Walking a Fine Line

Walking a Fine Line The following is adapted with permission from the University of Dallas Fall ‘01 General Physics I Laboratory Manual, Adaptation: John Boehringer

One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration versus 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 has traveled and whether it is speeding up or slowing down. In this experiment you will use a motion probe to determine this information by plotting a real time graph of your motion as you move across the classroom.

Problem To develop an understanding of motion graphs by analyzing graphs made by walking in front of a motion probe. You will use a motion probe to see what a graph of your motion looks like when you perform the following motions: a) walk slowly towards the motion probe, b) walk slowly away from the motion probe, c) walk quickly towards the motion probe, and d) walk quickly away from the motion probe.

Things to keep in mind: 1. The motion probe is the origin or reference point from which distances are measured. 2. The motion probe detects the closest object directly in front of it (including your arms if you swing them back and forth as you walk, or anything else that might come in line-of-sight with the probe). 3. The probe will not correctly measure things that come within 0.3 meters.

Objectives 1. Analyze the motion of a person walking across the room. 2. Predict, sketch and test distance vs. time kinematics graphs. 3. Predict, sketch and test velocity vs. time kinematics graphs. Materials Windows PC Vernier Motion Detector Lab Pro Interface Meter Stick Vernier LoggerPro software Masking Tape

Preliminary Questions (Answer these BEFORE you begin.) 1. Use the coordinate system with the origin at far left and distances increasing to the right. Sketch the distance vs. time graph for each of the following situations: (be sure to label your axes)  An object at rest 2 meters from the motion detector

 An object starting at 2 m and moving in a constant speed

 An object starting at 2 m and moving in the negative direction with constant speed  An object that is accelerating in the positive direction, starting from rest at 0 m.

2. Sketch possible velocity vs. time graphs for each of the situations described above on the same graphs, but using a different color pen or pencil.

Procedure Part I: Distance versus Time Graphs 1. Connect the motion detector to channel 1 of the LabPro and then the LabPro to the PC via the super USB cable included in the LabPro kit.

2. Place the motion detector so that it points towards an open space at least 2 meters long. Use short pieces of masking tape on the floor to mark the 0.5 m, 1m, 1.5m, 2m distances from the motion detector. Be sure your are set up such that your motion probe will not “talk to” another probe that is directly facing it.

3. Perpare the computer for data collection by opening the “Exp 01A” file from the Physics with Computers files under Logger Pro in your harddrive. One graph will appear on your screen with vertical axis scaled as distance from 0 to 5 meters and horizontal axis scaled as time from 0 to 10 seconds.

4. Using Logger Pro, produce a graph of your motion when you walk away from the detector with constant velocity. To do this, stand about 0.5 m away from the face of the probe and have your partner click Collect. Walk slowly (no more than 1 meter in 10 seconds) away from the motion detector when you hear it begin to click. Sketch the graph you obtain on the axes below. Be sure to label your axes numerically. 5. Make another position vs. time graph by walking quickly (no more than 2 meters in 8 seconds) away from the motion detector. Sketch the graph below.

6. Create a position vs. time graph by walking slowly towards the origin. Start 2 m away from the motion probe and walk at the same rate you walked in step 4. Sketch the graph below. 7. Make a position versus time graph by walking quickly towards the origin. Start 4 meters away from the detector and walk at the same rate you walked in part 5. Sketch the graph below.

Drawing conclusions 1. Describe the difference between the graph you made by walking away slowly and the one you made by walking away quickly.

2. Describe the difference between the graph you made by walking toward the origin slowly and the one you made by walking quickly. 3. Complete the table below to summarize your findings: ACTION Moving Slowly Moving Moving Slowly Moving toward the Quickly away from Quickly away origin toward the the origin from the origin origin Slope (+ or -) Slope of graph (Larger or smaller)

4. Explain the significance of the slope of a distance versus time graph. Include a discussion of the meaning of positive and negative slopes.

5. What type of motion is occurring when the slope of a distance versus time graph is zero?

6. What type of motion is occurring when the slope of a distance versus time graph is constant?

Assessing 1. Predict (by sketching) the graph produced by a person who starts at the 2 m mark, walks slowly and steadily away from the origin for 3 sec, stops for 3 seconds, and then walks toward the origin steadily and quickly. 2. Now do the experiment. Move in the way describes and graph your motion. Repeat if necessary. When you are satisfied with your graph draw it below.

