[Petrochemicals (OP)]

What is it that it that resists acceleration at higher velocities. If in relativity you are only aware within a frame of reference, why is high velocity acceleration so difficult?

- Newton is the force needed to achieve an acceleration  of 1 metre per second on a mass of 1kg,
-The joule is 1 Newton of force through one metre, 
- We know that to accelerate 1 kg at 10ms takes a force of 10 newton's,

Taking half distance of 5m, 1kg takes:

     -5(m)x10(ms)x1(kg)=50 joules per second per kg

To a quarter of the acceleration ie 2.5ms and 1.125 m covered in 1 second:

     -1.25(m)x2.5(ms)x1=3.125 joules per second per kg

But if you persist for  4 seconds you are at a velocity of 10ms, yet  ke=0.5mv^2 would signify you have 50 joules of energy for an input of 12.5 joules. If there is only force and energy and not a reference of  distance this is not prohibited.

I understand that the distance covered in the following 3 seconds will be greater than the 1.25 m covered in the first thus the equation should balance for Kinetic energy, ie in the 4th second you would be covering 8.75 metres not the initial second distance 1.25 metres.

[evan_au]

It depends on whether you are carrying the power source with you.
If you use a linear accelerator (ie the power source remains stationary)
- And accelerate a 1kg payload at 1 m/s²
- You will add 1 m/s every second
- after 1s, Kinetic Energy = 0.5J
- after 2s, KE = 2J
- after 3s, KE = 4.5J
- So the energy input needs to keep growing every second
- In practice, you hit a limit on how much power your stationary power source can add (or you run off the end of the linear accelerator).

If you have to carry the power source with you,
- And want to accelerate a 1kg payload at 1 m/s²
- The initial mass may be much greater than 1kg, because you need to carry the fuel (and reaction mass, if it is a rocket)
- So it typically starts accelerating much more slowly, because the mass is greater than 1kg
- But the acceleration increases over time
- Until your fuel and/or reaction mass runs out.

[Janus]

What is it that it that resists acceleration at higher velocities. If in relativity you are only aware within a frame of reference, why is high velocity acceleration so difficult?

In Relativity, nothing, as far as the accelerating frame is concerned, inhibits further acceleration. So, if you were accelerating at 1g.   You would measure your velocity as changing by 9.8 m/s every sec.
But, this doesn't mean that if you, for example, started at rest with respect to the Earth, that after doing this for 1 year by your clock, you would measure yourself as moving at a bit over 1c relative to the Earth (it ends up being closer to 0.79c)

This is a result of how velocities add up in Relativity.
Imagine you in this accelerating ship, and after accelerating to 0.1c relative to Earth, you drop off a space buoy ( this buoy maintains the same velocity relative to the Earth you had when you released it). You continue to accelerate until you are moving 0.1 c relative to this buoy. This will take the same amount of time by your clock as it did to get to 0.1c relative to the Earth.
If you now measure your speed relative to the Earth, you will find that is not 0.1c+0.1c = 0.2c,  but (0.1c+0.1c)(1+0.1c(0.1c)/c^2) = ~1.98c
If you now drop off another buoy, accelerate until you are moving at 0.1c relative to it, you will measure your velocity as being ~0.292c relative to the Earth.
Keep doing this and the consecutive velocities relative to earth will be:  0.381c, 0.463c, 0.538c, 0.605c, 0.665c...
Each time, the relative velocity to Earth increases by a smaller amount, even though, you noticed nothing changing about your acceleration.
It is not that "something resists your acceleration", it is that the very nature of time and space determine your measurements.

Relativity is a model for time and space and their measurement, It has nothing to do with outside influences inhibiting acceleration.

[Petrochemicals (OP)]

- So the input needs to keep growing every second

Yes, but why, gravity does not increase energy input during free fall. Is it resistance in the fabric of space time, is it localised within the gravitational field ? Dark matter?

with the risk of sounding like a new theories. One explanation could be that you are fighting time, or reaction rates, to slow reaction rates takes  energy input. This would suggest gravitational fields resist the acceleration.

