Exploring Kinematics with Motion Sensors (Stephen Herr)

Title: Exploring Kinematics with Motion Sensors

Google Spreadsheet

Principle(s) Investigated:

  • Gravitational acceleration
  • Kinematic equations
  • Graphing Data
    • Reference Points
    • Distance / Displacement
    • Slope
    • Linear vs. Non-linear relationships
    • Trend lines
    • Definite integrals / area under the curve
  • Displacement, velocity, acceleration
  • Speed of sound (how motion detector works, sonar, etc.)

Standards :

Eight Grade Physical Sciences

1.The velocity of an object is the rate of change of its position. As a basis for under­ standing this concept:

a.Students know position is defined in relation to some choice of a standard refer­ ence point and a set of reference directions.

d. Students know the velocity of an object must be described by specifying both the direction and the speed of the object.

f. Students know how to interpret graphs of position versus time and graphs of speed versus time for motion in a single direction.

9. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:

a. Plan and conduct a scientific investigation to test a hypothesis.

b. Evaluate the accuracy and reproducibility of data.

c. Distinguish between variable and controlled parameters in a test.

d. Recognize the slope of the linear graph as the constant in the relationship y=kx and apply this principle in interpreting graphs constructed from data.

e. Construct appropriate graphs from data and develop quantitative statements about the relationships between variables.

f. Apply simple mathematic relationships to determine a missing quantity in a mathematic expression, given the two remaining terms (including speed = dis­tance/time, density = mass/volume, force = pressure × area, volume = area × height).

g. Distinguish between linear and nonlinear relationships on a graph of data.

Grades Nine Through Twelve - Investigation and Experimentation

1.Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other four strands, students should develop their own questions and perform investigations. Students will:

a. Select and use appropriate tools and technology (such as computer-linked probes, spreadsheets, and graphing calculators) to perform tests, collect data, analyze relationships, and display data.

b. Identify and communicate sources of unavoidable experimental error.

c. Identify possible reasons for inconsistent results, such as sources of error or uncontrolled conditions.

d. Formulate explanations by using logic and evidence.

e. Solve scientific problems by using quadratic equations and simple trigonometric, exponential, and logarithmic functions.

f. Distinguish between hypothesis and theory as scientific terms.

g. Recognize the usefulness and limitations of models and theories as scientific representations of reality.

j. Recognize the issues of statistical variability and the need for controlled tests.

k. Recognize the cumulative nature of scientific evidence.

Materials:

Procedure:

  1. Set up motion sensor as show below in pictures 1 and 2.
  2. Open the attached file.ds, it should open the program called DataStudio
    1. Carefully place the basketball about 5 cm bellow the motion sensor.
    2. Click the green start button near the top of the screen to begin recording data.
    3. Drop the basketball
    4. After several bounces, click th basketball_datastudio e stop recording data.
    5. Add a quadratic fit to the Position vs. Time graph
    6. Add a linear fit to the Velocity vs. Time graph
    7. Find the mean acceleration value for a section of the Acceleration vs. Time Graph
    8. Enter your results in this spreadsheet.

Student prior knowledge:

  • displacement
  • speed
  • velocity
  • time
  • acceleration
  • gravity

Questions & Answers:

1. Write a linear equation (y=mx+b) for a section of your velocity vs. time graph.

2. What does the coefficient "m" correspond to in the kinematic equations?

3. Compare the experimental value of gravitational acceleration to the generally accepted value of 9.8 m/s^2. Why are these numbers different.

Photographs:

Picture 1

Picture 1

Position vs. Time

Velocity vs. Time

Acceleration vs. Time