A problem with KE = ½mv². Help.

[Farsight]

It's the sled and puck all over again:

 

The first puck accelerates the sled to .1m/s.

It now has Kinetic Energy 0.5 Joules.

 

The second puck accelerates the sled to .2m/s.

It now has Kinetic Energy of 2.0 Joules.

 

Four times the "work", twice the fuel. Because work and kinetic energy are a re-expression of the Force x Distance "stopping distance", and have no other inherent meaning or reality.

[Lsos]

Four times the "work", twice the fuel. Because work and kinetic energy are a re-expression of the Force x Distance "stopping distance", and have no other inherent meaning or reality.

 

How do you get four times the energy out of twice the fuel? It doesn't add up mathematically.

 

It has to be four times the fuel.

[Farsight]

It really is twice the fuel. Craig, where are you? Back me up here.

[Lsos]

Gasoline has 32000000 joules in a liter. If you want something, a puck lets say, to go from 0 to 32000000 joules of kinetic energy, you're going to have to burn at least that liter. Not half of it. There's no other way around it (uness the energy comes from somewhere else). If there was, I'd be making a perpetual motion machine right now.

[Farsight]

Lsos, here's a rehash an earlier post. And as far as I know it cannot be challenged:

 

Force is Mass x Acceleration, so if you burn constant fuel to produce a constant force for say 10 seconds you'll accelerate the rocket to say 1000m/s. If you repeat for another 10 seconds you'll accelerate the rocket by another 1000m/s. It's now going twice as fast as before, and you used twice as much fuel. But it's got four times the kinetic energy.

 

Work is Force x Distance, which we translate into kinetic energy. This is a way of thinking about "stopping distance". A rocket going twice as fast takes twice as much fuel to stop, and while it's stopping, it goes four times as far.

 

Impulse is Force x Time, which we can translate into momentum. It's a way of thinking about "stopping time". A rocket going twice as fast takes twice as much fuel to stop, and stops in twice the time.

 

Both are just different ways of thinking about a moving object.

 

Imagine a situation where a rocket kicks out its exhaust at 1000m/s. At the start of the burn, an outside observer sees the exhaust moving at 1000m/s, and the rocket hardly moving at all. Hence most of the "work" is going into the exhaust. Later when the rocket reaches 1000m/s, none of the "work" goes into the exhaust, because the observer notes that the exhaust is now moving at 0m/s. But if you're inside the rocket you feel a constant force and acceleration. You're burning a constant amount of fuel. Fuel has chemical "energy", so you naturally think about a constant transference of this chemical energy into kinetic energy via work. But now you're thinking about stopping time, not stopping distance, so you've got it wrong. Because physics treats work like the observer, and it's just a concept to do with motion. As is Kinetic Energy. It's just a way of writing down Force x Distance for stopping that rocket.

 

Energy is like Red. It's a property. You can see something that's Red, but you can't have the Red without the something. I've grown up thinking that Matter is made out of Energy, but there is no Energy.

 

It doesn't exist.

[Qfwfq]

Lsos, look at it the other way around: the slower the sled is moving, the smaller the fraction of the fuel's energy that goes to increase the sled's kinetic energy. The pucks take the rest of it.

[Farsight]

Lsos: our posts overlapped. Re your gallon of gasoline, you can't directly relate the chemical energy therein to the energy gained by the rocket. See post 49:

 

If the whole sled/puck system was travelling at 1000 m/s and we fired the spring gun, the puck's velocity would increase by the same old 50 m/s, so it gains 10,250 Joules. The sled's velocity decreases by the same old 0.1 m/s which means it loses 10,000 Joules. The difference is the 250 Joules in the spring...

[ronthepon]

Allright, so you people are considering the case where the energy of the fuel goes partly into acceleration of the craft, rest goes waste, as burnt gases or whatever.

 

However, if we say... no assert, that all the energy goes into moving the craft, then it will be as I said. Four times the fuel for twice the speed.

[ronthepon]

Just incase there is any doubt on my assertion, and I'm not immediately there to answer it, I'll give crystal clear reason for it.

 

Two times the speed, four times the kinetic energy.

 

Four times the kinetic energy, four times the energy required to be removed from the system.

