Mechanics Week 8

Week 8 - Investigating Forces

In Class Activity Plan (Word, Pdf)

Week 8: Investigating Forces

10 min Whiteboard - Motivating a Shift to Forces

PURPOSE: Sets up a situation where energy isn’t useful in modeling a coffee cup, necessitating a shift to forces.

Create a complete model for a coffee cup sitting on a table

Note: This is a constant position model, so there isn’t much interesting and should take almost no time.

10 min Board Meeting or Instructor led discussion

PURPOSE: Build consensus about when energy isn’t useful in modeling situations, necessitating a shift to forces.

Video Example:

Note: This could be a white board meeting or a lecture/discussion led by the professor, but it should be a quick refresher of all the elements included in a model up until this point and a motivation to include forces.

  • Constant position model

  • How many pie charts?

    • 2 – but they don’t show any change in energy

  • Energy is about showing change, but we don’t have any change, so we need a new tool to model what’s going on

  • Enter forces

150 min total Investigating Forces Lab – Broken down into three parts (Word, Pdf)

PURPOSE: Sets up a situation where energy isn’t useful in modeling coffee cup, necessitating a shift to forces.

Note: While the Investigating Forces Lab comes as one large document, it actually works best when broken into three distinct parts. The first part moves from a model that only includes energy, to considering the role that force plays. The second part is “messing around” with the equipment to get a feel for forces. The third part is actually doing the experiment. In the guide all of these parts have been broken up, but refer to the same 9 page document.

15 min Whiteboard - Investigating Forces pg 1: Introducing force (15 of 150)

PURPOSE: Sets up a model using what they already know as a way to see how to incorporate forces into this model.

Video Example:

Technical Notes:

  • There is no equipment for the first part, only a thought experiment.

  • Have students put their model from page 1 on a whiteboard.

15 min Board Meeting (30 of 150)

PURPOSE: Build consensus on specific model using what they already know as a way to see how to incorporate forces into this model.

Video Example:

Note: You can skip this board meeting if short on time.

  • Note that there is an acceleration from rest to moving, but you don’t have to make everyone say that it will always accelerate

  • Correct system schemas with the person in the system

  • Is energy conserved? (Depends on whether they put the person in or out of the system)

  • What would happen if the cart were bigger? (Pies would be larger)

  • What model are we using?

  • The question on how the concept of force applies has no right answer, but it is important to elicit ideas about what they think will happen

35 min Investigating Forces pg 2–5: Messing around (65 of 150)

PURPOSE: Encourages them to seek patterns among data and to use data to support claims about the relationship between forces and models using kinematics.

Technical Notes:

  • For pulling using the force sensor, you get much cleaner data if you use a string rather than simply pulling on the hook with your hands. They should also “zero” the force sensors before taking data each time because the zero drifts during use.

  • Page 2 should be quick, they are learning how to use the force sensors

  • On page 4, don’t let them get away with simply writing F=ma for a rule, make them think about the evidence they have.

10 min Whiteboard - Investigating Forces p 5 (75 of 150)

PURPOSE: Propose patterns among data; establish relationships to be investigated in part three of the lab.

Make sure you get to force being proportional to both mass and acceleration, and that it has a direction in the following discussion

25 min Board Meeting (100 of 150)

PURPOSE: Builds consensus about patterns among data; establishes relationships to be investigated in part three of the lab.

Video Examples:

  • Push/pull is causing the motion

  • Force probe measures the amount of push/pull on the sensor

  • Forces & causes acting on the cart: Gravity (Earth), Pushing/pulling (Person), Contact (Track)

  • System Schema: Car/Person/Track with labeled interactions; useful for telling us where the forces are and what types of forces there are (emphasize arrowheads going both directions)

  • What did we learn from the first two experiments?

    • Force is proportional to acceleration

    • Force graph and acceleration graph look similar, but not the same

    • Does mass make a difference?

50 min Investigating Forces pg 6–9: Design your own experiment (150 of 150)

PURPOSE: Design experiments to test the relationships proposed in part two of the lab.

Technical Notes:

  • When they do their own experiments have them use the pulleys instead of just pushing and pulling, they get cleaner data this way. Note that if they want accurate numbers, they need to calibrate the force sensors (calibrate to 0 N with nothing on hook, then 9.8 N with 1kg mass).

  • This is a good lab to have them write up either their proposal for the experiment, or the complete model (evidence gives us rules) for homework

  • The instructor should enforce the need for students to get approval of their proposed experiments before they begin collecting data

  • Ideas for experiments include (but are not limited to):

    • Constant mass of car, change force (mass on pulley)

    • Constant force, change mass of car

    • Different directions of force, measure acceleration (for vector relationship)

    • Hardest to do, but important: get an a = 0 experiment with multiple forces acting on a single object

20 min Whiteboard - Investigating Forces pg 6–9

PURPOSE: Compare experimental designs and results of experiments testing the relationships proposed in part two of the lab.

NOTE: Emphasize the need for evidence to go with their claims in this part!

  1. What have you learned?

  2. What rules can you make? (Note: this is often done better if they focus on the rules from each experiment rather than trying to come up with one set of rules that arches over all the experiments.)

  3. What questions do you still have?

45 min Board Meeting

Note: This meeting is long, so it may need to be broken up into two. Address the discussion goals in chronological order to build up to the full Newton’s 2nd law.

Video Example:

Discussion Goals:

  • As force increases, acceleration increases

  • a = 0 when there is no force applied, even with a change in mass (indicates a multiplicative relationship)

  • Have a constant F if we change the mass and the acceleration in a proportional way

  • Force is a vector (depends on the direction)

  • So for every force, there is an acceleration, right?

  • To get the sum of forces, return to the coffee cup example – what forces are on it?

    • Why is there not an acceleration if there is a force?

    • So our equation is not complete: introduce ΣF = ma

    • It would be useful to have a new tool for keeping track of forces (hand out force diagram handout)

20 min Whiteboard - Analysis Tool: Force Diagrams (Word, Pdf)

PURPOSE: Introduce Force Diagrams as a new tool for modeling phenomena.

Have the students whiteboard the situation from the handout in order to make sure they think about what the force diagram represents

Seed:

  • Make sure you have groups doing both the forces are equal, and the forces not equal as the situation in the handout does not tell us whether the girl is moving at a constant speed or at a changing speed.

20 min Board Meeting

PURPOSE: Build consensus on use and interpretation of force diagrams as modeling tool in conjunction with system schema.

  • What does a force diagram show?

    • Direction, Size and amount of forces

    • Interaction causes the force (label in top right-hand corner)

    • Direction of the acceleration

  • Is every interaction a force?

    • Every interaction can be described by a force

    • Modeling! We don’t need to deal with each and every interaction; the choice of what we are modeling helps guide us to include/exclude interactions.

  • System schemas: 1 arrow for each interaction, labels are important, consistency with the force diagrams