I think this is a very interesting problem, dropping two 3:1 mass superballs to bounce off the floor:
After some puzzling, and I didn't contrive this, I think 3:1 is the MAGIC RATIO!
https://en.wikipedia.org/wiki/Elastic_collision
I seem to get that the big ball stops dead, and the small one bounces up with 2X the downward velocity, which is 4x its initial energy being a square thing, so goes 4X as high as the initial drop height!
It's the way that you get 3-1 = 2 and 3+1 = 4....
Experiment seems to confirm this. The small ball flies away and the big ball seems to stop on the floor. But I could be wrong... 🤔
I have also been observing Black Holes, which amazes me, and doubtless you too. 😎
The central star is the Cygnus X-1 blue companion. 35mm, f2.8, 4 seconds, ISO 800. It is feeding the Black Hole, so is a huge X-Ray source, identified in the seventies, as the first proven one.
Cygnus is a great constellation, being on the Milky Way. I also got to see M29, which is a faint Pleiades type cluster, but will wait for better observing conditions for that one.
https://en.wikipedia.org/wiki/Cygnus_X-1
It's a 9th magnitude star, so my camera skills are getting good, one feels. 🙂
After some puzzling, and I didn't contrive this, I think 3:1 is the MAGIC RATIO!
https://en.wikipedia.org/wiki/Elastic_collision
I seem to get that the big ball stops dead, and the small one bounces up with 2X the downward velocity, which is 4x its initial energy being a square thing, so goes 4X as high as the initial drop height!
It's the way that you get 3-1 = 2 and 3+1 = 4....
Experiment seems to confirm this. The small ball flies away and the big ball seems to stop on the floor. But I could be wrong... 🤔
I have also been observing Black Holes, which amazes me, and doubtless you too. 😎
The central star is the Cygnus X-1 blue companion. 35mm, f2.8, 4 seconds, ISO 800. It is feeding the Black Hole, so is a huge X-Ray source, identified in the seventies, as the first proven one.
Cygnus is a great constellation, being on the Milky Way. I also got to see M29, which is a faint Pleiades type cluster, but will wait for better observing conditions for that one.
https://en.wikipedia.org/wiki/Cygnus_X-1
It's a 9th magnitude star, so my camera skills are getting good, one feels. 🙂
Yes, he may have meant a capacitive sensor, but I still do not get how it would demonstrate a link between electricity and gravity.
(A capacitive switch consists of two conducting plates separated by an insulator, so is basically a capacitor. The proximity of a conducting finger changes the capacitance between the plates and this change operates the electronics associated with the touch switch.)
Try this:
When the large ball strikes the ground, its momentum switches from -p to p. Now you can consider the process as a two ball collision. The small ball of mass m traveling down with momentum m√(2gh) and the large ball of mass M traveling up with momentum M√(2gh). This gives the momentum conservation condition:
(M−m)√(2gh) = m(vm) + M(vM)
Explanation of terms:
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There is the movement of a mass.... or no capacitance variation... I don't know.... 🙂
I suppose there is gravity in play between any different masses - and perhaps even within a "mass"... so its probably a quantum effect...😉
---- look, we are back on topic ;-D
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Townsend Brown is associated with the Biefeld-Brown effect which is an electrical effect where extremely high voltages can produce a type of propulsion associated with several anti-gravity theories.
Brown invented the effect but claimed Biefeld to be his mentor and co-experimenter. However, university records show no evidence of any research or experiments being carried out by Biefeld/Brown.
Brown himself seemed to think the effect demonstrated a connection between electricity and gravity, which he thought was being negated by the high voltage.
I think we can file member Earths' contribution under hooey!
Source: https://en.wikipedia.org/wiki/Paul_Alfred_Biefeld
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Just because electromagnetism and gravity share some of the same maths doesn't mean they are the same thing at all... though I don't know if the String Theorists fancy their chances. 🙄
I have been refining the two body elastic collision problem because nobody else will. For the large superball and a very tiny one, the tiny ball leaps up to 9X the height. That's the theoretical limit.
We know if the balls are the same size, they just bounce off each other with the same speed. The 3:1 ratio is indeed interesting as a sort of optimum slingshot x4 energy gain.