 

Four times the negative work to be added to the system.

(Remember that negative work refers to a condition in which displacement and force are opposite to each other.)

 

So for four times the work to be put in, we will need four times the fuel.

 

Although this post may not be nessecary, comment on any mistakes you feel it may contain.

[Farsight]

However, if we say that all the energy goes into moving the craft

 

I'm not sure if that's possible, Ronthepon. But let's imagine it is:

 

Imagine you're in a 1 Megatonne starship. You have a "Warp Drive" that carries out the total conversion of dilithium crystals into energy. You then use this energy to exert a gravitational spacewarp force on your starship. Under normal cruising operations you consume 1mg of dilithium in a second to create a force that accelerates or decelerates the starship by 100m/s. Force = Mass x Acceleration no matter what speed you're doing, so you don't have to increase the force or consume greater and greater quantities of dilithium as your speed increases. The opposite is true when you decelerate.

 

So:

 

If you're travelling at 2000m/s per second you can consume 10mg of dilithium crystal in 10 seconds to slow yourself down to 1000m/s. In that 10 seconds your average speed was 1500m/s, so you've travelled 15000m.

 

Then you consume another 10mg of dilithium to slow yourself down to zero in the next 10 seconds. In that 10 seconds your average speed was 500m/s, so you travelled 5000m.

 

So you really do use twice the fuel. Not four times the fuel. It's twice the fuel, twice the momentum, twice the time. But it's four times the stopping distance, and four times the "kinetic energy". The fuel energy is disconnected from the kinetic energy, because the kinetic energy isn't really there. It's just a way of saying Force x Distance, which is how it was defined via "work" in the first place. Like I said, one way to think about it is "Stopping distance".

 

Slippery stuff, this energy.

[ronthepon]

That is right. I'll have to check this bit by bit on paper now, I guess.

[Farsight]

Craig, we could really use your valuable expert input here. I for one feel that "energy" has like totally slipping out of my fingers.

[CraigD]

This is a way of thinking about "stopping distance". A rocket going twice as fast takes twice as much fuel to stop, and while it's stopping, it goes four times as far.

Popular’s claim is correct that a rocket going twice as fast takes twice as much fuel to stop, and that it goes four times as far (though we’d do well to avoid potential confusion, and call what the rocket expels “reaction mass” rather than fuel).

Four times the "work", twice the fuel. Because work and kinetic energy are a re-expression of the Force x Distance "stopping distance", and have no other inherent meaning or reality.

How do you get four times the energy out of twice the fuel? It doesn't add up mathematically.

Lsos is correct that geting four times the energy out of twice the fuel doesn't add up mathematically.

Allright, so you people are considering the case where the energy of the fuel goes partly into acceleration of the craft, rest goes waste, as burnt gases or whatever.

Ronthepon’s is on the right track to explain the confusion by suggesting that, in addition to the rocket’s kinetic energy, we must consider the kinetic energy of its exhaust.

 

We’re assuming in the examples we’ve discussed in this thread that the rocket is doing a constant amount of work per unit time – that is, that is has a constant power – during its deceleration maneuver. What is not constant is the amount of work that produces the kinetic energy of the rocket, and the amount that produces the kinetic energy of the exhaust.

 

To see how this ratio changes, let’s look at the case of a 1000 kg rocket expelling 1 kg/s of reaction mass to change its velocity from 200 m/s to 0 m/s in 20 seconds. (As usual, to keep the calculations simple, we’ll ignore that a real rocket would no longer mass 1000 kg after expelling 1 kg/s for 20 seconds)

 

The law of equal and opposite reaction (conservation of momentum) tells us that to change the rocket’s velocity by 10 m/s, we must change the reaction mass’s by -10000 m/s. This is a work of 50050000 J. Doing this much work in 1 second, as our example states, requires a power of 5005000 W.

 

Here’s a table showing 2 different 1 second intervals:

       Rocket              Exhaust
      Velocity    Energy  Velocity    Energy  
Before      200  20000000       200     20000
After       190  18050000     10200  52020000
Change           -1950000            52000000

Before      100   5000000       100      5000
After        90   4050000     10100  51005000
Change            -950000            51000000

Though, being signed, it’s a bit confusing expressing change in the two energies as simple ratio, not that [math]\Delta[/math]rocket/[math]\Delta[/math]total ratio changes from about 4% in the first example to 2% in the second.

