Re: [Phys-L] Demonstrating energy and levers

[John Denker <jsd@av8n.com>]

On 11/19/2013 06:25 PM, Doug Peltz wrote in part:

> Does anyone have a good idea for how to show the energy input on one side
> of the lever and the energy output on the other side?

I'm not sure I 100% understand the question.  I will
say a few words that might be a partial answer, or
perhaps stimulate somebody to come up with a better
answer.

I reckon it helps to exploit the idea of /equilibrium/
i.e. forces in balance.

Case 0:  out of balance, weight=1 distance=4 on one side
Case 1:  weight=1 distance=4 in balance with weight=1 distance=4
Case 2:  weight=4 distance=1 in balance with weight=4 distance=1
Case 3:  weight=4 distance=1 in balance with weight=1 distance=4

The point here is that when the system is in balance,
you can /move/ the thing using only a tiny force.
Ideally the force would be zero.  In practice, with
suitable engineering the force is three or four orders
of magnitude smaller than the unbalanced force seen in
case 0.

The fact that cases 1, 2, and 3 all exhibit equally good
balance, equally good cancellation of forces is a pretty
big hint that there is something special about the 
weight*distance product.  I'm not sure this rigorously
"proves" anything, but it is certainly consistent with
the basic energy story.

==============

Here's another line of evidence:  Imagine a "unit raiser"
that can be used once to deliver a unit amount of energy,
namely one unit of weight times one unit of vertical
distance. You can build a whole ensemble of such things,
all alike.  You need to use four of them to raise one unit 
of weight by four units of vertical distance.  You also 
need four of them to raise four units of mass one unit of 
vertical distance:
  *) If necessary, chop the large mass into quarters and 
   raise them one at a time.
  *) Or harness four raisers together to lift the whole
   mass at once.

This looks to me like a tangible, operational embodiment
of the idea of unit energy.

====

There are probably dozens of other things like this.  No
one of them is a convincing "proof" by itself, but taken
together they add up to some pretty strong evidence.
 -- levers
 -- pulleys
 -- gears on a bicycle
 -- transmission on a car
 -- electrical transformers
 -- hydraulic jacks
 -- etc. etc. etc.

If energy could explain only one or two things, nobody
would be interested.

=========================

> Here is a bad idea just to help show what I mean: I heat up 1 cup of water
> on side A by 10 degrees,

We agree that's a bad idea (but thanks for mentioning
it). I recommend staying away from thermal processes 
at this stage of the game, because irreversibility 
muddies the water rather badly.

(It is smart and helpful to clarify where the question
is coming from, even if it means mentioning bad ideas
in this forum.  It's good communication.  In contrast,
IMHO it's not good practice to mention bad ideas in 
front of students at the introductory level.  They've
got enough bad ideas already.)

===================================

To answer a question that wasn't asked:  It helps to
remind students that the physics energy is different
from the vernacular notion of energy that they've
been hearing about for years.  The Department of 
Energy is worried about some notion of /available/
energy or /useful/ energy;  this is important, but
it is *not* the same as the physics energy.

Also, when somebody says "please conserve energy
by turning out the lights" they are not using the 
physics notion of energy *or* the physics notion 
of conservation!  So the students are pretty much 
guaranteed to be confused twice over, through no 
fault of their own.