# On this thought experiment in which kinetic energy seems to be created

1. Oct 30, 2005

### eosphorus

plz help on this thought experiment in which kinetic energy seems to be created

first i would like to set two things straight: first this is a question of something that seems very strange to me not an affirmation, second my intention is not to challenge but to try to help trying to improve this sad world where kids starve for energy problems among other things, after this introduction here is my thought experiment and the impossible conclusion i reach, thats why i would apreciatte very much someone pointing the mistake on my experiment, here it goes:

imagine two counterotatory tetherballs unwrapping around the earth,
they have a mass of 1000 kg each, a initial radius of 1000 km, a final radius of a million km and the initial speed, the same than the final speed, of 1000 m/s. someone may say that because of conservation of angular momentum the speed in the end will be 1000 times smaller than the initial one because the radius has increased a thousand times, but then consider that if it goes from a radius of 1 million km to a radius of 1000 km then the speed of the tetherballs would increase 1000 times without having apported any energy to the system

so once the tetherballs have a radius of 1 million km you send one away to meet the universe cutting the cable and to the cable of the other tetherball you add a component that transforms the cable into rigidness, now being the cable rigid, the speed of 1000m/s and the distance of 1 million km the linear speed of the ball will be transferred to earth as rotation

you have started with a given linear kinetic energy and you end with rotational kinetic energy 1000 times bigger than the initial one because the speed is the same but the radius 1000 times bigger so the momentum transferred to earth seems 1000 times bigger than the initial one

plz forgive me if i have made an obvious mistake but thats why i post it here

2. Oct 30, 2005

### Staff: Mentor

Forget your exaggerated "1000 km" tethers. The same point can be made with an ordinary tetherball arrangement:

(1) The tetherballs are counter-rotating, so no angular momentum is transferred to the Earth.

(2) The angular momentum of each tetherball is not conserved; a torque acts on it. (But the total angular momentum is conserved. It remains zero.)

(3) Ignoring the drop due to gravity, the speed of the ball does not change since no work is done on the ball. You can view the ball's KE as translational or rotational, either way the KE doesn't change:
$${KE}_{trans} = 1/2 m v^2$$
$${KE}_{rot} = 1/2 I \omega^2 = 1/2 (m r^2) (v/r)^2 = 1/2 m v^2$$

3. Oct 30, 2005

### Moonbear

Staff Emeritus
eosphorus, can you please explain some of the assumptions you're making here. They don't make a lot of sense to me. I know I'm not a physicist, so maybe I've missed something.

Do you mean the tetherballs are counter-rotary to each other, or to the Earth's rotation?

How did they get there? Have these giant tetherballs magically appeared? The energy to reach that speed and radius had to come from somewhere, so where? I've played with my fair share of tetherballs on the playground, and they always needed a good hard smack to get started. I'd have been impressed if they spontaneously started spinning.

Okay, this seems reasonable, someone could argue this, so why is it not the case in your system? If you know there's a counter-argument or problem with your assumptions, and can't explain why it should be ignored, then do we really need to go any further with the thought experiment for you to find the flaw you're looking for?

Have you ever been on the receiving end of a snapped cable? How do you account for the recoil (or whatever the proper physics term would be) when that cable is cut?

How do you make the cable rigid? What's the mass of this cable, and how much energy do you need to use to transfer some new material along the length of this cable quickly enough that the giant tetherball doesn't start wrapping around the Earth the other way before you can make it rigid? You're talking about transferring some material that adds rigidity along a 1 million km cable instantaneously! :surprised That must require an amazing amount of energy input! Can you account for that?

If anything, wouldn't you ultimately lose energy when you release that one tetherball? It seems everything else would cancel out from the energy that has to go into getting the balls rotating in the first place. Can your scenario work without invoking magic to get the tetherballs started?