Gasoline has 32000000 joules in a liter…

This can be confusing, since, in our examples, we haven’t paid much attention to where the actual energy being converted into kinetic energy came from. Reaction mass doesn’t need to generate any power – our examples assume that something like a spring-loaded gun, a bicycle pump, or a nuclear reactor is actually accelerating the reaction mass. Note, however, that the energy density of burning gasoline, 44,000,000 J/kg, isn’t too far from the 50,050,000 J/kg the example above requires, indicating that a gas-burning rocket wouldn’t need to be much different.

[Farsight]

Thanks for that Craig. I understand it clearly. It's a re-expression of our sled and puck.

 

What I find interesting about all this is how energy seems to depend on your viewpoint. For example, assume that the megatonne starship had passed through a wormhole into an Alternate Universe that was utterly empty. Whilst conducting experiments to verify this, you take a ride in a small 1000kg shuttle craft. After a while you look up and see that the starship is heading towards you at 1000m/s. Initially you think that the starship kas Kinetic Energy of:

 

½ x 1000000000 x 1000² or 500000000000000 Joules

 

Then a voice crackles over the radio asking you to stop the shuttle. When you query this, the controller says the starship hasn't moved, and it's the shuttle that's moving. Now you think that the shuttle has Kinetic Energy of:

 

½ x 1000 x 1000² or 500000000 Joules

 

Perhaps in a way you were right both times. Perhaps an object of mass M only has a kinetic energy KE in relation to an observer with a velocity difference of V. The question for me is whether an object has any absolute kinetic energy at all. Which makes me wonder "does energy really exist?" It seems to be utterly relative, with no reality of its own. And if it doesn't exist in the first place, I'm not surprised that it can be neither created nor destroyed.

[sebbysteiny]

Popular, what a great question.

 

Yes, energy does exist. What you have noticed is that relative to one observer, an object has one kenetic energy, whilst relative to another moving observer, it has a different kenetic energy. It appears that the laws of physics depends on speed at which you travel. You could really study this concept of relative frames and see if the laws of physics really are consistant. You could call this, the theory of relativity: oh wait a minute, it's already been done. You are following in the footsteps of the one and only Alberth Einstein. Good job.

 

So what is the resolution to your problem?

 

Essentially, S^2 - V^2 = constant in all reference frames (or something like that). S = position vector in 4d space time in any particular reference frame, V = relatative velocity of object in that frame.

[arkain101]

Perhaps in a way you were right both times. Perhaps an object of mass M only has a kinetic energy KE in relation to an observer with a velocity difference of V. The question for me is whether an object has any absolute kinetic energy at all. Which makes me wonder "does energy really exist?" It seems to be utterly relative, with no reality of its own. And if it doesn't exist in the first place, I'm not surprised that it can be neither created nor destroyed.

 

This is precisely what I have been presenting and developing. ALthough it comes with a long list of required principles or postulates, whatever you would like to call them.

 

Things like, mass is relative. Meaning if it was the starship moving towards you, it would also mean the whole measureable universe around you would be moving with it towards you.

 

Its takes awhile to explain and its complicated to comprehend.

Mass's would be mathamatically relative. Energy needs to be slightly redefined.

It is a real thing but can be relative. By this I mean, that if we look at your ship and the startship had collided. The energy involved could apply to either ship. Depending on your observation frame you could measure the energy to have slowed down the starship or sped up the star ship, or slowed down the shuttle or sped up the shuttle. It dends which object appears at rest to you.

[sebbysteiny]

Having said all that, we don't need to journey down relativity to explain this.

 

Basically, in EVERY frame of relative motion, energy is conserved and momentum is conserved in all interactions. It may be that a different frame would measure different energy and momentum, but the laws will still work.

 

Problems arise only when you try to use the KE of one frame in calculations involving another frame.

 

However, there is one problem with this view, and that's about the speed of light.

 

In every frame, no matter how fast or who is observing, the speed of light has been observed to be the same. This is the point where newtonian mechanics breaks down and Einstein's relitivity takes over.