At 12:26 pm 12/04/2006 -0500, Harry wrote:
> If you are bicycling fast enough you can cross a
> wooden plank spanning ditch before the plank breaks.
>
> Normally we say this is because it takes time for the
> plank to deform and >break when subjected to a weight.
>
> However, consider for a moment an alternative and
> naive(?) explanation: it is because you weigh less
> when you are moving than when you are stationary.
> The idea is your motion reduces your gravitational
> mass independently of your inertial mass while
> gravitational acceleration remains unchanged.
When I first read this post I was tempted to take
what one might call the Dr Pork approach and dismiss
it without thinking.
That would have been a mistake because on reflection
I can see that such quosi modo (Introit - not Victor
Hugo) questions force one to think about the
fundamentals of mechanics.
We can start off by imagining the plank has a slight
slope down towards the other side of the ditch.
In this case the bike need not touch the plank at all
and is effectively weightless as it crosses the ditch.
You can take the plank away and the bike will arrive
safely on the other side.
Similarly, a cop pursuing a robber can defy the
"Law of Gravity" by flinging himself across the gap
between a high building and a slightly lower one
without dashing himself to pieces in the alley below.
The problem with Gravity is that most laymen think
of it as a Force. And the problem with the layman's
notion of Force is that it is a static concept which
does not involve time. The gap between the building
is a kingdom in which King Force's rule is absolute.
Enter it, and SPLOSH - you are raspberry jam on the
pavement below. One instant you are at the top of
the building and the next you are mangled on the
ground. It's a discrete change - one might even
describe the attempt to cross the forbidden zone a
quantum leap from life to death.
It is reminiscent of the way that an electron jumps
from one level to another. Where is the electron in
between? It isn't anywhere (allegedly). What is the
time interval between it leaving one level and
arriving at the other. There isn't any interval
(allegedly). But then quantum physics was always more
the playground of physicists who preferred maths to
engineering. <g>
If you want to understand the way gravity works you
want to forget about Force altogether. You want to
erase the word from your vocabulary. You want to
think about motion - and motion involves time.
Quod non agit, non existit as Leibniz observed.
What kind of motion? The # raindrops keep falling
on my head # kind. although since gravity raindrops
are rather faster than the watery kind, perhaps a
hail of bullets being fired from the robber's
accomplices in a 'copter provides a more realistic
image.
If the cop leaps across the gap fast enough he can
evade the bullets save for a flesh wound or two
but if he dallies too long he will finish up a
cheese grater.
Now the motion which really interests us is not
the motion of the bullets but the motion of the
bike/cop as it/he traverses the gap. This is a
motion nested within a motion - a velocity of a
velocity - and this immediately raises a problem
because we are using the same words at two
different levels which causes confusion in any
hierarchical system. If you call both the
headmaster and his assistant, headmaster, then
you are not going to know when you are talking
to the decision maker. A workable hierarchical
system needs to have very distinctive names for
each level of command otherwise there is chaos.
One system where chaos is anathema is the Army.
In the army you have a plethora of distinctive
names and badges so that everyone knows exactly
who they are talking to and what authority the
person wields. Private, Corporal, Sergeant,
Lieutenant, Captain, Major, Colonel, Brigadier,
General - to name but the single barrelled ranks.
One knows exactly who one is dealing with in the
army.
In case anyone thinks, "Ah! we have a name for
the second order velocity. We have acceleration."
Now we haven't! Acceleration is the portmanteau
term which includes both velocities - just as
"squad" might include both
the private ("...a velocity")
and his corporal ("the velocity of...").
Likewise, jerk is a portmanteau word equivalent to company, say; jounce is a
portmanteau word equivalent to regiment - and so on.
The trouble with portmanteaus it that they get increasingly complicated and
difficult to understand. This is because they fail to shift their datum which
is at the level of private in the case of the army and distance/time in the
case of dynamics.
So, you can see that, in a sense, Harry is right. You do weigh less when you
are moving than when you are stationary. In effect you have been promoted from
Private to Lance-Corporal 8-)
Cheers,
Frank