Last edited: Oct 30, 2005
4. Oct 30, 2005

### nemosum

Sorry Moonbear, I know you're a Super Mentor and all that, and are ceratinly more qualified than I am, but that was kind of a riddiculus post in my opinion. I mean give the guy a break. Of course it's impossible to rigidify a 1000 km tether, but if you tried to solve all aspects of a single problem before posting it it would never be posted. Some times you just have to say "It's impossible, but hypothetically if it DID happen then..."
Take a look at the Relativity forum. We're constantly saying "If you were traveling 97% of the speed of light then..." Can you think of any machine known to man that could propel a human being at 97% of the speed of light? Of course not, but we still say things like that so that we can discuss other questions within the hypothetical situation. Just something to think about.

5. Oct 30, 2005

### Moonbear

Staff Emeritus
But if it's really impossible, why waste time on it? He asked what's wrong with the scenario, and impossibility of one of the assumptions required to make it work seems like a big problem to me. And, actually, all I asked is if we make the assumption that it is done, then it's necessary to factor in the energy required to do it. Since the claim is that in the end there's some gain of energy, if he's forgetting to subtract out a major input of energy that would tip the balance toward the negative side, isn't that important, even if just hypothetical?

Ah, but there's a difference between a situation that is hypothetical because we don't have the technology to accomplish it vs ignoring the conditions required to obtain that state. In those hypothetical relativity questions, is it relevant how you got to 97% of the speed of light? I'm guessing it probably isn't, just that somehow you got there. In the "thought experiment" that is part of this thread, since it seems eosphorus is attempting to claim he has found a way to create kinetic energy, it is important to consider what it would take to set everything in motion according to his scenario, is it not? I don't care what he uses to make the tether rigid, just that he factor in the energy expenditure to accomplish it.

6. Oct 30, 2005

### ZapperZ

Staff Emeritus
That's not the same thing. We CAN propell particles close to c (try 99.9999%). So it is not a purely hypothetical question. Even if WE can't get there, our physics must work when we apply it to these objects or else the particle accelerators that we design will be garbage.

Secondly, a "thought experiment" should at least be "realistic". To provide a thought experiment that requires a phenomenon at the planck scale, for example, would be ridiculous. It may be interesting, but is it important? If one cannot answer that last part, no one is going to pay attention to such ideas. If such things cannot attain any reasonable effects, then it will never be considered as verified or become an accepted part of physics - and yes, I would include String theory in that.

Zz.

7. Oct 30, 2005

### nemosum

You do have some very good points Moonbear. I jumped to the conclusion that you were dicrediting his question, when I thought it was a good one. But your right, he should take into account how the tethers got moving in the first place. I'm still not clear on what he was asking with the rigid tether. I must admit I haven't taken calc. yet so I can't work out any equations for him.

8. Oct 30, 2005

### ZapperZ

Staff Emeritus
You are also missing a lot of "history" to this question. Let's just say this ISN'T the first time this type of question by this person has been addressed here.

Zz.

9. Oct 30, 2005

### eosphorus

you are right doc al mathematics seem to prove me wrong but thers something i still dont see

probably when you were a kid you have played on a playground with this spinning plattform that has a fixed wheel and the kids turn there for fun

if i kick the spinning platform with my leg 10 cm from the center and then 10 m from the center i see very clearly in my imagination that the platform will spin much more in the second case so seems that the transformation of linear kinetik energy into spinning kinetic energy depends on the radius with which this is applied

the tetherballs are counterotatory to each other, i do this in order to not work being tranferred to earth since theres no rotation of the earth cause by the tetherballs to make thing easier lets imagine a still earth

of course the tetherballs must be put into space and be given a initial velocity but im not saying that energy is created from nothing but that seems that energy can grow

in order for conservation of angular momentum to be acomplished you need to apport energy to the system, planets double their velocity when halving the radius because potential gravitational energy is transformed into kinetic energy but in the case of a tetherball the internal kinetic energy must remain the same because not energy at all is applied into the system

the recoil will be minimal because of the mass of the earth so big and th tension in the string which is equal to the centrifugal force is very low because the radius is very big

in order to make the cable rigid you should use a chain whic slabons could be blocked this needs almost no energy because you are not pushing but blocking

of course i would lose energy when releasing one of the balls so the final enrgy should be half of what i stated but still seems to grow

10. Oct 30, 2005

### Staff: Mentor

If I understand you correctly, the explanation is simple: You were trying to turn an object which had considerable rotational inertia. If you apply the force further from the center, you'll generate more torque for the same force and will more easily get the wheel turning. This is Newton's 2nd law applied to rotation.
Angular momentum will be conserved as long as no external torque is exerted on the system. You are correct that gravity does work on the planet as it nears the sun, thus increasing the planet's KE. Since gravity exerts no torque on the planet, its angular momentum remains fixed.

