Re: Inertial reaction
Bill McMurtry ( weber@powerup.com.au )
Wed, 11 Mar 1998 17:48:29 +1000
At 17:27 10/03/98 -0500, you wrote:
>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
>
Hi Jim and all,
Assume the beam is 'infinitely stiff', i.e. it will not flex on impact (for
the sake of clarity). Also assume that there are no losses in the pivot or
in windage.
At the moment I am not really interested in vibration in the
beam/spring/falling masses system (once again for the sake of clarity -
call me a reductionist). If we can simply examine the system in terms of
action/reaction, between the falling, impacting masses and the balanced
beam, this may help to clarify the question.
Obviously when a falling mass impacts the beam there is a transfer of
energy from the gained inertial momentum (gravitational energy) of the
falling mass to the beam. There is a reaction in the beam. Because both
ends of the beam are subject to the same reaction from two equal falling
masses, the bean should not move (without any spring/catch mechanism). This
is quite obvious as the energy/force equation on both ends of the beam are
equal when both masses are equal, are dropped at the same time and from the
same height. What is not so obvious (to me at least) is what happens to the
beam when there is a spring/catch situated at one end of the beam that is
capable of capturing and storing ALL of the gained inertial momentum of one
of the falling masses.
If reaction in the beam is the result of gained inertial momentum being
transfered from the falling masses to the beam on impact, then what will
the beam do if the gained inertial momentum of one mass is captured and
stored? Does the beam still experience a balanced reaction to the falling
masses or will the beam experience an unbalanced reaction due to the
captured energy in the spring/catch mechanism?
Anybody?
Bill.