Two balls of equal mass are hung from the same pivot by bars of equal length. If one ball is raised and released, when it impacts the other ball it transfers all of its momentum and comes to a dead stop.
If one of the balls is replaced by a ball of half the mass on a bar of twice the length, what happens when the heavier ball is raised and released?
Newton's Balls and Leverage
Moderator: scott
-
alexjrgreen
- Enthusiast
- Posts: 45
- Joined: Fri Jan 15, 2010 1:28 pm
Newton's Balls and Leverage
Ars artis est celare artem
re: Newton's Balls and Leverage
I'm pretty sure you need an odd number of balls in a newtons cradle. If anyone can confirm that would be good.
http://www.youtube.com/watch?v=JV6EvtheIuk
http://www.youtube.com/watch?v=JV6EvtheIuk
re: Newton's Balls and Leverage
What goes around, comes around.
re: Newton's Balls and Leverage
Newtons Cradle is a brilliant demonstration of Conservation of Momentum, and how Momentum (Mass x Velocity) can be freely converted into an Impulse (Force x Time) and back again.
The really interesting thing is when the balls are of dissimilar masses. This is the experiment that shows that when an Impulse is transfered to a smaller mass, the smaller mass experiences a faster Acceleration and reaches a higher Velocity than the bigger mass that delivered the Impulse.
However - there is no net energy gain or momentum gain in the total system. This is because when the big mass hits the small mass, it cannot transfer all of the momentum. The smaller ball accelerates away faster than the bigger ball is moving - so contact is lost, and the Impulse (Force x Time). The end result is that the bigger ball keeps on moving - at a reduced Velocity, and in the opposite direction.
If all the Momentum was transfered from the big ball to the small ball - there would be an obvious increase in Energy (since Energy is a maths trick based on Squaring Velocity). A Proportional increase in Velocity would become a Disproportional increase in Energy. The two equations (MV and 0.5MVV) are not equal. If Momentum was conserved (as it surely is) then energy could not be conserved - it would have to increase (IF we could transfer all the momentum - unlike Newtons balls).
I believe it is essential to full understand Newtons balls - and then look beyond, as there is a definate Time limitation to the Impulse transfer.
This is where Pequaide has shown the way, with Tethers and Yo-Yo's and other methods of transfering Impulse so that the full Momentum of the larger mass can be transfered, and the larger mass comes to a halt.
The really interesting thing is when the balls are of dissimilar masses. This is the experiment that shows that when an Impulse is transfered to a smaller mass, the smaller mass experiences a faster Acceleration and reaches a higher Velocity than the bigger mass that delivered the Impulse.
However - there is no net energy gain or momentum gain in the total system. This is because when the big mass hits the small mass, it cannot transfer all of the momentum. The smaller ball accelerates away faster than the bigger ball is moving - so contact is lost, and the Impulse (Force x Time). The end result is that the bigger ball keeps on moving - at a reduced Velocity, and in the opposite direction.
If all the Momentum was transfered from the big ball to the small ball - there would be an obvious increase in Energy (since Energy is a maths trick based on Squaring Velocity). A Proportional increase in Velocity would become a Disproportional increase in Energy. The two equations (MV and 0.5MVV) are not equal. If Momentum was conserved (as it surely is) then energy could not be conserved - it would have to increase (IF we could transfer all the momentum - unlike Newtons balls).
I believe it is essential to full understand Newtons balls - and then look beyond, as there is a definate Time limitation to the Impulse transfer.
This is where Pequaide has shown the way, with Tethers and Yo-Yo's and other methods of transfering Impulse so that the full Momentum of the larger mass can be transfered, and the larger mass comes to a halt.
Anything not related to elephants is irrelephant.
-
justsomeone
- Addict
- Posts: 2098
- Joined: Tue Dec 30, 2008 5:21 pm
re: Newton's Balls and Leverage
Quote from ABHammer:
LOL Dax
I remember many of sour fingers playing with those.
Alan
Alan, I think your thinking about a different kind of balls if your fingers
were " sour ".