[Bored chemist]

Yes, but why, gravity does not increase energy input during free fall.

It does.
However, near the Earth's surface the change of force with height  is small because we "start" 4000 miles up from the centre.

[Bored chemist]

with the risk of sounding like a new theories.

That's not a "theory", is it?

Incidentally, since Petrochem has announced to the world that he doesn't like facts, could someone copy this data to him please?

[Kryptid]

Yes, but why, gravity does not increase energy input during free fall.

It does, actually. Gravitational potential energy is converted into kinetic energy.

[jeffreyH]

Time dilation makes further acceleration difficult. If you are in an inertial frame and observing an accelerating frame, everything in the accelerating frame becomes slower with respect to you as the velocity increases. This includes the combustion of fuel. This is why, eventually, you would need an infinite amount of energy to attain light speed. Therefore, it is impossible.

Relativistic gamma applies to the rate of change in the accelerating frame.

[Petrochemicals (OP)]

Yes, but why, gravity does not increase energy input during free fall.

It does, actually. Gravitational potential energy is converted into kinetic energy.

Gravitational acceleration remains the same, potential changes with different heights, it increaces/decreaces in energy due to distance from the gravitational baseline, in line with potential energy and distance newtons, but that would be acceleration with/against gravity and its potential

 If you accelerated for 1 second from the surface of the earth at 10ms you would get nowhere, at 20ms you would be accelerating at 10, but this would stall and you would fall back to the earth. Acceleration in open space does not have this quality.

Without a gravitational reference, if a force of 10 newtons can accelerate lerate for the first second, why not the 2nd? If, like a pulse jet I accelerated in second intervals, without knowing my velocity,  would I be accellerating the same amount with each pulse?

[wolfekeeper]

Actually, it's virtually the same when you accelerate in a gravitational field as when you accelerate in free space. The only difference is if the gravitational field varies in intensity. You say that the 10 m/s^2 acceleration makes no difference, but if you're not standing on the ground, the field of reference you should refer to is the one accelerating downwards at 10m/s^2, and in that frame of reference you have actually done work.

[Origin]

If you now measure your speed relative to the Earth, you will find that is not 0.1c+0.1c = 0.2c,  but (0.1c+0.1c)(1+0.1c(0.1c)/c^2) = ~1.98c

I didn't notice this till just now.  You wrote 1.98c instead of .198c.

[jeffreyH]

If you accelerated for 1 second from the surface of the earth at 10ms you would get nowhere, at 20ms you would be accelerating at 10, but this would stall and you would fall back to the earth.

If this were true then Harrier Jump Jets have a problem.

[Kryptid]

If you are accelerating, then by definition, you are not "getting nowhere".

[Petrochemicals (OP)]

If you are accelerating, then by definition, you are not "getting nowhere".

Watt ? If I apply a force to create an acceleration of 10ms2 against gravity (which is 10ms) I get nowhere. So against gravity , a force of 10N per kg is not considered acceleration ? Why would this be justified in relativity ?Where does the energy go to (you are not allowed to say heat)  What is resisting the acceleration and how ?

(The watt is described as holding constant against one newton)

[Halc]

If you accelerated for 1 second from the surface of the earth at 10ms you would get nowhere, at 20ms you would be accelerating at 10

This statement mixes coordinate systems without being explicit, rendering the statement meaningless.  It essentially says 10 is zero and 20 is 10, which is just wrong.  Also, ms is a 1000th of a second, not a unit of acceleration.  Acceleration might be measured as 1g or 10 m/sec², but certainly not in milliseconds.

What you seem to be attempting is a statement saying that 10 m/sec² of proper acceleration is equivalent to being stationary in a accelerated reference frame where the local proper acceleration is also 10 m/sec².

If I apply a force to create an acceleration of 10ms2 against gravity (which is 10ms) I get nowhere.

Under Newtonian mechanics, gravity is a force, and your force upwards is exactly balanced by the gravity force downward, resulting in zero inertial acceleration of a rock sitting on the ground. Surely this isn't news to you.