3. Is your prediction the same as your final result? If there are any discrepancies describe the reasons you think they occurred.

4. a) For the graph below, describe from which time to what time you are not moving

b) you are moving away from the origin

c) you are moving toward the origin

5. a) For the graph above (the same graph you used for number 4), during which time are you moving the fastest?

b) During which two time intervals are you moving the same speed? Part II: Distance versus Time Graph Matching 1. Prepare the computer for data collection by opening the “Exp 01B” file from the Physics with Computers files under Logger Pro in your harddrive. A plotted distance versus time graph should appear.

2. Plan amongst your group and write below how you could walk to produce this graph.

3. To test your prediction, choose a starting position and stand at that point. Start collecting data by clicking Collect. When you hear the motion detector begin to click, begin walking as you have planned. Does your graph match the one given?

4. If you were not successful repeat the process until your motion closely matches that graph provided. When you are satisfied, ask you teach to compare your graphs and check the box provided on this lab handout.

5. Prepare the computer for data collection by opening the “Exp 01C” file from the Physics with Computers files under Logger Pro in your harddrive. A new plotted distance versus time graph should appear.

Repeat steps 2 – 4 using this new, target graph.

Making a mathematical Model Is there a way to determine how fast you are moving from your graphs? Yes! We can determine a model for finding this speed by using the tools integrated with the logger pro software.

1. Starting from about 0.4 meters from the detector, walk slowly away from the detector while data is being gathered. You will see a graph of motion on the screen as you walk.

2. Move your mouse along the tool buttons at the top of the screen. As you hover over each a title will appear. Find the Examine tool. Click on the Examine tool to trace along the graph. Use the mouse to move and select a point near the beginning of your constant movement portion of the graph. Record the value of x and y from the screen in the table below. Repeat this for a point near the end of the line. Position Time from y value of graph from x value of graph (meters) (seconds) Point near the start Point near the end

Now determine your average speed by calculating the change in position divided by the change in time: changeinposition x v    average changeintime t

3. Find several position, time coordinate pairs and enter them in the table below. Calculate average speeds in the last column by taking the difference in position and dividing it by the difference in time for that point and the previous one. Do likewise with the time values. Point Number Position Time Average Speed from y value of from x value of (m/s) graph graph (meters) (seconds) 1 2 3 4 5 6 7

4. Would you say that your average speed is constant? Explain your reasoning.

5. Now let’s construct a linear model of your motion by fitting a linear equation, y = mx + b, to your data. Note that here your y-variable is position and the x- variable is your time. This is somewhat counter intuitive since we often use “x” to represent displacement when we are problem solving. In this form, the y- intercept, b, represents what important position?

What does the slope, m, represent? 6. This software allows us to easily fit a line to your collected data. In the Trace mode we used earlier, click and drag a rectangle to highlight the relevant portion of your data. Now click on the function tool [f(x)]. Select a linear equation to fit. Next click on Try Fit. The line and the equation will appear in your window. If the fit looks good, go on. What is the slope of the line? (Don’t forget to include your units!)

7. How does your slope compare with your calculated average speed above?

8. What can you conclude about the slope of a straight-line position versus time graph?

Part III: Velocity versus Time Graph Matching 1. As time permits you can try matching velocity versus time graphs by using files “Exp 01D” & “Exp 01E.” Use the space below to describe how you would walk to create these graphs and show your instructor when you have achieved a satisfactory plot.

Graph File D:

Graph File E:

2. What type of motion is occurring when the slope of the velocity versus time graph is zero?

3. What type of motion is occurring when the slop of the velocity versus time graph is not zero? What is the physics word for this type of behavior? Test your answer with the motion detector. Extending 1. Given your answer to number 3 (above) what do you suppose the graph of position versus time will look like for a velocity graph of constant, zero slope velocity versus time plot?

2. What about for the position graph where the velocity graph shows a constant, but non-zero slope?

3. Are there any calculus concepts which apply here? What do we use to find the “slope” of a curve? Is that even possible? What does it mean in physics?