LOL Dax
I remember many of sour fingers playing with those.
Alan
Alan, I think your thinking about a different kind of balls if your fingers
were " sour ".
re: Newton's Balls and Leverage
I guess that his left ball was slightly near to ground...
... not a big deal...
:)
( sometimes it's hard to control.)
... not a big deal...
:)
( sometimes it's hard to control.)
It is interesting how a Newton's cradle can transfer the impulse, and in a sense MASS across a distance at very high speed. In fact with the cradle the transfer across all those intermediary balls seems almost instantaneous.
This may be useful in transferring mass across a wheel and I am wracking my brain to see how this can be done.
This may be useful in transferring mass across a wheel and I am wracking my brain to see how this can be done.
-
Wubbly
- Aficionado
- Posts: 727
- Joined: Sat Jun 06, 2009 2:15 am
- Location: A small corner of the Milky Way Galaxy
- Contact:
re: Newton's Balls and Leverage
Newton's cradle is a perfect example of both conservation of momentum and conservation of energy at the same time.
http://www.lhup.edu/~dsimanek/scenario/cradle.htm
Energy (1/2 m v^2) and momentum (m v) are two beautiful equations that are not irreconcilable if one considers that they are two seperate things. One is a number (a scalar quantity), and the other is something completely different - it's a direction, oh and BTW that direction happens to have a number associated with it called its magnitude. Momentum is a vector. Energy is not a vector. If you take away the direction from momentum and just look at the magnitude of momentum, you no longer have the thing called momentum. Energy can be captured, stored, and the entire value can be given to another object of a different sized mass (minus frictional and other losses of course). Momentum does not work that way. You can't give an object's momentum entirely to a seperate object of a different size because when you interact with another mass, you have the directional component of momentum to deal with, and you end up sharing the directional component of momentum in some way between the two masses. By comparing the scalar energy with only the magnitude of the momentum vector, one might argue that they are mathematically irreconcilable, but this analysis is comparing energy with only a part of momentum, and is ignoring the full definition of momentum. Energy and momentum really are two different things which can both be conserved if one doesn't throw away the definition of momentum in the process.
Since momentum is a vector, the law of conservation of momentum could be thought of as the law of conservation of momentum vectors. The conservation of energy doesn't have a direction associated with its value. Two different things, each having its own proper use, that can coexist peacefully together.
http://www.lhup.edu/~dsimanek/scenario/cradle.htm
Energy (1/2 m v^2) and momentum (m v) are two beautiful equations that are not irreconcilable if one considers that they are two seperate things. One is a number (a scalar quantity), and the other is something completely different - it's a direction, oh and BTW that direction happens to have a number associated with it called its magnitude. Momentum is a vector. Energy is not a vector. If you take away the direction from momentum and just look at the magnitude of momentum, you no longer have the thing called momentum. Energy can be captured, stored, and the entire value can be given to another object of a different sized mass (minus frictional and other losses of course). Momentum does not work that way. You can't give an object's momentum entirely to a seperate object of a different size because when you interact with another mass, you have the directional component of momentum to deal with, and you end up sharing the directional component of momentum in some way between the two masses. By comparing the scalar energy with only the magnitude of the momentum vector, one might argue that they are mathematically irreconcilable, but this analysis is comparing energy with only a part of momentum, and is ignoring the full definition of momentum. Energy and momentum really are two different things which can both be conserved if one doesn't throw away the definition of momentum in the process.
Since momentum is a vector, the law of conservation of momentum could be thought of as the law of conservation of momentum vectors. The conservation of energy doesn't have a direction associated with its value. Two different things, each having its own proper use, that can coexist peacefully together.
Last edited by Wubbly on Fri Aug 06, 2010 5:53 pm, edited 1 time in total.
The concept of vectors is a convenient fudge. I don't accept it as valid in all cases.
For example: two balls of steel with a mass of 1000 kg each and traveling at speed of 1000 m/s - but exactly 180 degrees opposed - collide.
On paper - the momentum of each ball exactly cancels out to zero.
In practice, the ball disintegrates into zillions of pieces which fly out in all directions.
