A problem with KE = ½mv². Help.

[arkain101]

I don't see why the rocket wouldn't take 4x the distance to stop. The same eqautions apply whether the force comes from the ground or propellant or gravity or anything. The same reasoning to why it would take 4x the distance to stop apply as well...it takes it only 2x the time to stop when travelling twice as fast, but since its average velocity is greater, it has to have travelled more than 2x the distance. 2x the velocity and 2x the time = 4x the distance.

 

right. I do agree. I am just questioning a possible thought.

[ronthepon]

By the way, what is the equation for kinetic energy according to relativity?

 

Not 1/2mv^2, I'm sure.

[arkain101]

By the way, what is the equation for kinetic energy according to relativity?

 

Not 1/2mv^2, I'm sure.

 

according to wiki.

 

Energy in Relativity

Energy and the four-momentum's time term:

 

E = p4c = mu4c = γmc2

Kinetic energy:

 

 

mc2 = Rest Energy

Other useful energy-momentum relations:

 

 

[ronthepon]

That is indeed complex. No wonder I never came across it.

 

Do we use relativity's results in rocketry? Most probable, but just verifying to be sure.

[arkain101]

I dont think there is any need to use relativistic techniques in rocketry except for communication devices to make up for billionths of time dialtion. None of our main technologies really exceed much more than 10km/s if I remember correctly and that is pushing it!

Fastest man made object was a return of a probe from a comet or meteor. It came back just recently and hit earth at 11.11 km/s

[CraigD]

… what is the equation for kinetic energy according to relativity?

 

Not 1/2mv^2, I'm sure.

The equations (Usually 2 or 3, though they can be algebraically combined into 1) for kinetic energy according to the Theory of Relativity, are:

[1] [math]E = Mc^2[/math]

 

[2] [math]M = \frac{M_{rest}}{\sqrt{1-(\frac{v}{c})^2}}[/math]

Where E is an object’s total energy, v its speed (as measured by a non-accelerating observer), [math]M_{rest}[/math] it’s mass when v = 0, M its relativistic mass for any value of v, and c the speed of light.

 

Kinetic energy is just change in total energy due to change in velocity, that is:

[3] [math]E_{kinetic} = Mc^2 – M_{rest}c^2[/math]

 

For low values of v, these relativistic equations give nearly the same result as the classical

[math]E_{kinetic} = \frac{1}{2}M_{rest}v_{classical}^2[/math].

 

As v approaches c ([math]v_{classical}[/math] is allowed to exceed c) , the disagreement between classical and relativistic results increase.

 

Post #57 has a couple of examples comparing classical and relativistic kinetic energy calculations.

 

The formulae Arkain give agree with the one I gave. In particular [math]E = \gamma mc^2[/math]

 

Is a simplified version of [math]E_{kinetic} = Mc^2 – M_{rest}c^2[/math],

 

Where “gamma” [math]\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/math], and m refers to [math]M_{rest}[/math]

 

If you start with the 3 basic equations, relativistic energy calculations aren’t too difficult to understand and perform.

[arkain101]

Goon on ya craig. I wasnt very sure about those equations and that above post helped out. I remember using them in highschool a little bit.

 

post #56 or so.

Popular: If Momentum is the same as Inertia, and Impulse, which is Force x Time, and if Kinetic Energy is Force x Distance, is there a deep concept available here? Is Distance the same as Space? Is Mass the same as Inertia? And is the relationship between "Mass" and "Energy" a re-expression of the relationship between time and space?

 

Relativity does show this connection as Craig explained. Although I think there is one more part to it.

 

What exactly is seperating or preventing relativity from meshing with quantum theory?

 

I think I have an idea. Relativity has not been able to explain things like strong and weak nuclear force with the concept of gravity it presents.(?)

[Kriminal99]

Science is rigorously derived. It contains no internal mistakes or contradictions. Zero. Not a one. Not a single internal problem exists anywhere within its entire fabric. Nada, zip, zilch. That is how science is done. That is the standard that any change or addition must meet.

 

Physics, Resnick, Halliday, Krane, 4th Ed, Vol 1, p 138.

Three text inches. Learn some physics.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://www.motionmountain.net

Learn some physics.

 

Whether mathematical prediction exactly matches empirical observation is the giggle. Newton is not off by a factor of two.

