Mechanics Week 13

Week 13 - Investigating Spring Forces & Circular Motion

In Class Activity Plan (Word, Pdf)

Week 13: Investigating Spring Forces & Circular Motion

90 min Investigating Spring Forces (Word, Pdf)

PURPOSE: Investigate situation that can’t be modeled with constant acceleration; introduce Hooke’s Law; introduce relationship between forces and energy.

Video Example:

Video Example: (Predictions)

Technical Notes:

  • The force sensors need to have their direction reversed so that both the motion sensor and the force sensor see the same direction as positive

  • We probably want each group to have a different spring

  • They’re going to be coming back to energy at the end of this lab using the force versus displacement graph and the energy stored in the spring

Seed:

  • Consider the situation of a person just constantly stretching the spring

    • Draw pie charts for this situation

    • Where does the energy from the person go?

10 min Whiteboard - Investigating Spring Forces

PURPOSE: Summarize results of investigation

Video Examples:

Video Examples: (Boarding1, Boarding2)

  1. What did you learn?

  2. What rules can you make?

  3. What questions do you still have?

45 min Whiteboard Discussion

PURPOSE: Investigate situation that can’t be modeled with constant acceleration; introduce Hooke’s Law; introduce relationship between forces and energy.

Video Example:

Video Example: (Discussion)

Goals:

  • Hooke’s Law: F = -kd (the slope of the F vs d graph is the spring constant)

  • Energy stored in the spring: consider the units of the area under the F vs d curve (get to energy stored in the spring); need to point out this is negative (makes sense because the integral is negative)

20 min Whiteboard - Spring problems: Compression Spring (Word, Pdf) & Crates from a spring (Word, Pdf)

PURPOSE: Practice modeling situations using Hooke’s law; integrating non-constant acceleration situations into existing models.

Note: Do one in class and assign the other for homework

25 min Board Meeting

PURPOSE: Build consensus around modeling situations using Hooke’s law; integrating non-constant acceleration situations into existing models.

Video Examples:

Video Examples: (Boarding1, Boarding2, Boarding3)

40 min Instructor led discussion - Thinking about circular motion

PURPOSE: Introducing circular motion, special type of constant a modeling.

Video Example:

Video Example: (Four perspectives)

Using bowling balls and rubber mallets:

  • Ask the students, how would you have to hit the ball in order to get it to move in a circle? Try it.

  • Should find that they need to hit the balls toward the center of the circle (or perpendicular to the motion or something similar).

  • Confirm with video from Rutgers: http://paer.rutgers.edu/pt3/experiment.php?topicid=5&exptid=56

  • Have the students make a motion map for the ball

  • Divide the class in quarters, and have each of them find the direction of the acceleration for each ¼ of the motion map on their whiteboard

    • They already know about impulse, so it might be useful for them to be thinking about the force that is changing the momentum in this case

30 min Whiteboard Discussion

PURPOSE: Use motion maps to determine uniform circular motion as a special case of a constant acceleration model.

  • Looking at each section’s acceleration and force diagrams, what can we say about the direction of the acceleration? The net force?

  • Either show the geometric derivation of the centripetal acceleration or give the handout to get to a = v²/r

    • Handout: Centripetal Acceleration Derivation (Word, Pdf)