Tuesday, July 15, 2014


I seem to have fallen behind on my formal model summaries -- although it feels a bit more like they've accelerated away from me / blurred together a bit while I wasn't looking.   So, forthwith I present a summary and implementation thoughts for the forces unit(s).

Force Model Summaries - Balanced and Unbalanced

Paradigm Lab / Scenario - Whacking a bowling ball with a rubber mallet to make it go with a constant speed, speed up, slow down, make a 90 degree turn, and go in a circle.  Hitting the ball makes it speed up, slow down, or turn (all forms of acceleration).  Not hitting the ball makes it either stand still or go at a constant speed (if it's already moving).

Force Rules

First Rule of Forces:  A force is defined as an interaction between two objects (and both objects must be included when naming a force with agent-victim notation).

Second Rule of Forces:  In all "non-spooky forces" (i.e. everything but "Earth force" (gravity), electromagnetism, and nuclear forces) the two objects must touch.

Force Diagrams
Forces on an object can be represented by force diagrams with

  • a point that represents the object
  • arrows representing all the forces on that object
    • all starting from / pointing away from the point, in the direction of the force
    • labelled F_{letter representing agent / letter representing object}
    • with lengths at least qualitatively showing relative strengths of the forces
  • force arrows that are not aligned with the logical axes of a scenario (e.g. along a ramp) can be drawn with two parts -- one along each of those axes, that add up to the original vector; these are called components.
  • Adding the forces along each axes (taking direction into account) tells you whether the forces on an object are balanced or unbalanced (and how big the unbalanced force is) 

Verbal model summary
"To have an acceleration, you need an unbalanced force."

Equation Summary
a = F_{unbal} / m
f_{surface_on_object} = mu{k or s} * F_{surface_on_object}

Additional Key Force Experiences / Investigations

  • normal force - conceptually bridged from an obviously deforming surface to much stiffer ones
  • weight vs. mass - a relationship between weight and mass is experimentally derived (hey!  W = mg, where g ~ 10 N/kg is the gravitational field strength)
  • Newton's Third Law - try every possible combination of two objects acting on each other and figure out that:  "The force that object A puts on object B is equal to the force that object B puts on object A, in the opposite direction" 
  • Newton's Second Law - measure how changing force and changing mass of a system change the acceleration, to experimentally derive a = Funball / m (the equation summary)
  • free fall - measure the acceleration of some falling objects; realize that it's always near 10 m/s/s as long as the object isn't too big / light (beach ball)
  • friction - how do many different factors affect the frictional force opposing a constant speed motion?  Figure out that they key factors are the material and the normal force, which is encapsulated in f = mu * table force, where the static friction adjusts to the pulling force until the object starts sliding, at which point the kinetic friction is approximately constant.
Force Model Implementation

The study of forces, especially balanced forces, is the area of mechanics where I have least used the modeling materials prior to this workshop.  The ninth grade FME curriculum I've been using spends several units building up a qualitative study of different types of static forces (weight, magnetic, friction), Newton's Third Law, pressure and buoyancy, and force vectors.  It leads with the idea that an object at rest must have balanced forces and works with that for several units before getting to objects in motion and learning anything about kinematics.  And then it has, as previously mentioned, a big gaping hole where acceleration and Newton's Second Law should be.  (Which is why I've used much more of the modeling constant acceleration model materials.)

There are some areas where what I've done manages to overlap pretty closely with what's described above.  I did use the idea of defining a force as an interaction, classifying contact vs. non-contact forces, and the agent-victim notation (can't remember where I picked this up...).   I have the Preconceptions in Mechanics book and have done a version of the normal force bridging discussion (old foam coach cushions work okay for the "foam" part).  And my weight vs. mass lab and friction labs were very similar (although a bit less free-form) to the ones we did in this unit.  However, there is very little formal discussion or use of force diagrams in my current curriculum, and since the mechanics instruction leads with forces rather than kinematics, we have to wait a while to get to the moving part of Newton's First Law and Newton's Second Law.

I will give the modeling ordering a shot with my ninth graders this coming year, and I will also try being more rigorous about force diagrams.  I have struggled to help ninth graders wrap their heads around vectors graphically, especially the components part, and I can't tell yet whether this approach will help with that or not.  I strongly suspect I will follow Bryan's lead and cut the ramp problems out of my ninth grade problems.  I have tended to qualitatively derive Newton's Second Law with kids pushing other kids on scooters, and while I might extended that to pushing carts with constant forces on tracks next year, I'm pretty sure I will NOT be dong the Modified Atwood Machine with them (unless they invent it themselves).  I haven't done the force-probe version of Newton's Third Law, and I will definitely bring that in.  And I think doing the free fall lab with the motion detectors seems easy and useful, and will bring that in.

Overall, my prior instructional approach has generally failed to dislodge the "motion = unbalanced forces" preconception from a significant chunk of my students, and left an even bigger chunk of my students uncertain what a net force was and how one could relate it to a numerical acceleration.  So there's definitely room for improvement!

Did we do a practicum lab for forces?  If not, does anyone have a favorite one?

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