Under general relativity, there is no gravity force, only the proper acceleration of the rock, so the rock indeed does not stay put in any local inertial frame, but is rather continuously accelerated upward, curving its worldline from the otherwise straight geodesic it would have taken.  There is only gravity in Newtonian mechanics, so if you reference it, you using Newtonian mechanics.

So against gravity , a force of 10N per kg is not considered acceleration ?

Not if it's balanced by an equal an opposite force, no.

Why would this be justified in relativity ?

There is no gravity under general relativity (I'm assuming you're talking about Einstein's relativity and not Galilean relativity).  There is acceleration of the rock under GR, as evidenced by its curved worldline.

Where does the energy go

Acceleration and energy are different things. Under Newton mechanics, the ISS accelerates all the time at nearly 1g and yet gains and loses no significant potential or kinetic energy.  Acceleration is absolute, but energy is relative, so any relation between the two is a coordinate effect.

The rock doesn't change potential, so there's no reason its potential energy should change, and PE is the only objective energy that can be attributed to the rock.  The rest (KE in particular) is a coordinate quantity, and the same acceleration might make the KE go up in one frame and down in another. There's just no direct relation. You want to give the rock a lot of KE?  Just consider it in a frame where it's moving fast.

The logical frame for the rock is the locally accelerating reference frame in which it is typically at rest, and so despite the continuous acceleration, there is no change to its KE at all. If you want a different answer, you need to specify a different coordinate system than the one in which we typically consider the rock.

[Kryptid]

If you are accelerating, then by definition, you are not "getting nowhere".

Watt ? If I apply a force to create an acceleration of 10ms2 against gravity (which is 10ms) I get nowhere. So against gravity , a force of 10N per kg is not considered acceleration ? Why would this be justified in relativity ?Where does the energy go to (you are not allowed to say heat)  What is resisting the acceleration and how ?

(The watt is described as holding constant against one newton)

Applying a force is not the same thing as accelerating. If I try to lift a rock that weighs 600 kilograms, the rock is obviously not going to accelerate despite the fact that I am applying a force to it. If it isn't moving, then it isn't accelerating.

Where the energy goes depends upon the situation. In the above example, it does indeed become waste heat produced by my muscles.

[Petrochemicals (OP)]

If you are accelerating, then by definition, you are not "getting nowhere".

Watt ? If I apply a force to create an acceleration of 10ms2 against gravity (which is 10ms) I get nowhere. So against gravity , a force of 10N per kg is not considered acceleration ? Why would this be justified in relativity ?Where does the energy go to (you are not allowed to say heat)  What is resisting the acceleration and how ?

(The watt is described as holding constant against one newton)

Applying a force is not the same thing as accelerating. If I try to lift a rock that weighs 600 kilograms, the rock is obviously not going to accelerate despite the fact that I am applying a force to it. If it isn't moving, then it isn't accelerating.

Where the energy goes depends upon the situation. In the above example, it does indeed become waste heat produced by my muscles.

That is completely contrary to Einstein's free fall analogy. If the elevator is accelerated at 10ms2 for one second, the elevator passenger is accelerating, yet to the outside observer it is "going nowhere". This would suggest that acceleration is working opposite to the convention.

[Kryptid]

An outside observer would be able to see that the elevator (and by extension, everyone and everything on board the elevator) is accelerating. It is the person on board who cannot tell whether they are accelerating in free space or whether they are stationary in a gravitational field.

[Petrochemicals (OP)]

An outside observer would be able to see that the elevator (and by extension, everyone and everything on board the elevator) is accelerating. It is the person on board who cannot tell whether they are accelerating in free space or whether they are stationary in a gravitational field.

Nope, an elevator on the earth surface accelerating at 10ms for 1  second in Earth's gravity according to the passenger would be accelerating but to the observer it would be just enough to relieve the force on the surface. The hovering Helicopter has to fight gravity with an equal force.

[Kryptid]

just enough to relieve the force on the surface.

I... am not sure what you mean by "relieve the force". Is the elevator accelerating or not? Acceleration is not relative in relativity. If it's sitting still on the Earth's surface, it's not accelerating.