Recently there was some discussion of using a real-world "theme"
to help with motivation and topic-selection in a physics course.
Also back in 2011 there was some discussion of "rich context"
exercises. It is never easy to cook up good exercises (rich
context or otherwise), and several of the examples that were
cited http://groups.physics.umn.edu/physed/Research/CRP/crexample.html
were embarrassingly bad, but still it seems clear that having a
supply of *good* real-world examples would be very helpful.
I mention this because of last night's Mythbusters episode. The
MacGuffin for this episode was a viral video purporting to show a
guy who wrapped himself in bubble wrap, jumped off a three story
building, and landed unharmed.
It is an easy physics exercise to prove that the video absolutely
must be a fake. Here's some real-world background information:
-- Fighter pilots are routinely subjected to about 9 Gs for a few
seconds at a time ... with the help of fancy G-suits and specialized
training.
-- When jumping off buildings, Hollywood stuntmen design for 10 G
deceleration at the bottom. More than 10 G would be considered
dangerous.
It's easy to calculate that the scenario in the video involves /at least/
100 Gs. You can calculate a lower bound without doing any experiments,
and without knowing anything about the properties of bubble wrap.
Hint: jbex - xvargvp raretl gurberz
So IMHO this is a case of fake ignorance. For entertainment reasons,
the hosts /pretended/ to not know that the video was obviously fake.
Tangential remark: We must always keep in mind the distinction
between entertainment and science. Mythbusters is an entertainment
show, and there's nothing wrong with that. However, entertainment
is not the same as science. The show claims they're doing science,
but they're not.
For example, there is are excellent entertainment reasons -- but
no good scientific reasons -- for attaching rocket motors to the
roof of a '67 Chevy.
There is such a thing as overlap, e.g.
-- Science in service of entertainment, such as the physics of
sports, or designing Hollywood special effects.
-- Entertainment in service of science, such as pedagogical
"motivation" which involves a certain amount of entertainment.
Still, even when there is overlap, it is worth keeping track of
which is which.
===
In any case, there are numerous real-world questions that arise in
connection with crashes and crash-protection. There is plenty of
real motivation for such questions, even if we dispense with bogus
motivation such as fake viral videos.
Let's take a step back suppose you really did want to cushion a fall
or crash. How would you do it? Example real-world applications
include:
-- Hollywood stunts.
-- Car crashworthiness: seat belts, crumple zones, airbags, etc.
-- Impact attenuators (e.g. barrels) at roadway gore points.
-- Arresting wires on an aircraft carrier.
-- Landing a rover on Mars.
-- Belaying a climber.
-- Egg-drop contest.
-- et cetera.
The egg-drop contest is only half-real, because the objective and the rules
are somewhat artificial ... but it can be seen as a stand-in for the other
applications on the list. Sometimes it is necessary to simplify things for
pedagogical reasons.
If you're serious about cushioning a crash, obviously you're not going to
use bubble-wrap, but what are you going to use? What properties should the
system have?
Tangentially related question: Given that bubble wrap is no good as an
energy absorbing material, the question arises: what *is* it good for?
Why do people use it?
Another tangent: Using bubble-wrap for crash protection is like building
a boat out of duct tape: It's not practical, but it makes for an interesting
exercise in improvisational engineering.
Suppose the objective is to decelerate something (or somebody) safely in the
minimum possible distance. This leads to some amusing "calculus of variations"
questions.
The ideal is to apply the maximum allowable force over the entire stopping
distance. This is obvious if you draw the graph of force versus distance, and
consider the area under the curve. If you're doing this with a Hookean spring,
it means you want to have a spring with a very long natural length, and a lot
of preload. Without the preload, the force would only gradually ramp up from
zero, which would double the stopping distance. You also need something
like a conical spring, so that it can crush flat without coil hitting coil.
Now suppose that rather than a long spring, we have bubble wrap with small
bubbles that undergo head-on polytropic compression, such that PV^γ = constant,
where the adiabatic exponent (γ) is about 1.4. Again draw the graph of force
versus distance, and consider the area. Calculate the optimal preload. Show
that for head-on compression the stopping distance is significantly worse than
the ideal. Explain how the stopping distance could be improved by switching
to non-head-on compression, e.g. by using plumbing or levers or some such.
===============================
There are many other Mythbusters episodes where they could have gotten a much
better result if they had thought about the physics a little bit. One example
that just cracks me up is the "360 degree swing" episode, where they attached
a rocket to a pendulum, and fired the rocket at the /top/ of the arc. They
would have been much better off firing the rocket at the bottom of the arc,
where the velocity was highest.
Energy = force dot dx.
Power = force dot velocity.
This depends on the interesting fact that rockets tend to put out constant force.
The same applies to turbojet engines, which explains why real-world jet aircraft
tend to need long runways (low power at low airspeed) and why the engines are more
efficient at high speed (high power at high airspeed).
This stands in contrast to piston-driven propellers, which to a fair approximation
tend to put out constant power rather than constant thrust.
Another example: Their analysis of "birds on a truck" was verrry incomplete.
Hint: Good science-fair project.
Another example: Their analysis of "killer cable snap" was verrry incomplete.
Hint: Good science-fair project ... but do it on a tiny scale and be careful.
More generally, when we see something like Mythbusters, we should keep the good
parts and discard the bad parts.
-- They seem to have a good eye for selecting topics that are entertaining.
-- They are good at prototyping and improvisational engineering.
-- They are not good at doing actual science.
So my recommendation is to use the show as a source of interesting topics and
open-ended questions. Then select a topic and investigate it more broadly and
more scientifically.
Then (!) please write up an outline of your analysis. Put it on the web and
notify the list, so that other people can use it. There are hundreds of people
on this list. If each person contributed one or two good real-world exercises,
it would make the world a much better place.