We could also argue that the sum total of all those vectors also adds up to zero.
So either way you look at it - the final Momentum of this system = zero, more or less.
But is that the best way to look at it? We still have exactly the same mass (2000kg) of steel, and it is moving at very high velocity (minus liberated heat and light and sound etc) .... the only problem is that it is all moving in different directions, so we can't really make good use of it. But that is simply an engineering challenge ... internal combustion engines make good use of fuel exploding in all directions.
This is a good example of why Vector Momentum as a concept does not fully represent "quantity of motion".
Describing the Energy of this system side-steps this issue by simply squaring Velocity, making it an abstract concept that turns negative numbers into positive numbers. This way of crunching the numbers does provide acknowledgement of the "quantity of motion" when particles are spraying out in all directions. But i'm not convinced it is the perfectly full and accurate model of "quantity of motion".
I'm not so interested in the cases where Momentum & Energy can be reconciled - I'm looking for the cases where they can't. And I believe they exist.
For example: two balls of steel with a mass of 1000 kg each and traveling at speed of 1000 m/s - but exactly 180 degrees opposed - collide.
On paper - the momentum of each ball exactly cancels out to zero.
In practice, the ball disintegrates into zillions of pieces which fly out in all directions.
We could also argue that the sum total of all those vectors also adds up to zero.
So either way you look at it - the final Momentum of this system = zero, more or less.
But is that the best way to look at it? We still have exactly the same mass (2000kg) of steel, and it is moving at very high velocity (minus liberated heat and light and sound etc) .... the only problem is that it is all moving in different directions, so we can't really make good use of it. But that is simply an engineering challenge ... internal combustion engines make good use of fuel exploding in all directions.
This is a good example of why Vector Momentum as a concept does not fully represent "quantity of motion".
Describing the Energy of this system side-steps this issue by simply squaring Velocity, making it an abstract concept that turns negative numbers into positive numbers. This way of crunching the numbers does provide acknowledgement of the "quantity of motion" when particles are spraying out in all directions. But i'm not convinced it is the perfectly full and accurate model of "quantity of motion".
I'm not so interested in the cases where Momentum & Energy can be reconciled - I'm looking for the cases where they can't. And I believe they exist.
-
Wubbly
- Aficionado
- Posts: 727
- Joined: Sat Jun 06, 2009 2:15 am
- Location: A small corner of the Milky Way Galaxy
- Contact:
re: Newton's Balls and Leverage
Since momentum is a vector, then you would have to throw out the law of conservation of momentum as being valid in all cases (unless you believe momentum is also misdefined).The concept of vectors is a convenient fudge. I don't accept it as valid in all cases.
Squaring velocity is not an abstract concept. It represents something that is both real and measurable. Work is force x displacement. Force is mass x acceleration (both measurable). Displacement is measureable. So the work (force x displacement) represents something that is both real and measurable. In the ramp calculations, the work performed from the top of the ramp all the way to the bottom of the ramp represents a quantity that is both real and measurable. If you look at the velocity at just the bottom of the ramp, square it, multiply it by the mass, and then divide the whole thing by two, you get the energy at the bottom of the ramp. This energy number is exactly equal to the sum of all the work performed from the top of the ramp to the bottom of the ramp. Energy can be thought of as stored work.... by simply squaring Velocity, making it an abstract concept ...
The work performed along the ramp is real and measurable. The work performed along the ramp is exactly equal to the energy at the bottom of the ramp. The energy is calculated based on velocity squared. Therefore an equation using velocity squared represents something that is both real and measurable. It's really not circular logic, (unless you believe energy is misdefined).
This is not my personal idea, but yes - I believe both Energy and Momentum are misdefined, and the Vector concept is part of the problem.
Semantics: Energy and Momentum as defined in physics are what they are. They are their own self referencing system, so as far as that goes, all is well and good. By "misdefined", what I mean is that I believe there is something about mass in motion that we don't completely understand yet. We understand the maths model that has been built over the years - certainly. But does that maths model represent actual 'reality' in all circumstances (such as inside the Bessler wheel or any other true PM device).
