[email hidden] wrote:
< extensive snippage >
Quoted message said:I think that the end of a rigid, uniform 62"-long object
topples over and whomps into the ground significantly more
slowly than the same object held horizontal and dropped from
62", but I'm hoping that someone either has a simple
equation that I can follow, a more complicated equation that
I can't follow but will take on faith, or even an
explanation that the end of the toppling beam doesn't go
more slowly than it would in free fall.. . - - - .
| / . - - - .
|/_ _ . - - - .That is, how fast does the dot hit the ground in the two
figures above if it starts out 62" above the ground? I think
that it's going slower when it topples, but I want
reassurance.Along similar lines, does anyone know of a sneaky
demonstration that would slow these two paths down enough to
make them clear, something like Galileo's trick of rolling
balls down inclines to slow the effect of gravity and show
that large and small balls accelerate at the same rate?For anyone interested, here's a page with a miniature
falling chimney (two sections topple at different speeds)
and the short-armed cup and ball trick (a short beam
accelerates faster):http://www.physics.umd.edu/lecdem/outreach/QOTW/arch3/a043.htm
Thanks,
Carl Fogel
There is no simple answer for the time it takes a toppling pole
to topple, since it depends on how big the initial imbalance
or disturbance was that caused it to fall. If the pole was very
well balanced, and undisturbed, it could take an arbitrarily
long time to fall, even though unstable.
If the disturbance that makes it fall is small enough not to
impart significant kinetic energy to the pole, it is fairly
straightforward to compute its speed of groundwhompage, at least
in the case of pivoting without its base slipping, and the usual
ignoring of air resistance. The potential energy of the center
of gravity of the pole falling to ground level is converted to
kinetic energy of the pole rotating about its pivot point.
Knowing the change in potential energy, and the moment of inertia
of the pole about its pivot, you can solve for its angular velocity,
and its speed of whompage of any point on the pole.
Dave Lehnen