11. Oct 31, 2005

### eosphorus

i have just thought of a different setting for the same concept which makes the problem much easier though still impossible to solve for me so i would appreciate some help

i have 2 weights of 10 tons each united by a 2 meter weightless bar and this set is able to spin around an axe horizontally

i take two bars of very light and resistant material, that for simplification would be weightless, 10 km long each and i stick them to the weights incresing the radius of the set to 10km and 1 m

two guys give a pair of forces to the set with a kick of the leg, lets consider this kinetic energy applied to be equivalent at 1kg at a speed of 100 km/h each, something like a football, but they do it at 10 km and 1 m from the center

the linear kinetic energy of the kicks has been transformed into spinning kinetic energy so this last one cant be compared with the initial linear kinetic energy

so i break the bar that unites the two weights and let them go by the tangent

my question is neglecting gravity what speed will have the two weights?

12. Oct 31, 2005

### Staff: Mentor

If I understand you correctly, your example is like a giant dumbell: Two masses separated by a massless bar, rotating about an axis perpendicular to the bar passing through the center of mass of the system. The distance from the axis to each weight is 10 km + 1 m. I will assume this is correct.

We must take care not to confuse force, energy, and momentum, as these are distinct concepts. For the sake of argument, I will define a "kick" as imparting a given linear impulse (which is $F_{ave} \Delta t$). Realize that the same kick will have greatly different effects depending on what you kick: Give the same impulse to a boulder and a golf ball and expect different responses. It is not true that the same energy will be transferred in both cases. The same momentum will be transferred (by definition), but not the same energy. You will transfer much more energy to the golf ball, which will go flying. (Kinetic energy is proportional to speed squared.)

Now consider the effect of the same "kick" applied to your rotating dumbell at different points. The same linear impulse will have a different effect depending on where it is applied, since the torque generated will depend on the distance from the axis. Thus the kick applied at a distance of 1 m will impart a rotational impulse of $1 \times F_{ave} \Delta t$, while a kick at a distance of 10,001 m will impart a rotational impulse of $10001 \times F_{ave} \Delta t$. The rotational inertia remains the same, thus the kick at 10,001 m will have a much greater effect, transferring much more kinetic energy to the dumbell. (Note that the linear impulse is the same, regardless of distance.)

Another way to state this is simply that the angular momentum associated with a linear impulse is proportional to the distance from the axis at which it is applied.

What matters is how much energy is transferred to the dumbells. If two opposite kicks are made at 1 m and at 10,001 m, the translational momentum and energy imparted is zero in both cases. But the angular momentum (and thus the speed of the dumbells) is 10,001 times greater when the kick is done at a distance of 10,001 m versus 1 m.

I hope I did your example justice (without making any mistakes). (But I don't see the connection to your tetherball example.)

13. Oct 31, 2005

### eosphorus

"The distance from the axis to each weight is 10 km + 1 m. I will assume this is correct."

no the distance to the axe from each weight is 1 m but then two weightless bars extend another 10 km increasing the radius to 10 km and 1 m

my doubt is in the case of two 10 tons masses that can spin around an axe being the masses at 1 m of the center each

if i hit the 10 tons weights with a pair of 1 kg masses at 100 m/s with a radius of 1 m,exactly where the weights are, energy is conserved because the whole kinetic energy from the 1 kg mass is transferred to the 10 tons masses

but if i hit with the same pair of 1kg masses at a speed of 100 m/s with a radius of 1 cm seems to me that the 10 tons will move much less that if i hit them with a radius of 10km

in the case of hitting with 1 cm radius seems that kinetic energy has been reduced while if i hit with 10 km radius, having the weights a radius of 1 m, seems that kinetic energy has been created

thats why i put the example of the tetherball in which although the kinetic energy remains constant the potential energy seems to grow in an outwards tetherball while seems to reduce in an inwards one

