Who can answer this technical conundrum and apparent paradox re ft/lb energy?

[Airsporterman]

So that's why .22 is better than .177!
(apart from all the other reasons )

ASM

[harvey_s]

Think of the two of us wandering round an orchard picking apples...
After I've put 1 apple in my bag, I slosh you round the noggin with my bag - you laugh and belt me back...
A little while later I've got 20 apples in my bag, I slosh you playfully round the noggin again...but I haven't just belted you with the energy of the last apple I put in - all the others came along for the ride & I call an ambulance.
The apples here are the rate of change in velocity.

[Turnup]

Think of the two of us wandering round an orchard picking apples...
After I've put 1 apple in my bag, I slosh you round the noggin with my bag - you laugh and belt me back...
A little while later I've got 20 apples in my bag, I slosh you playfully round the noggin again...but I haven't just belted you with the energy of the last apple I put in - all the others came along for the ride & I call an ambulance.
The apples here are the rate of change in velocity.

So the more mass you have in the bag the harder it hits.......what has this to do with the non linear relationship between velocity and energy??

[andrewM]

Thank you for the further contributions, much appreciated. The difference between the examples here and 'O' level physics was that in the latter, we learned about formulae. We did not seek an explanation for the logic behind the formulae provided. I am grateful for your thoughts on this for it is difficult to explain, as the contributions demonstrate.

Rgds
A

[ccdjg]

Food for thought. If you believe that Einstein's famous equation E = mc² is correct, then you already accept that energy is related to velocity squared and not just velocity.

If physics had said that E =mc then then there would have been hell of a lot less energy in nuclear reactions and the sun, nuclear power stations and the atom bomb would never have existed.

[Turnup]

Food for thought. If you believe that Einstein's famous equation E = mc² is correct, then you already accept that energy is related to velocity squared and not just velocity.

If physics had said that E =mc then then there would have been hell of a lot less energy in nuclear reactions and the sun, nuclear power stations and the atom bomb would never have existed.

You really should not confuse relativity with Kinetic Energy. Just because v squared appears in both does not mean that the two have any equivalence, since no object with mass can ever achieve the velocity of c.

Einstein's formula explains what the outcome is if you convert some mass into energy, and rather thought provokingly suggests that the two might be different manifestations of the same thing. Nuclear reactions have demonstrated the correctness of that theory, but this has absolutely nothing to do with what is happening with a mass moving at speeds well below the speed of light.

[Turnup]

Thank you for the further contributions, much appreciated. The difference between the examples here and 'O' level physics was that in the latter, we learned about formulae. We did not seek an explanation for the logic behind the formulae provided. I am grateful for your thoughts on this for it is difficult to explain, as the contributions demonstrate.

Rgds
A

Well when I studied O level applied maths we did learn exactly how the equations of motion are derived - and were required to demonstrate not knowledge of the formulae but where they come from. It generates understanding as opposed to mere knowledge. All of them can be derived mathematically with no reference to any real world experiment or measurement. To my disappointment my parents moved house and I was unable to follow that particular course - shame cos I was one of those weird peeps who actually enjoyed applied maths.

[ccdjg]

You really should not confuse relativity with Kinetic Energy. Just because v squared appears in both does not mean that the two have any equivalence, since no object with mass can ever achieve the velocity of c.

Einstein's formula explains what the outcome is if you convert some mass into energy, and rather thought provokingly suggests that the two might be different manifestations of the same thing. Nuclear reactions have demonstrated the correctness of that theory, but this has absolutely nothing to do with what is happening with a mass moving at speeds well below the speed of light.

I fully appreciate that kinetic energy cannot be directly related to the intrinsic energy of a mass at rest. I was simply trying to demonstrate that energy, something that we cannot define in anyway other than mathematically, has the dimensions of mass times velocity squared irrespective of what form that energy might take or how it is derived.

[harvey_s]

So the more mass you have in the bag the harder it hits.......what has this to do with the non linear relationship between velocity and energy??

