Graph Matching

One of the most effective methods of describing motion is to plot graphs of distance, 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.

objectives

  • Analyze the motion of a student walking across the room.
  • Predict, sketch, and test distance vs. time kinematics graphs.
  • Predict, sketch, and test velocity vs. time kinematics graphs.

Materials

TI-83 Plus or TI-84 Plus graphing calculator
EasyData application
Motion Detector and data-collection interface
or CBR 2 orGo!Motion and direct calculator cable
meter stick
masking tape

Preliminary questions

1.Sketch the distance 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.

  1. An object at rest
  2. An object moving in the positive direction with a constant speed
  3. An object moving in the negative direction with a constant speed
  4. 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

Part l Preliminary Experiments

1.Connect the Motion Detector.

  1. Open the pivoting head of the Motion Detector.
  2. If the Motion Detector has a sensitivity switch, set it to Normal.
  3. Turn on the calculator. Connect the Motion Detector, data-collection interface, and calculator. (If you are using a direct-calculator cable, you do not need a data-collection interface.)

2.Place the Motion Detector so that it points toward an open space at least 4m long. Use short strips of masking tape on the floor to mark the origin and the 1m, 2m, and 3 m distances from the Motion Detector.

3.Set up EasyData for data collection.

  1. Start the EasyData application, if it is not already running.
  2. Select from the Main screen, and then select New to reset the application.
  3. Select from the Main screen, then select Time Graph…
  4. Select on the Time Graph Settings screen.
  5. Enter 0.05 as the time between samples in seconds.
  6. Select .
  7. Enter 200 as the number of samples and select .
  8. Select to return to the Main screen.

4.Make a graph of your motion when you walk away from the detector with constant velocity. To do this, stand about 1m from the Motion Detector and have your lab partner select . Walk slowly away from the Motion Detector when you hear it begin to click quickly. The graph will be drawn as you walk. After data collection is complete, a graph of distance vs. time will be displayed.

5.Sketch what the distance vs. time graph will look like if you walk faster. Check your prediction with the Motion Detector. To take more data, select , then , then to overwrite the latest run and start collecting data.

6.Try to match the shape of the distance vs. time graphs that you sketched in the Preliminary Questions section by walking in front of the Motion Detector.

Part Il Distance vs. Time Graph Matching

7.Return to the Main screen by selecting if necessary.

8.EasyData can generate random target distance graphs for you to match, such as the sample shown here. Your graph will probably be different.

  1. Select , then select Distance Match.
  2. Select , then , then to see your custom target graph.

9.Write down how you would walk to produce this target graph. Sketch or print a copy of the graph. The vertical axis runs from 0 to 3 meters, and the time axis runs from 0 to 10 seconds.

10.To test your prediction, choose a starting position and stand at that point. Start data collection by select . When you hear the Motion Detector begin to click quickly, walk in such a way that the graph of your motion matches the target graph on the calculator screen.

11.If you were not successful, repeat the process until your motion closely matches the graph on the screen. To repeat with the same graph, select . Print or sketch the graph with your best attempt.

12.Perform a second distance graph match (Steps 9–11) by selecting .

13.Answer the Analysis questions for Part II before proceeding to Part III.

Part IIl Velocity vs. Time Graph Matching

14.EasyData can also generate random target velocity graphs for you to match, such as the sample graph shown here. Your graph will probably be different.

  1. Select to return to the Main screen.
  2. Select , then select Velocity Match.
  3. Select , then , then to view your target graph.

15.Write down how you would walk to produce this target graph. Sketch or print a copy of the graph. The vertical axis runs from –0.5m/s to +0.5m/s, and the time axis runs from 0 to 10seconds.

16.To test your prediction, choose a starting position and stand at that point. Start data collection by selecting . When you hear the Motion Detector begin to click quickly, walk in such a way that the graph of your motion matches the target graph on the calculator screen. It will be more difficult to match the velocity graph than it was for the distance graph.

17.If you were not successful, repeat the process until your motion closely matches the graph on the screen. To repeat with the same graph, select . Print or sketch the graph with your best attempt.

18.Perform a second velocity graph match (Steps 15–17) by selecting .

19.Remove the masking tape strips from the floor.

Analysis

Part II Distance vs. Time Graph Matching

1.Describe how you walked for each of the graphs that you matched.

  1. Explain the significance of the slope of a distance vs. time graph. Include a discussion of positive and negative slope.
  1. What type of motion is occurring when the slope of a distance vs. time graph is zero?
  2. What type of motion is occurring when the slope of a distance vs. time graph is constant?
  3. What type of motion is occurring when the slope of a distance vs. time graph is changing? Test your answer to this question using the Motion Detector.
  4. Return to the procedure and complete Part III.

Part III Velocity vs. Time Graph Matching

  1. 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?

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.

Stadium Drop Lab

Galileo concluded that all objects regardless of mass undergo the same acceleration due to gravity. He experimented by dropping objects of similar shapes but different densities from various heights. Working in pairs you will be recreating one of the most famous experiments of all time.

Pre-Lab Questions:

1. What should the graphs of the displacement, velocity and acceleration look like for an object undergoing a constant acceleration?

2. What exterior force are we and Galileo ignoring?

3. What should be the time to ground and the velocity of an object be for an object dropped from the height of ten meters?

Lab Materials:

- 2 different round objects (ball and marble)

- Timing device

- Measuring Tape

- Graphing Calculators

Lab Procedures and Analysis:

1. Bring two round objects to the football stadium.

2. One partner will stay on the ground and time duration of drop and the other will drop each object one at a time from different heights (at least 10) use the steps (repeat 5 times at each height).

3. Find the average time of each drop height and error for time and measure height of drop (include error based on measuring tool).

4. For the larger of the two items enter averaged times as list 1 in your calculator and heights as list 2.

5. Plot a graph using list 1 as x axis (time) and list 2 as y axis (height).

6. Use the regression feature and find quadratic of best fit, give function and comment on constant found in front of x2 term.

7. Make list 3 the square of list 1. List 3 will be time squared

8. Plot a graph using list 3 (time squared) vs list 2 height.

9. Use regression feature and find line of best fit for list 3 vs list 2, give line and comment on constant found in front of x term.

10. Using your both approximation of constant of acceleration approximate Velocity at impact using for the object, should be 0 and a will be your two accelerations will be from 6 and 9

11. Graph your times vs final velocities for each height.

12. Repeat 4-11 for smaller object

Example Chart:

Quadratic Equation / Line of Best Fit / Velocity 1 / Velocity 2
Large object
Small Object

Conclusions:

1. Did your curves for displacement and velocity match your expectations?

2. Compare your graphs from 8 and 11 what do you conclude?

3. Compare large and small object results what should and what did you conclude?

4. Does your data support Galileo's findings? Explain why or why not.

5. Acceleration due to gravity is accepted to be 9.8 m/s2, give the four values of acceleration you calculated and explain why your values are different, comment on possible errors.