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[Phys-L] Re: Analyzing movies: Speed, with Keanu Reeves



Brian Blais wrote:
... one calculates a take-off angle of a little less than 5
degrees necessary to get across, which doesn't seem like a
whole lot to me. I could even accept that I wouldn't
recognize a 5 degree ramp at the end of the bridge from the
distances shown in the movie.

Now, I imagine that the worst part of this is the "particle"
assumption.

One additional factor that you could take into account at the
introductory physics level is the G-load-factor. Obviously
you can't have a ramp shaped like this

/
__________/

with a sharp corner, because you'd pull infinite Gees at
the corner. So, calculate the size and shape of the
rounded-off transistion region. Hint: the best shape is
parabolic. Hint: most aircraft are certified for +3.8 Gees.
Aerobatic aircraft are certified for +6 Gees. A bus might
be stronger, but probably not much stronger. And passengers
sitting on bench-style seats in the bus would be verrry
unhappy at 4 Gees, and would risk loss of consciousness at
6 Gees. So ... pick a number like 4 Gees, and calculate
how long the transition region would have to be. Hint:
it's a nontrivial length.

Another issue that can be discussed at the intro level is
the fact that the passengers would be weightless during
flight. Since busses don't come with aerobatic-style
seat belts and harnesses, you'd have passengers and
everything else floating up off the seats. They don't
show any such thing in the movie (which is too bad; it
would have added to the melodrama).

Certainly any rotation of the bus would cause it to land on
its side.

That addresses the roll axis. You also need to worry about
yaw and pitch. Pitch is particularly interesting, since
the takeoff pitch attitude is markedly different from the
required landing pitch attitude.

You can calculate the consequences of having not quite the
right attitude for landing.

A bus with the engine in the rear would be aerodynamically
unstable in yaw and pitch ... meaning any small initial
error would grow during flight.

A quantitative discussion of the yaw, pitch, and roll issues
would be beyond the scope of the usual intro-level physics
class.

There may be friction losses that I am not
accounting for also.

Sure, there will be "some" friction ... but it won't
be too huge, and can be neglected to a first approximation.

In any case, the Reynolds number for a 70mph bus is pretty
big, so inertial forces (which depend on the mass of the
air) should dominate over frictional forces (which depend
on the viscosity of the air).