This matters if you are thinking about particle colliders I reckon, and I like this sort of easily memorable idea.
Continuing my investigations of important astronomical discoveries, I was looking at Cepheus near the pole star last night.
Delta Cephei varies between mag 3.5 and 4.3 every few days, it was the defining Cepheid variable, a type of star used to estimate Galaxy distances:
https://en.wikipedia.org/wiki/Delta_Cephei
Zeta and Epsilon are convenient comparison stars. Also interesting is red giant Mu, the Garnet Star, though my camera has not rendered it too well. William and Caroline Herschel liked this star.
There is an even redder one in Cancer near the Beehive Cluster, and I will try and snapit when Mars wanders near in a weeks time.
I have been refining the two body elastic collision problem because nobody else will. For the large superball and a very tiny one, the tiny ball leaps up to 9X the height. That's the theoretical limit.
We know if the balls are the same size, they just bounce off each other with the same speed. The 3:1 ratio is indeed interesting as a sort of optimum slingshot x4 energy gain.
This matters if you are thinking about particle colliders I reckon, and I like this sort of easily memorable idea.
Continuing my investigations of important astronomical discoveries, I was looking at Cepheus near the pole star last night.
Delta Cephei varies between mag 3.5 and 4.3 every few days, it was the defining Cepheid variable, a type of star used to estimate Galaxy distances:
https://en.wikipedia.org/wiki/Delta_Cephei
Zeta and Epsilon are convenient comparison stars. Also interesting is red giant Mu, the Garnet Star, though my camera has not rendered it too well. William and Caroline Herschel liked this star.
There is an even redder one in Cancer near the Beehive Cluster, and I will try and snapit when Mars wanders near in a weeks time.
First, M collides with the ground. Then, M and m collide, after which m has a positive, upward velocity.
M can have positive or negative velocity, depending on the ratio m/M. If it has negative velocity, it will collide with the ground again.
This site shows how to use the energy and momentum conservation equations to solve for the velocities after the collision: https://physics.stackexchange.com/questions/75425/collision-of-two-balls
However, the manipulation is all too much for my ageing and addled brain!
I don't know why you keep trying to explain my perfectly clear explanation! I knew exactly what I was doing. And please stop all the quotes. Completely unnecessary.
https://en.wikipedia.org/wiki/Elastic_collision
I have given the equations in the top post. All you have to do is put in the masses and initial velocities taking care of plus or minus sign for direction up or down.
This is a 2:1 ratio:
For a 3:1, the big mass stops dead at 0v, and the smaller one goes off at 2v. Which means it carries off all the Kinetic Energy.
https://en.wikipedia.org/wiki/Elastic_collision
I have given the equations in the top post. All you have to do is put in the masses and initial velocities taking care of plus or minus sign for direction up or down.
This is a 2:1 ratio:
For a 3:1, the big mass stops dead at 0v, and the smaller one goes off at 2v. Which means it carries off all the Kinetic Energy.
I was simply giving a reason why one might think "the big ball seems to stop on the floor" as you said in your description.
I was just trying to be helpful, but I shan't bother in future.
As the rock travels through spacetime, its speed relative to the expansion of the Universe slows down.
Ethan explains this here in terms of the rate of expansion of the Universe (which is a speed per unit distance): https://bigthink.com/starts-with-a-bang/ask-ethan-64-what-happens-to-matter-as-the-universe-expands/
I like to think of it as a bit like running to catch a bus that is moving away from you - your speed relative to the bus slows down.
Ethan explains this here in terms of the rate of expansion of the Universe (which is a speed per unit distance): https://bigthink.com/starts-with-a-bang/ask-ethan-64-what-happens-to-matter-as-the-universe-expands/
I like to think of it as a bit like running to catch a bus that is moving away from you - your speed relative to the bus slows down.
