recorded for 20 seconds (or until you click the Stop button) and
plotted as a function of time. Paste the
plot into your log.
(Highlight the graph, click Edit, Copy, then switch to Word and
- (b) Measure the distance from the sensor as a function of
time as you walk away from the sensor steadily but at a somewhat
higher speed. Paste the plot into your log.
- (c) Measure the distance from the sensor as a function of time as
you walk slowly and steadily towards the sensor. (Pick on a good initial
distance.) Paste the plot into your log.
- (d) Measure the distance from the sensor as a function of
time as you walk towards the sensor steadily but at a somewhat
higher speed. Paste the plot into your log.
Describe the graphs. Elaborate on the
differences between the graphs when walking at different speeds and when
towards or away from the sensor.
Click "Delete all Data Runs". Open a new page.
Measure the distance from the sensor as a function of time as
you walk toward and away from the sensor. Try to move in such a way, as to produce a plot of
position versus time, which matches an existing plot.
Right click on the link motion.txt and safe the
file as motion.txt in the Documents folder.
- In Capstone click "File, Import Data" and import the file motion.txt from the Documents folder.
- Drag a Graph icon onto the main display. Add a second plot.
- For one of the plots select position for the y-axis and for the other
plot select User Data 2. Expand the plots to show all data.
- Discuss with your partners how you think one of you
should move to match the displayed
- For one of you: Position yourself approximately 40 cm in front of the motion sensor and
click "Record". You have four seconds to adjust your
position. Then your distance from the motion sensor will be recorded
for 20 seconds and plotted. Try to match your motion plot to the plot
already on the screen. Repeat the experiment several times, until you are satisfied with the match.
Once the graph has been successfully matched, complete the
- Copy the best matched graph into
- In your own words, describe in
detail how the person moved to create the specific graph. Include information like the direction of motion
and how fast the person was moving. Your
description should refer to all important intervals on the graph.
When did the person have the greatest speed?
When was the person not moving?
When did the person have positive and
when did the person have negative velocity?
When did the person have zero velocity?
- Add a second plot of velocity versus time to your best
matched graph. Use "Highlight range" to select a data range
starting at 3 seconds and ending at 6 seconds on this plot. Click the
statistics button (the sum symbol) and choose to display the mean and the
standard deviation. The mean gives your average velocity in the time
interval between 3 and 6 seconds and the standard deviation gives the
estimated uncertainty in this value. Repeat this for other straight
Record what you are doing in your log.
Try to produce one of the position versus time plots shown in the figure below.
(your reproduction does not have to be perfect, just close.) Also record the corresponding velocity versus time plots.
- Paste your best attempts into you log.
- Describe the velocity versus time plots.
- Is your velocity constant? If not, how is it
- Are you accelerating? If yes, what is the
direction of your acceleration?
Use the motion sensor
to study your natural walking gait.
Have one person start at least five steps away from the motion
sensor. He/she should walk towards the sensor as naturally as he/she can, stop
for an instant, and walk backward away from the sensor.
Look at the position and velocity versus time data for the walk. Repeat the experiment if necessary. When you are satisfied with
the data, adjust the graph axes to best display the data.
Copy the graph to your log and give it a meaningful name.
Use the graphed walking data to answer the following questions in your log.
- Describe in words what the position and
velocity graphs are telling you about your motion. Give as much detail as you
- Even though the velocity lines are basically straight, do they
display a little "wiggle"
Compare your graphs with those of other groups. Do
the graphs of all groups show this wiggle?
What does the wiggle tell you?
- Identify on your graph where in the wiggle are you speeding up and slowing down.
Where in your gait could you be speeding up or slowing down? Examine the
push off and heel strike portions of your gait.
- Determine your stride length from your data. How did you do this
determination? Does this value seem reasonable?
- From your graphed data, estimate your average walking speed.
Convert your log into a session report, certify with you signature that
you have actively participated, and hand it to your instructor.