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As I have explained many times before, energy is a scalar, i.e. it has no direction..

a=9.81m/s2 ... linearly fixed velocity constant

the carriage gains relativistic mass

electro-negativity holding electro-positivity in place

Quote from: TheBoxa=9.81m/s2 ... linearly fixed velocity constantQuoteThis is a contradiction.The roller coaster trolley, while it is falling vertically accelerates under the force of gravity.This means that the velocity is not fixed, but is increasing linearly.And the distance fallen is increasing quadratically.My own fault for putting an ambiguity sentence, yes the speed increases per meter, but I meant that 9 .81m/s2 is a constant rate on earth but nether mind. Quote from: TheBoxthe carriage gains relativistic massQuote from: TheBoxelectro-negativity holding electro-positivity in placeWhile Einstein was able to make amazing deductions from imagining electric trolley-buses traveling near the speed of light, I think it is more sensible for you to first come to terms with the kinetic energy of electrically neutral trolleys traveling nowhere near the speed of light.

This is a contradiction.The roller coaster trolley, while it is falling vertically accelerates under the force of gravity.This means that the velocity is not fixed, but is increasing linearly.And the distance fallen is increasing quadratically.

What is kE apart from vivid imagination?

We have a closed system so the roller coaster that receives that energy must have gained mass!.

Quote from: Thebox on 27/03/2016 00:10:41What is kE apart from vivid imagination?The purpose of physics is to build predictive mathematical models of things that happen. Classical mechanics describes what happens to objects larger than a molecule, moving at substantially less than the speed of light, for periods between the big bang and the foreseeable future. Three quantities are conserved in a classical interaction: mass, energy and momentum. Energy turns up in a number of forms, mostly as kinetic, potential and heat. The formal concept of kinetic energy as ½mv^{2} was a stroke of brilliance in the 17th century, though the relationship between KE and PE had been surmised thousands of years earlier and used by whoever invented the bow and arrow. The conservation principle has been understood and applied by every engineer from Newcomen to NASA.The discovery of radioactivity added a twist as it seemed that energy could appear ex nihilo but it turns out that the small correction factor E = mc^{2} completely accounts for the measured mass loss in nuclear decay and the observed momentum of the daughter particles.

Energy turns up in a number of forms, mostly as kinetic,

The speed of the fall creating an illusion that the object has gained something, the only thing gained is distance and falling acceleration Fn.

Force of impact increases with motion, +h (height)= + force, +force delta direction = parallel distance traveled.

If you get hit by a bus, it leaves very little to the imagination.... You wouldn't call the resulting damage poppycock!

And you can ignore relativistic mass (which is so small for a roller coaster or a bus that we can't hope to measure it).

I would call that force, the force of the bus was greater than my inertia

+speed = + force

1kg + 2my = ?mx

The rest energy of matter

Quote from: Thebox on 27/03/2016 00:50:48The rest energy of matter is irrelevant to classical mechanics, in which, by definition, mass is conserved.

Huh? you already measure it . Relativistic mass is what you call kE but which is really increased relativistic weight. The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest. Take a 5kg object at ground state0.5*9.81=4.905NNow raise this object 5 m h, 0.5 * 49.05= 24.525n relativistic weightThen convert 24.525n into a ground state mass to get the equivalent. 24.525n = 2.5 mass at ground state or 25kg approxF=ma2.5*9.81= 24.525n at ground state

No. You are on the wrong track here. I am not quite sure what track you are on, but it ain't right...

F = m*a means force = mass times accelerationforce is in units of Newtons (N = kg*m*s^{–2})mass is in units of kilograms (kg)acceleration is in units of m*s^{–2}

I take it that if the energy to raise this 5Kg mass has come from an Earth bound source the Earth has also lost the same amount of relativistic mass.Due to the daughter atoms from the spit uranium atoms having less mass

I would call that force, the force of the bus was greater than my inertia,

And that means in plain English?

The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest.

Force is rate of change of inertia. You can't equate force with inertia.

Quote from: Thebox on 27/03/2016 02:38:35The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest. Not true. The higher you lift an object, the less it weighs because the gravitational field is divergent. F= GmM/r^{2}, if you recall.Terminal velocity depends on the shape of a falling object, and the density and viscosity of the medium through which it falls. It's about 150 mph for a human body, from any height above a couple of hundred feet. I don't think this is what you meant. You can calculate ground impact velocity (ignoring air resistance) by putting mgh = ½mv^{2}, i.e. by assuming that energy is conserved. But even though the calculation is simple and the answer is always correct, I'm sure you will not believe it.