Electric charges seem similar to gravity because they both create a field that extends to infinity. Magic happens when electric charges move and something similar might happen when mass moves. Energy is stored in magnetic fields and electric fields when charges move and gravitational energy might be stored in 2 perpendicular fields of a similar kind when mass moves. The energy that a moving mass stores manifests itself as an increase in mass. It does seem that some kind of field is needed to store this kinetic or gravitational energy. If a mass is just a collection of particles then what makes the particles become heavier? Work is done on a mass when it is accelerated and this energy appears to be stored in a field generated by the moving particles. I could believe that gravity is caused by the motion of any particle at any scale that warps the space around it and then every other particle will be drawn to that warp in space. This warp will travel at the speed of light from its point of origin and must be refreshed constantly or the gravity warp would disappear. When that gravity particle is set in motion then a warp in space with velocity occurs and the distorted gravity field created by that moving warp may be where Einstein's relativistic energy or mass is stored. It follows that more warping means more energy storage and the warp must become unmovable at the speed of light. It must be true that warping space takes energy and that is why we must live in a collapsing universe. It may take 10 trillion years to happen but energy is always dissipating in our expanding universe.
Is the expansion we see really a collapse?
Collapsing - yes! It will indeed collapse into a big crunch! 😉
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Collapsing - yes! It will indeed collapse into a big crunch! 😉
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The accelerating electrons in a transmitter antenna generate changes in the electromagnetic field that propagate outwards at the speed of light as electromagnetic waves.
In an analogous fashion, accelerating masses generate changes in the curvature of spacetime that propagate outwards at the speed of light as gravitational waves.
I'm not sure what the topic is here anymore, but @James361 led us into puzzling where the increased mass in Special Relativity comes from, then led us into Veritasium's video about Energy not being conserved in General Relativity.
Both topics are actually a 100 years old!
Increased mass with velocity is Special Relativity in Minkowski flat SpaceTime. The Lorentz factor. Which doesn't even need or mention Gravity.
It is a correction to Newtonian Mechanics, as is the famous E = mc^2 equating mass to energy.
For 300 years we worked with Kinetic Energy = 1/2 mv^2, here double underlined on the right, but then added refinements on either side of the expression.
Take the Taylor series for the Lorentz Transform and multiply by mc^2 and you get the whole Special Relativity refinement. And the Lorentz Transform is what increases mass.
It is a theory of moving frames of reference, reconciling the speed of light being constant for all observers but the Laws of Physics being the same for all. Time, Mass, Energy, Momentum is all modified.
See, you half mv^2 is in there. That's Newtonian Mechanics.
Of course, in General Relativity the muse might like to add the Cosmological Constant or Energy-Momentum Tensor or some expression for the volume of the Expanding Universe, too.
But not in my Universe. Only Cosmologists like Sean Carroll will care. https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
General Relativity started out as a consideration of accelerating frames of reference, but turned into a theory of Gravity.
Considering how weak you are on simple calculations with rubber balls and Energy and Momentum, I think its good to know when you are out of your depth.
But don't let me stop you having a go at General Relativity. https://www.preposterousuniverse.com/grnotes/
Both topics are actually a 100 years old!
Increased mass with velocity is Special Relativity in Minkowski flat SpaceTime. The Lorentz factor. Which doesn't even need or mention Gravity.
It is a correction to Newtonian Mechanics, as is the famous E = mc^2 equating mass to energy.
For 300 years we worked with Kinetic Energy = 1/2 mv^2, here double underlined on the right, but then added refinements on either side of the expression.
Take the Taylor series for the Lorentz Transform and multiply by mc^2 and you get the whole Special Relativity refinement. And the Lorentz Transform is what increases mass.
It is a theory of moving frames of reference, reconciling the speed of light being constant for all observers but the Laws of Physics being the same for all. Time, Mass, Energy, Momentum is all modified.
See, you half mv^2 is in there. That's Newtonian Mechanics.
Of course, in General Relativity the muse might like to add the Cosmological Constant or Energy-Momentum Tensor or some expression for the volume of the Expanding Universe, too.
But not in my Universe. Only Cosmologists like Sean Carroll will care. https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
General Relativity started out as a consideration of accelerating frames of reference, but turned into a theory of Gravity.
Considering how weak you are on simple calculations with rubber balls and Energy and Momentum, I think its good to know when you are out of your depth.
But don't let me stop you having a go at General Relativity. https://www.preposterousuniverse.com/grnotes/
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May we dispense from personal references if they don't contain praise and congratulations and in so, gravity towards a warm and friendly atmosphere in the thread... 🙂
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