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Re: [Phys-L] Textbook Errors re Waterjet Levitation



On 10/20/19 10:55 AM, Scott Orshan wrote a bunch of good
stuff. Without disagreeing with any of that, let me offer
an /additional/ way of thinking about the issues.

In /addition/ to (not instead of) stating the third law in
terms of forces, we can state it in terms of /momentum/.
The third law expresses conservation of momentum.

This way of looking at it has tremendous practical and
pedagogical advantages, including:

1) On the FCI, several of the questions that students find
most troublesome are IMHO just smart-alecky trick questions,
more word games than physics questions. The word "force"
has numerous definitions, not just the technical physics
definition but also plebeian vernacular definitions, many
of which involve some notion of causation:
"The bandit /forced/ the lady to drop her purse."
IMHO it is unsporting to formulate questions that beg
for the plebeian interpretation, and then to mark that
interpretation wrong.

This is relevant to the momentum discussion, because
although momentum has its own set of multiple definitions,
the momentum-ambiguities are enough different from the
force-ambiguities that comparing the two is a good way
to detect when you're being swindled.
"Is the momentum transferred from the large truck to
the small car the same as the momentum transferred
to the small car from the large truck?"
When you phrase it in terms of momentum, the correct
answer is self-evident.
(In contrast, the corresponding force question is
much more of a problem for students. Keep in mind
that the large truck is the /causative/ factor,
which evokes the plebeian definition. Do not
pretend that the latter is obviously wrong,
because it isn't. Real live physicists take
turns using both definitions All The Time. It
is a matter of context-switching, not right or
wrong.)


2) Leaving aside questions of definition, there are some
situations where the momentum approach is vastly more
/convenient/ than the force approach. At some super
high level the two approaches are formally equivalent,
but at the down-and-dirty practical level one may be
much more convenient than the other, depending on the
circumstances.

In particular, for anything having to do with fluid
dynamics, the momentum approach is strongly recommended.

Once upon a time I went through the exercise of
rederiving the standard equations of fluid dynamics
in terms of force instead of momentum. Yikes! What
a mess! Ugly concepts. Unnecessarily complicated
equations. Trust me, you don't want to go there.

Now, I have no training on rocketry, but as far as I can guess, in a
flared nozzle the vertical component of the pressure along the nozzle
provides the upward thrust.

Nozzles are important for various reasons, /none/ of
which are essential to the topic of today's discussion.
The important thing is that the fluid that leaves the
rocket carries momentum. This is as simple as simple
can be. Draw a boundary around the rocket. If (say)
leftward momentum is flowing outward across the boundary,
then by the third law (i.e. conservation), the amount
of leftward momentum within the boundary must be
decreasing, or, equivalently, the rightward momentum
must be increasing. That is correct, concise, and
complete.(*) I would happily give full credit to such
an answer.

(*) I'm being slightly glib about the distinction
between momentum and momentum_per_unit_time, but
let's not worry about that. Restrict attention to
some particular interval of time if you want to be
rigorous.

Newton's 3rd is not about "stuff".

That's true, and there are good pedagogical reasons for
mentioning it, and even going into some detail about it.
In the water jet, there are *two* conservation laws,
both of which are important. Students perceive a paradox
if they confuse the two.
-- water is conserved
-- momentum is conserved

The amount of water is a scalar. The jetpack is not a
source or sink for water; that is, there is no accumulation
of water anywhere. So at any point, the inflow and outflow
of water must balance. In less-technical terms, the inflow
and outflow "cancel".

However, that does not mean that "everything" cancels!

Momentum is a vector. Each parcel of water in the the
feed-tube has upward momentum. So the feed-tube performs
upward transport of upward momentum. Meanwhile, the water
streaming out of the nozzle (normally, mostly) performs
downward transport of downward momentum.

These two contributions do not cancel! In fact, they
add. If you draw a boundary around the jet-pack and
pilot, *both* the feed-tube and the open streams produce
an increase in upward momentum within the boundary.

In the steady state, when the jet-pack is hovering, the
fluid-mediated transfer of momentum just balances the
gravitational transfer of momentum. Or, returning to
force language: The fluid dynamical forces balance
the gravitational forces.

Let's be clear: Downward transport of downward momentum
is the same as upward transport of upward momentum. There
is a double negative.

If you want to get fancy about it:
-- Amount of water is a scalar.
---- Transport of water is a vector, since you have
to specify the direction of transport.
-- Amount of momentum is a vector.
---- Transport of momentum is a second-rank tensor,
since you have to specify the direction of
transport.

It requires a bit of sophistication to diagram momentum
flow, but there are ways of doing it ... and this is a
bajillion times easier than trying to keep track of all
the forces that act on a parcel of fluid. One way of
diagramming it is discussed here:
https://www.av8n.com/physics/force-intro.htm#sec-momentum-flow

A proper analysis of the jet-pack is not easy.
Nothing involving fluid dynamics is ever easy.
Keeping track of the momentum is by far the simplest
correct explanation.
Keeping track of the forces would be much more complicated
(unless you skip a whole lot of details, at which point
you have thrown out the baby and kept only the bathwater).

Similar words apply to other fluid-dynamics situations,
including airplanes, sailboats, sports balls, et cetera.




On 10/20/19 10:55 AM, Scott Orshan via Phys-l wrote:

There are so many popular misconceptions about Newton's 3rd Law that
it is hard to know where to begin.

Newton's 3rd is not about "stuff". It is about forces. The worst
words are Action and Reaction, because those are easily
misinterpreted as things that happen, rather than simultaneous force
pairs.

The classic, "Q: How does a rocket work? A: Newton's 3rd Law" has
gotten countless students credit on exams, but is absolutely
meaningless. Everything works via N3, so it explains nothing.

A rocket works because the nozzle creates a pressure gradient. Lots
of force pushing up, external pressure at the bottom.

Now, I have no training on rocketry, but as far as I can guess, in a
flared nozzle the vertical component of the pressure along the nozzle
provides the upward thrust. The horizontal component is equal all
around, and the nozzle has to work hard not to explode, while
redirecting the hot exhaust downward, exactly the same way as the
bend in the firehose or the levitating waterjet.

A straight firehose with a non pressure reducing nozzle (the water
pressure stays constant until it has left the nozzle), basically a
pipe, connected to the hydrant would not have a backwards thrust. In
fact, the friction should produce a forward pull, causing the pipe or
hose to stretch. The reaction force is inside the fire hydrant, where
the vertical water flow from underground is turned 90 degrees.

Forces explain the changes in motion, but not all of those are
apparent. Conservation of momentum tells us that if something starts
moving one way, something else has to start moving the opposite way.
That other thing is often the earth, which is why these problems are
sometimes hard to work out.

An airplane in level flight or a helicopter hovering at a fixed
altitude are forcing a lot of air downward. If air moves downward,
what moves up? The answer is the earth, but its huge mass makes that
motion imperceptible. Later, the downward moving air hits the ground,
pushing the earth away.

When considering the entire closed system, include the earth.