[Phys-L] Re: A Third law question

[jsd at AV8N.COM (John Denker)]

Rick Tarara wrote:
> ... students are
> asked to hold a massive disk in their hand and then accelerate it upwards.
> She could understand that to do so, she had to increase the force of her
> hand on the disk to be greater than the force of the earth on the disk.
> What took the next 1/2 hour (and I think without ultimate success) was to
> try and understand how the disk was able to increase its force back on the
> hand so that N3 would hold.  I talked to her about inertia--about the
> resistance of the mass to changes in motion.

Hmmmmm.

>  I had her holding a 5 kg mass
> and then trying to accelerate it horizontally (to take out the gravitational
> factor).

Good.   I would have started with horizontal inertia;  a situation
with gravitational forces mixed with inertial forces just muddies the
water.

Don't make her hold it;  suspend it on strings, wheels, air bearings,
or whatever.

> I dropped that mass into her hands to have her experience the
> increased force (of her hand and on her hand) necessary to produce the
> needed acceleration to stop the mass.  She declined (wisely) to try and
> catch the falling mass with her hand in contact with the top of the table.
> We talked about moving things in space and I brought out an air track so we
> could look at a 'frictionless' situation.  In the end though, she was still
> having trouble.  She could 'understand' how she increased the force of her
> hand on the disk but couldn't really accept the inertia arguments about how
> the disk increased its force back on the hand.  'Where does the disk get the
> extra force when I push up with more force than its weight?' was her
> repeated question.

Y'all can probably guess what I'm going to say:
         CONSERVATION OF MOMENTUM.
The third law is a thinly-disguised statement of conservation of momentum.

If the student is asking "where does it come from" it suggests she is looking
for some sort of conservation argument.  Alas, force is not a conserved quantity.
Forces come and go.  MOMENTUM IS CONSERVED.  The conservation laws are primary
and fundamental.

The question "where did the force come from" is unanswerable.
The question "where did the momentum come from" is easily answerable, profound,
and important.

I would go back to square one and restate everything in terms of momentum.
I would mention the connection between force and momentum, but I would not
rely on it;  I would treat momentum as primary and fundamental.

A useful demo involves two students on skateboards.  If either pushes the
other, both go flying.  Momentum is conserved.

   Pulling with ropes is a sometimes-helpful refinement.  It decreases
   the temptation for one teenager to try to tip the other off his board
   with a sideways push.

Also the Newton's cradle toy can be operated in a mode that demonstrates
the flow of momentum:  pull back ball #1.  The other balls are initially
stationary.  Ball #1 swings and hits ball #2, which hits #3, which hits
#4, which hits #5, which goes flying.  There was a net loss of momentum
from ball #1.  Momentum flowed through balls #2, #3, and #4 but did not
accumulate in them.  There was a net increase in momentum into ball #5.
(This is too advanced for the first day, and certainly too advanced for
a student who is having trouble with the basic concepts, but it is
tremendously useful later in the program.)