Storing Cookies (See : http://ec.europa.eu/ipg/basics/legal/cookies/index_en.htm ) help us to bring you our services at overunity.com . If you use this website and our services you declare yourself okay with using cookies .More Infos here:
https://overunity.com/5553/privacy-policy/
If you do not agree with storing cookies, please LEAVE this website now. From the 25th of May 2018, every existing user has to accept the GDPR agreement at first login. If a user is unwilling to accept the GDPR, he should email us and request to erase his account. Many thanks for your understanding

User Menu

Custom Search

Author Topic: "g" paradox...  (Read 20350 times)

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
"g" paradox...
« on: June 08, 2009, 06:02:02 AM »

  ...you can watch at :   http://www.youtube.com/watch?v=NFJPQLhWPvA    with the title "Falling Meter  Stick With Coins".

    In a classical lab-demo (Hinged stick-falling ball),you can see the acceleration paradox,when a ball and a board are released together,the end of the board outstrips its center of mass,leaving the board behind.

    That is,if you allow a board to rotate under the influence of gravity,the free end will accelerate at a rate greater than "g".

    We know that,gravity accelerates all objects at same rate...on the vertical line.

    This time,the relation between angular acceleration and linear acceleration,gives us a free-fall paradox (you remind the theory about the closed loop in gravity and the null result...).

    Here can be an "open gate" for our topic :if between two points,on the vertical line,for the same mass,we can obtain two different falls (velocity,acceleration,momentum....)...their inequality,can be a starting point for us...a "heavy angular fall"  vs.  an "easy linear up".

      All the Bests!  /  Alex   

Yucca

  • Hero Member
  • *****
  • Posts: 884
Re: "g" paradox...
« Reply #1 on: June 08, 2009, 07:15:05 AM »
Hi Alex,

I think it happens because the ruler is rigid and fixed at one end. The middle of the ruler wants to fall at freefall speed. But because one end is restrained it cant fall at freefall speed. The difference is transmitted as torque to the free moving end through rigid lever action and so the end falls faster than freefall speed. Conversely the end that is now falling faster than freefall will be exerting a negative torque, trying to slow the whole thing down.  Only one point on the ruler falls at freefall speed, every other point being either faster if further away from the fulcrum or slower if closer. The whole system finds force equilibrum, by redistributing the kinetic energy.

In my mind it´s not a paradox, sadly I think if one analysed the movement and applied integral calculus then it would be net neutral so the whole system kinetic energy would be the same as if the ruler were dropped half the height with both ends free, of course I could be wrong. The simplest way to test would be with impact analysis using a really rigid beam with a bit of weight to it:

Test1:
allow a 1m beam to swing downward, one end travelling 40cm. The other end travelling 0cm. Analyse the impact force by seeing how far a pencil can be pushed into a slab of plastiscine by the fast moving beam end.

Test2
allow a 1m beam to drop freely, neither end restrained, through 20cm. Analyse the impact force by seeing how far a pencil can be pushed into a slab of plastiscine by the middle of the beam.

I think in both tests the resulting impact will be the same when many drops are performed to eliminate noise.

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #2 on: June 08, 2009, 07:58:58 AM »

       Hi  Yucca !

  The term "paradox" is not mine...you can encounter on net.

  Paradox is a statement that seems absurd or self-contradictory,but may be true.

  You can watch short movies on net with the tag "Falling chimney",regarding the same puzzle.

  If you type "Falling stick" on net,you can find a plenty of information:it's simply classic lab-demo in elementary physics.We need proof no more ...the phenomenon is real...nothing new under the Sun!

         All the Bests! / Alex

Yucca

  • Hero Member
  • *****
  • Posts: 884
Re: "g" paradox...
« Reply #3 on: June 08, 2009, 07:40:50 PM »
Hi Alex,

It doesn't seem absurd or contradictory to me, just normal rigid body dynamics in action. But maybe it's a paradox to some?

best, Yucca.

Yucca

  • Hero Member
  • *****
  • Posts: 884
Re: "g" paradox...
« Reply #4 on: June 08, 2009, 09:40:04 PM »
My explanation above is somehwat abstract, it's difficult to explain it simply. But imagine this thought experiment, it will make things alot clearer:

Take a 1m long very rigid and lightweight stick, say a thin carbon fibre pole.

Pivot one end of the stick on the edge of a table.

Now 25cm from the pivot point attach a length of string, tied to the stick.

On the free end of the string hang a 1kg weight.

Now lift the sticks free end until it is horizontal, the 1kg weight hanging on the string below.

Now release the stick....

The 1kg weight will fall at nearly 1g, but of course we all know the end of the pole, 1m away from the pivot, will be accelerating vertically alot faster than 1g because it has to cover more distance. The end is being forced down by the inboard weight, acting through the rigid body of the stick, forcing the sticks tip to accelerate well beyond 1g.

This is exactly the same as a uniform ruler doing the same thing, only in my thought experiment above the effect is exaggerated for easier visualisation.

The whole system acts perfectly conservatively, no magic here unfortunately.

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #5 on: June 08, 2009, 09:49:28 PM »

         Hi Yucca !

   In my opinion,the root of this paradox (apparently contradiction that,maybe contains within it  a germ of truth ) is reffering to that fictitious "point" mass.

   The gravity applies to every atomic nucleus,but the mass has a different distribution :linear (a board) or compact,around a center (ball).

   So,the real distribution of mass (atomic system),can  "unlock" this real (or illusory...?!) puzzle.