Mass cannot move at Velocity Squared, or a fraction thereof. That is what I mean when I say that any maths model involving Velocity Squared is Abstract.
We have a solid, water-tight maths model that is BASED on the assumption that PM is impossible. Using this maths model will NEVER find PM to be possible, because this model is BASED on that assumption.
We have to look beyond, but only IF we have a desire in our mind to find true PM.
Every single atom in existence is in Perpetual Motion. Why? Do YOU fully understand why?
Semantics: Energy and Momentum as defined in physics are what they are. They are their own self referencing system, so as far as that goes, all is well and good. By "misdefined", what I mean is that I believe there is something about mass in motion that we don't completely understand yet. We understand the maths model that has been built over the years - certainly. But does that maths model represent actual 'reality' in all circumstances (such as inside the Bessler wheel or any other true PM device).
Mass cannot move at Velocity Squared, or a fraction thereof. That is what I mean when I say that any maths model involving Velocity Squared is Abstract.
We have a solid, water-tight maths model that is BASED on the assumption that PM is impossible. Using this maths model will NEVER find PM to be possible, because this model is BASED on that assumption.
We have to look beyond, but only IF we have a desire in our mind to find true PM.
Every single atom in existence is in Perpetual Motion. Why? Do YOU fully understand why?
-
alexjrgreen
- Enthusiast
- Posts: 45
- Joined: Fri Jan 15, 2010 1:28 pm
re: Newton's Balls and Leverage
Apparently I wasn't sufficiently clear...
A mass of 1kg is hung from a pivot by a bar of length 1m. A mass of 2kg is hung from the same pivot by a bar of length 50cm. The 2kg mass is raised and released. What happens?
A mass of 1kg is hung from a pivot by a bar of length 1m. A mass of 2kg is hung from the same pivot by a bar of length 50cm. The 2kg mass is raised and released. What happens?
Ars artis est celare artem
-
Bill_Mothershead
- Aficionado
- Posts: 329
- Joined: Sat Feb 02, 2008 5:52 pm
- Location: Phoenix, AZ
re: Newton's Balls and Leverage
Is this a trick question?A mass of 1kg is hung from a pivot by a bar of length 1m. A mass of 2kg is hung from the same pivot by a bar of length 50cm. The 2kg mass is raised and released. What happens?
The weights are attached by "bars" to the same pivot.
But one attachment "bars" is twice as long as the other.
So the weights have an unequal distance to the pivot.
They have a different swing radius. The weights never touch each other.
So what does happen when the heavy weight (with short bar)
smashes into the long bar of the lighter weight?
Does the bar bend or break off?
A picture is worth a thousand words. I think I can picture it now. Do you mean essentially two pendulums being used like Newtons Balls? And then extending the length of one pendulum ... interesting idea. Worthy of experiment to see what really happens.
My guess is that the ball would still rise to the same height regardless. IF all the momentum is transfered then the identical mass will experience the same Force for the same period of Time and therefore the same Acceleration and will therefore reach the same velocity. AFAIK, the horizontal component can be ignored, so the deceleration of gravity will do the same work on both balls in the same period of time.
Then again - thinking as I write - maybe the greater radius means that the second ball takes a longer amount of time to rise the same height. If that is the case, then it will experience a longer deceleration from gravity and probably not rise as high as a result.
Either way, I wouldn't expect a height gain. But I would like to see an experiment. Should be easy to do.
My guess is that the ball would still rise to the same height regardless. IF all the momentum is transfered then the identical mass will experience the same Force for the same period of Time and therefore the same Acceleration and will therefore reach the same velocity. AFAIK, the horizontal component can be ignored, so the deceleration of gravity will do the same work on both balls in the same period of time.
Then again - thinking as I write - maybe the greater radius means that the second ball takes a longer amount of time to rise the same height. If that is the case, then it will experience a longer deceleration from gravity and probably not rise as high as a result.
Either way, I wouldn't expect a height gain. But I would like to see an experiment. Should be easy to do.