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## 29 December 2016

### Start Teaching Newton's 2nd Law Without Numbers or Equations

You've gone through a unit on motion; your students know the difference between velocity and acceleration.  (Or, at least some of them do, some of the time.) Now you're ready to introduce F = ma.  What do you do first?

I think most physics teachers, and certainly most textbooks, recognize the necessity of diving into free body diagrams right away.  Somehow, you must show the difference between an individual force and the NET force.  I concentrate on getting students to write out the object applying and experiencing the force; this helps avoid including fictitious forces (like "force of motion"), and it makes a future discussion of the third law child's play.

But, what do you do with those free body diagrams, other than make them?

(1) Some books and teachers jump to a mathamatical treatment of F = ma.  Practice problems in which the free body is used to determine the value of the net force, use the second law to determine acceleration, then use kinematics to get something like the initial or final speed of an object, or its time in motion.  Then you can do the reverse -- use motion information to calculate net force, and then the amount of an individual force.

(2) Others go from the free body diagram to a semi-quantitative treatment of F = ma.  That is, show mathematically and experimentally that at constant mass, a larger net force yields a larger acceleration; for constant acceleration, a larger mass demands a larger net force.  Linear graphs can be created to verify the second law relationship.

While I get to both (1) and (2), I don't start there.  I start merely with free body diagrams and the direction of motion.

But Greg, you say.  Free body diagrams have nothing to do with the direction of motion.

Yes.  That's the point.

Before I do any work with the relationship F = ma, I ask every possible question I can think of about how the object is moving.  Here we're considering motion in a line only; circular and projectile motion are for later on.

For example: This cart experiences a 3 N force to the left, and a 2 N force to the right.

* Which way is the net force on the cart?  (Left, because the greater forces act to the left.)

* Which way is the cart's acceleration? (Left, because net force is always in the direction of acceleration, and we just said net force acts left.)

* Which way is the cart moving? (No clue.  Acceleration and motion aren't simply related.  The cart could be moving left and speeding up, or moving right and slowing down.)

* Could the cart be moving to the right?  (Sure -- if the cart is slowing down.  Note that the most common answer which is utterly unacceptable is "Yes, if another object applied another 2 N force to the right.")

* Could the cart be moving left at 1 m/s?  (Sure, as long as its speed a moment later is greater than 1 m/s.  NOT "Yes, as long as its mass is 1 kg.")

* Could the cart be moving left at a constant speed of 1 m/s?  (No way.  The cart experiences a net force, so the cart has an acceleration, so the cart's speed must change.)

It's useful to let students play with the phet simulation "force and motion basics."  In class, I have students do a series of experiments in which they predict the force necessary to cause an object to speed up or slow down.  We don't worry about the actual value of acceleration, just the directions of motion and acceleration.

Once my students are rolling their eyes at these sorts of questions, answering with the same voice that my son uses when I remind him to wear a jacket to school on a cold day... well, then you're ready to move on to lessons (1) and (2) above.