Quote from: chiralSPO on 27/03/2016 11:45:53No. You are on the wrong track here. I am not quite sure what track you are on, but it ain't right... A bit contradictory mate, you say you are not sure what I am talking about yet you claim it is not right.

QuoteF = m*a means force = mass times accelerationforce is in units of Newtons (N = kg*m*s^{–2})mass is in units of kilograms (kg)acceleration is in units of m*s^{–2}Huh? why are you putting - 2

Force = mass times accelerationforce is measured weight , in Newtons, a=9.81m/s2

which means that for every meter falling it increases its acceleration *2

You lost me , I know what F=ma means, or I thought I did. Let me confirm, for 1kg mass we put 0.1 in the calculation for mass?F= 0.1 * aacceleration is 9.81m/s2for the first meter 9.81m/s2nd meter 9.81m/s*23rd meter 9.81m/s*3?

an object at rest on Earth has inertia, this inertia is created by the linear force of gravity

vt = v0 + a*t2If in object is initially not moving (v0 = 0) and then begins to fall at a = 9.81 m/s2it will be moving at 9.81 m/s at 1 second, 39.24 m/s at 2 seconds, 88.29 m/s at 3 seconds, 156.96 m/s at 4 seconds...

Quote from: evan_au on 28/03/2016 22:01:19vt = v0 + a*t2If in object is initially not moving (v0 = 0) and then begins to fall at a = 9.81 m/s2it will be moving at 9.81 m/s at 1 second, 39.24 m/s at 2 seconds, 88.29 m/s at 3 seconds, 156.96 m/s at 4 seconds...The correct formula is vt = v0 + a*thence at 1 second, v=9.81 m/s, at 2 seconds v=19.62, and so on.or if you want to calculate distance st = s0 + v0*t + ½*a*t²

no. For 1 kg, F = 1*a (and for 23 kg, F = 23*a)

So, to answer the original question, (1) k.e. is a scalar equal to ½mv^{2} and (2) we find that if an object falls from rest through a height h in vacuo, gh = ½v^{2}. Which is not at all surprising for those who understand the meaning of "acceleration". The interesting bit is the discovery (phenomenologically attributed to Galileo, maths by Newton) that g = GM/r^{2} near the surface of a large spherical planet. Like it or lump it, Mr Box.

Energy only "exists" in the minds of the child-hating idiots who write the National Curriculum. For the rest of us, it is a number that tells us something about things that happen.

Interestingly, it's what the police mostly talk about in road safety lectures. If Mr Plod understands it, and can somehow transfer that understanding to speeding teenage halfwits, it seems strange that anyone who contributes to this forum has a problem with it.

It may be abstract but it certainly isn't meaningless.

Do falling objects regardless of their mass have the same terminal velocity?

I clearly understand it but like to dig deep for a deeper understanding

Quote from: Thebox on 30/03/2016 08:21:05 I clearly understand it but like to dig deep for a deeper understandingThere's nothing deeper to understand. The kinetic energy of a mass m moving at velocity v is ½mv^{2}. It's a useful concept because (by experiment) energy is conserved in classical physics, so we can use it to predict what happens when our moving object interacts with something else.

Except that kinetic energy that is constant has no acceleration.

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.

p_{0}=F_{n} etc

Quote from: TheBoxI am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle. This thread is discussing conservation of Energy (of which Kinetic Energy and Potential Energy are two forms), under the influence of a gravitational field.Emmy Noether came up with a very general concept which links conservation laws to symmetries in nature.The Conservation of Energy (and its component Kinetic Energy) is proved in the following example:http://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy [Links inactive - To make links active and clickable, login or click here to register] Occasionally, conservation of momentum comes up in this thread - this is another principle which can be proved by Noether's theorem.Quote from: TheBoxDo falling objects regardless of their mass have the same terminal velocity?"raindrops falling through air to reach terminal velocity" is a complex system in which it is extremely hard to add up all the tiny contributions of kinetic energy which are distributed amongst all the individual air molecules. So if you wish to understand kinetic energy, look at objects falling in a vacuum (or the proverbial cannonballs falling from the leaning tower of Pisa) - it is so much easier to analyze. You can see something real, without being diverted into fractal flurries of turbulence which dissipate lots of energy and get you nowhere.Quotep_{0}=F_{n} etcThe mathematical notation used in Noether's Theorem may look superficially similar to some equations previous posted in this thread. It is not.

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle. Is it F=ma?