## Studio Session 2

### Vectors

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.

Exercise

Use an on-line simulation from the University of Colorado PhET group to explore vector addition.

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 vectors.

(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 direction)?

### 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 20 cm.

Equipment needed:

• Motion sensor
• Meter stick
• Cardboard

How does the motion sensor work?

An electrostatic 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 Condition, 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.

Exploration

• 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 click Paste.)
• (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.

Experiment 1

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 graph.
• 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.

Data Analysis:

Once the graph has been successfully matched, complete the following:

• Copy the best matched graph into your log.
• 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 line sections.
Record what you are doing in your log.

Experiment 2

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 changing?
• Are you accelerating?  If yes, what is the direction of your acceleration?

Experiment 3

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 can.
• 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?  Explain!