Re: Inertial reaction

James J. Jiamachello ( (no email) )
Tue, 10 Mar 1998 17:27:12 -0500

Bill McMurtry wrote:
>
> Hi all,
>
> I pose a simple mechanical question to which, I hope, there is a
> simple answer.
>
> Suppose we have a balanced beam pivoted at the centre and at rest
> horizontally (like a see-saw or teeter-totter).
>
> Above each end of this beam are suspended two equal masses.
> Both masses are at equal height.
> The masses are positioned so that when dropped each will strike
> opposite ends of the horizontal beam at equal distances
> from the central pivot point.
>
> In this arrangement if both equal masses are dropped at the same time
> and therefore impact the balanced beam at the same time,
> the beam will remain horizontal and balanced.
>
> Each end of the beam experiences an equal reaction
> to the gained inertial energy of each mass falling under the influence
> of gravity.
>
> Suppose we place a device at one end of the beam so that on impact the
> gained inertial energy of one mass is captured and stored.
snip
> Would the balanced beam experience, on impact of the two
> falling masses, an unequal reaction due to the gained inertial energy
> of one mass being captured and stored by the spring/catch mechanism?
>
> Comments?
>
> Bill.

Hi Bill

The easiest way to see what happens is to draw a diagram
and show all the forces at their location on the beam.

Then do a balance equation to see how the forces interact for
the initial conditions.

If the beam is stiff to the point of no flexure then the pivot
absorbs all the force generated. Stored energy device is not
activated, nothing to store.

If the beam is flexible then it would vibrate when the masses
first hit it and the vibrations would dampen out based on the combined
mass of weights and beam on the pivot point.

If you then considered the spring/stored energy component attached at
one end of the beam then it would change the vibration response of the
beam and mass. This means both the initial impulse and the subsequent
vibrations dampening out.

The extra stored energy device makes the analysis more complex as the
vibrations would travel back and forth in the beam-mass assembly.

An then to make it more interesting you can make each item a system
with its own frequency response characteristics and play around
with the interactions to achieve a lasting resonance to get the most
out of dropping the weights.

Check out HighText Publishing Inc. "Modeling Engineering Systems",
by Jack W. Lewis a very cool intro to modeling such questions.

Jim