   Anyway,the classic physics teaches and demonstrates (see lab-demo) that ,here is a net difference if a mass falls on a vertical line (without inertia ),or on a circular,curved line/trajectory (with inertia)...

   The next step is on-the -spot:to imagine  a closed loop =curved fall down+linear rise up.

   At:   www.geocities.com/iacob_alex/Some_Drafts/untitled023.jpg  on the top of the page ,you can see this trajectory(blue line),for a certain application.

           All the Bests! / Alex         

Yucca

  • Hero Member
  • *****
  • Posts: 884
Re: "g" paradox...
« Reply #6 on: June 08, 2009, 10:59:41 PM »
Hi Alex,

I'm still unsure, do you believe this effect might have hidden OU aspects to it?

I suppose the concept of "point mass" could be considered fictitious. But even if plancks constant does not apply to matter, if matter has infinite resolultion, if it is not a discreet system, then it will act exactly the same.

I fail (and it may be my failing) to see how whether it's a discreet or continuous system comes into play in this effect. Could you explain that a little further for me please?

Do you agree with my thought experiment above using the carbon fibre stick and weight? If so, can you see how a uniform stick obeys the same effect, just not as exagerated.

I assume you're not making the mistake of thinking all of the falling mass is at the tip, so I'm curious to know if you think there's something I may have missed here.

Yucca

  • Hero Member
  • *****
  • Posts: 884
Re: "g" paradox...
« Reply #7 on: June 08, 2009, 11:14:32 PM »
   Anyway,the classic physics teaches and demonstrates (see lab-demo) that ,here is a net difference if a mass falls on a vertical line (without inertia ),or on a circular,curved line/trajectory (with inertia)...

   The next step is on-the -spot:to imagine  a closed loop =curved fall down+linear rise up.

   At:   www.geocities.com/iacob_alex/Some_Drafts/untitled023.jpg  on the top of the page ,you can see this trajectory(blue line),for a certain application.

           All the Bests! / Alex         

Curved fall down, linear rise up. I think the potential and kinetic energies involved in both will sum to exactly the same amount, just the interplay between potential and kinetic will be distributed differently in each case.

If you have a hunch that there's something to it then I can only recommend experimenting. In this field the experiments can be made with real cheap materials and really easily.

I'm not saying there's nothing to the idea, just that it doesn't excite me enough to go to the top of the list of experiments to perform. Weird effects can often be found while looking for other things, experimenting is good!

Something that's somewhat related is Bruce De Palmas experiments with a falling object. He dropped it spinning and he dropped it not spinning. He got different acceleration profiles....?:

http://depalma.pair.com/gyrodrop.html

Cheers, Yucca.

AB Hammer

  • elite_member
  • Hero Member
  • ******
  • Posts: 1253
Re: "g" paradox...
« Reply #8 on: June 09, 2009, 02:12:16 AM »
Thank you Alex for posting.

 What I see is that all the weights on the yardstick want to go down at the same time. But the yardstick is in the way. So there is more pressure on the yardstick to go faster on the loose end because of the weight of the upper end on the table. So it is accelerating the loose end of the yard stick.

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #9 on: June 09, 2009, 07:04:29 AM »

  ....can give access to a simple unbalance relation ,for a possible  mass circulation (in a  closed gravity trajectory) : curvilinear fall down acceleration> linear jump up acceleration...?!

        All the Bests! / Alex

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #10 on: June 15, 2009, 07:45:51 AM »

   ...can be expressd with an elementary problem (test) : a rotating stick.

      Some expressive comments you can find at:   www.astrophysik.uni-kiel.de/~hhaertel/PUB/mathe_phys.pdf

     " Mathematics cannot express and answer to the question about the causality behind this process.There must be "something" besides gravity".

      A test (and calculus...) can be made for angles larger than 40 degrees (cos2/3).

      The essence of mathematics is to measure,but of physics is to explain "what?"...

             All the Bests! / Alex

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #11 on: June 19, 2009, 02:33:18 AM »

   ...or "falling stick/chimney..." has a direct and essential connection with any spoke(let's say stick...) that falls and uses the power of gravity.

      Any design must have at least one spoke("stick") and a rim,or two spokes (in a lever/pendulum concept) or more,as you like...

      As you see,the "g" paradox problem, is inevitable ("is in the cards"),if we want to play reality,but not a vain product of the imagination.   

        All the Best! / Alex

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #12 on: July 03, 2009, 09:31:07 PM »

 ...you can watch and understand ,in a more accurate manner,if you make a single click :   
    www.youtube.com/watch?v=Mi16ws35JIQ

        All the Best! / Alex

onthecuttingedge2005

  • Hero Member
  • *****
  • Posts: 1336
Re: "g" paradox...
« Reply #13 on: July 03, 2009, 09:47:40 PM »
...you can watch and understand ,in a more accurate manner,if you make a single click :   
    www.youtube.com/watch?v=Mi16ws35JIQ

        All the Best! / Alex

Very nice Gravity demo, Thanks!

Jerry :)

iacob alex

  • Hero Member
  • *****
  • Posts: 1280
    • Stellarotor http://www.geocities.ws/iacob_alex/stanga.html
Re: "g" paradox...
« Reply #14 on: July 13, 2009, 06:14:36 PM »

     Hi Jim!

 I agree with you...but we have one more problem,if you watch the last message at "Self moving hoop"(   www.youtube.com/watch?v=GuTMYgQDUzs  ).
 So,now we have two problems:

   -falling stick with pennies
   -Milkovic's pendulum
 Anyway,in any attempt to imagine some designs,I think we must take into account the both situations.
  You know,the best teacher is reality...

        All the Best! / Alex