 

This type of thinking is ignorant and detrimental to society. What kind of mistakes do you mean? Any experiment can be biased very easily without anyone knowing the difference. Mistakes in reason are absolutely something that people should be on constant guard for. I know math professors who challenge the foundations of mathematics to the math professors and has other mathematicians swinging from the rafters at his formal lectures. Getting angry only shows that you want to prevent people from considering that you are wrong, which means you are wrong or you don't understand it well enough to easily deal with what that person has to say etc.

 

The philosophical foundations that science are based on even seem to be flawed. Not for an actual scientist but as far as sciences role in society. What is the purpose of a third person body of knowledge obtain from experimentation if you don't have access to it other thant through other people with different biases than you?

[sebbysteiny]

"This type of thinking is ignorant and detrimental to society. What kind of mistakes do you mean? Any experiment can be biased very easily without anyone knowing the difference."

 

This post is straying on the edge of 'philosophy of science' but what the hell.

 

This type of thinking is dangerous because it allows people to become willfully blind to the undesputable truth.

 

Whilst it is true that at the forefront of the sphere of knowledge, scientists regularly argue with each other and there are hundreds of different theories with very different implications, as experiments improve, the sphere expands and the theories that do not explain reality get thrown away leaving undisputable fact.

 

For example, you will not get somebody who believes that gravity moves upwards so that suddenly everything will fall off the Earth. The concept of kinetic energy is similar and has become undisputable fact in every case.

[arkain101]

The reason this topic has gone one, is the nature of natures square.

 

Many forces work magnitude of inverse square law, and velocits work in velocity related square.

 

Even light is squared when working out energy in a mass.

 

What makes this so? thats why the topic goes on.

[ronthepon]

The most possible reason I can think of for the reason of frequent appearance of inverse square laws, is because of the basic mathematical natures of areas.

Thats square, so most laws, especially which focus on 'per area things' will be inverse square.

[arkain101]

In physics, an inverse-square law is any physical law stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.

 

In particular the inverse square law applies in the following cases:

 

 

 

-The gravitational attraction between two massive objects, in addition to being directly proportional to the product of their masses, is inversely proportional to the square of the distance between them; this law was first suggested by Ismael Bullialdus but put on a firm basis by Isaac Newton;

 

-The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is Coulomb's law;

 

-The intensity of light radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source. An object (of the same size) twice as far away, receives only 1/4 the energy (in the same time period). More generally, the irradiance, i.e., the intensity (or power per unit area in the direction of propagation), of a spherical wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by absorption or scattering).

 

 

Now I realise the mathmatics involved. However, the more I study and observe, the more evidence I see suggesting that all things are a relationship of equal and opposite reaction. Thus causing all things to be in magnitudes of square, directly or inversly.

 

This I believe is Quantified action.

 

Kinetic energy falls into this same catagory. The work an object -that contains velocity- can perform is perportional to the square of its velocity.

 

All of this is MORE than just the way it goes from mathamatical derivitives(right word?). It is a relative operation in the natural universe.

 

What I believe I have been observing is it unites an idea that is more or less "relativistic quantum action"

[Farsight]

Uh oh, I think I've got it. Here we go guys, how's this:

 

Work is Force x Distance, which we can 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.

 

I think that's what's been bothering me. 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.

[ronthepon]

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.

Actually it should take four times the fuel.

 

Impulse is Force x Time, which we can translate into "Momentum".

Or the change of momentum. But yes, it has to do with time.

 

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.

Hang around a bit more, will you? I sense some problems in this. I'll check and say for sure later.

 

I think that's what's been bothering me. 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.

Errm, matter is not made, but it does translate into energy. Or, energy has mass.

[arkain101]

I think that's what's been bothering me. 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.

 

Right. It is the term used for measurement of change related to work or motion.

 

As you accelerate towards C, relative to other objects, the measured energy you are putting into accelerating starts going into the mass when you get going fast enough.

 

Instead of only a kinetic form.

 

There are many forms of energy. Electricity. Heat. Light. Motion.

They can all do work. The energy is never lost or created only changed.

[Farsight]

Arkain: The point is that there isn't really any "energy", and it never "takes a form". Something has "energy", but energy can't exist on its own.

 

Ronthepon: no kidding, it takes twice the fuel, not four times the fuel. Craig will back me up on this.

[ronthepon]

By four times the fuel I mean four times the work done.