"thus the kick at 10,001 m will have a much greater effect, transferring much more kinetic energy to the dumbell"

this is exactly what i dont see, how with the same initial kinetic energy the weights will acquire more or less kinetic energy depending on having more or less radius

then if i make the radius infinite remaining the weights at 1 m from the axe wouldnt the weight aquire infinite kinetic energy from an initial slight energy?

by the way doc im not trying to tease you im just that way i appreciate a lot your help

hey maybe galaxies shape in spirals because from an initial spark of energy universe is growing its energy

14. Oct 31, 2005

### Staff: Mentor

No problem. Assuming we define the "kick" as a linear impulse, all of my comments remain unchanged. (Of course, the rotational inertia of the dumbell is much less.)

Careful! If you "hit" the dumbell with a moving mass, total angular momentum will certainly be conserved, but energy is not necessarily conserved. Mechanical energy is only conserved if the collision is perfectly elastic--that is, if the mass "bounces off" of the dumbell. (Note that this "hit" is different than the "kick" (the linear impulse) that I defined in the last post.)

This is true! The amount of energy transmitted to the dumbell depends on where it's hit.

In no case is energy created. You seem to think that all of the energy of the incoming mass transfers to the dumbell--not true at all! If the collision is elastic, energy is conserved. But the amount of energy transferred to the dumbell is much greater if the impact is made at the greater radius. (The rest of the energy remains in the rebounding 1 kg mass.)

If the collision is inelastic (if the incoming mass sticks to the dumbell instead of bouncing off), then a good portion of the energy of the incoming mass is lost as thermal energy.

Ignoring gravity, the tetherball has only kinetic energy, which remains constant. No potential energy.

As I hope I explained, the amount of mechanical energy transferred to the dumbell depends on the details of the collision. This should make intuitive sense. Imagine shooting a bullet at two targets: a huge boulder versus a golf ball. The boulder will hardly move, getting very little of the bullet's energy. Much more energy will be given to the golf ball.

As I explained, no energy is created, just a greater portion is transferred to the dumbell.

15. Oct 31, 2005

### pervect

Staff Emeritus
I would like to suggest to eosphorous, since he seems to be interested in learning, that he find a high-school physics book and review the defintions of force, work, energy, and momentum.

I cant recommend any particular titles at this level. Maybe someone else in the thead can

This would be helpful to eosophorous in understanding the solutions to the problems he's asking, it would also help him ask questions much more clearly by using these words according to their accepted defintions .

16. Nov 1, 2005

### eosphorus

i thing pervect is right i have to work harder in my concepts

the transfer of kinetic energy is quite complex but if i consider that the impulse is given by two tensed bows i clearly see that the momentum acquired by the dumbell depends on with what radius the energy of the bows is applied

on this way if i apply the tension of the bows the momentum of the dumbell will vary with the radius, double the radius of the bows double the momentum of the dumbell, triple the radius triple the momentum, make the radius 1 million times bigger and you obtain a momentum 1 million times bigger and all with the same initial energy, the one stored in the bows

if this is correct i could use the big momentum of the dumbell to tense the bows farther than they started by putting untensed bows very close to the radius of the dumbell

plz forgive me for my persistence and ignorance

17. Nov 1, 2005

### eosphorus

i meant to put the bows very close to the axe when the momentum is very big

18. Nov 1, 2005

### Staff: Mentor

You need to start from the beginning and study systematically. One concept builds upon another. Get a book and work your way through it.
I don't know how you are applying the impulse with a tensed bow. Do you just mean pull back a bow string and let it smack into the dumbell? If so, similar issues would apply as in previous schemes. In any case, energy is not magically created. The only energy you have to work with is the energy stored in the bow. Letting the bow strike further out from the axis does not create energy, it just allows more of the energy to be transferred to the dumbell.