It was meant to show how adding a divisible number did not give necessarily the same small change.
You've taken it too literally - so my attempt to simplify a principle has failed...

[Turnup]

I fully appreciate that kinetic energy cannot be directly related to the intrinsic energy of a mass at rest. I was simply trying to demonstrate that energy, something that we cannot define in anyway other than mathematically, has the dimensions of mass times velocity squared irrespective of what form that energy might take or how it is derived.

OK....interesting. Leaving chemical energy aside as far too complicated, kW-H is dimensionally mass times velocity squared? What about e-V or calories?

[ccdjg]

For an airgun forum this thread is getting very esoteric, but interesting nevertheless.

Chemical energy is just another form of potential energy, and like any form of energy can be expressed in any units you want, kJ, eV, kcal etc, as units are just inventions of scientists to make their life easier. Units should not be confused with dimensionality. Energy has the dimensionality of mass X distance² divided by time² in whatever form it takes and that is immutable. Such a dimensionality is equivalent to mass X velocity², and is also equivalent to mass X distance X acceleration.

Yes, the energy unit kWh, i.e (power X time), does of course have the correct dimensionality for energy when you work it out.

[Turnup]

For an airgun forum this thread is getting very esoteric, but interesting nevertheless.


Yes, the energy unit kWh, i.e (power X time), does of course have the correct dimensionality for energy when you work it out.

But this is simply an assertion on your part (which I am not necessarily disputing).


When I think about electrical energy, I can't see where mass and velocity squared comes into it. Sure I can see that we can express energy in a variety of units by a conversion constant which has no dimension and I can intellectually accept these as equivalents but this does not mean that they are the same thing. If electrical energy is mass times velocity squared, the mass and velocity of what?

Show the proof starting from W-h = voltage * current * time

[ccdjg]

I think we may be getting into semantics here, but energy is one of those things that cannot be described by what it is, but only by what it does. All types of energy ultimately provide work or heat and so must have the same dimensionality which happens to be mass X distance² X time^-2 . This does not mean that the energy has to stem directly from mass or velocity or acceleration, and that is not what I have been saying.

Anyway to respond to your specific question, the basic SI units for Voltage are kg.m².s^-3. A^-1 (see Wikipedia for example) (kilogams, meters, seconds and amps) or mass x distance² X time^-3 X Amps

Your electrical energy W.h = V X A X time

So inserting the SI units for voltage into this, the Amps cancel out as does one of the time units, so the dimensionality boils down to mass X distance² X time^-2, which if you wanted to could be be interpeted as mass X velocity² .

[andrewM]

I did not know what I would start when I began this thread but it is certainly fascinating and demonstrates the degree of knowledge amongst the members of the forum; alas, so far as physics is concerned, there is very little I can contribute!

Rgds
A

[Turnup]

I think we may be getting into semantics here, but energy is one of those things that cannot be described by what it is, but only by what it does. All types of energy ultimately provide work or heat and so must have the same dimensionality which happens to be mass X distance² X time^-2 . This does not mean that the energy has to stem directly from mass or velocity or acceleration, and that is not what I have been saying.

Anyway to respond to your specific question, the basic SI units for Voltage are kg.m².s^-3. A^-1 (see Wikipedia for example) (kilogams, meters, seconds and amps) or mass x distance² X time^-3 X Amps

Your electrical energy W.h = V X A X time

So inserting the SI units for voltage into this, the Amps cancel out as does one of the time units, so the dimensionality boils down to mass X distance² X time^-2, which if you wanted to could be be interpeted as mass X velocity² .

But now you have substituted one assertion for another - the units of Voltage. I accept completely that the SI unit system is self consistent. I am pretty sure that a perfectly consistent system of units could be derived by starting with the Watt as one of the fundamental units and express all other units relative to that.

Not at all sure where this is all going now but it has been interesting and thought provoking.