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

[Turnup]

Thank you, all, for your learned responses. I have almost entirely forgotten what I learned in physics at school. Bill, can you explain, however, why kinetic energy and velocity is non-linear, in layman's terms? Thus, 10 ft/sec is nothing in itself but when added to a projectile already travelling at 550 ft/sec, it adds nearly 0.5 ft/lbs.

Rgds
A

On a technicality KE is not measured in ft/lbs (pronounced as "feet per pounds" in the same way that ft/sec is pronounced "feet per second") - the unit is ft-lb or ft.lb, pronounced "foot pound". A certain Airgun magazine has got this wrong over a long period of time. It is easier to understand things if you use the correct terminology, and confusing or downright misleading if you don't

Back to the thread.....

Energy is an expression of the capacity to do work. Work is force times distance (note that KE is measured in foot-lbs which is a mathematical way of stating feet times pounds - force times distance). The same force acting over twice the distance is twice the work or twice the energy.

So a moving mass can exert a force against something trying to slow it down - that is to say the moving mass is giving up some of it's energy into whatever is trying to slow it down. If we allow it to slow to a halt then it has given up all of it's energy and the amount of force it took multiplied by the distance it has had to cover is the amount of work it has done, and this is the kinetic energy it has given up.

Taking your example of 10 ft/sec vs. 550 ft/sec let us imagine we apply a slowing force to reduce the projectile's velocity by 10 ft/sec. (i.e. 10 to zero or 550 to 540).

We can choose the force such that it takes one second to reduce the projectile's velocity by 10 ft/sec. We need not bother to calculate that force for the purposes of this explanation provided we can agree that such a force is indeed possible.

For the same projectile, the force needed to do this will be the same in both cases.

In both cases the energy change is the force used times the distance covered.

In the first case the distance covered in that one second is less than 10 feet (if it were not slowing down at all it could only cover at most 10 feet in one second).

In the second case the distance covered is at least 540 feet (since it would travel 550 feet in one second if not slowing down at all and 540 feet in one second if moving at it's slowest velocity)

So in the two cases the force applied is the same, the duration of that force is the same (one second) but the distances covered in that one second are very different even if we take the best possible distance (highest possible energy) in case 1 as 10 feet and the worst possible distance (lowest possible energy) in case 2 as 540 feet this is 54 times more energy.

Which is about as non mathematical as I can make it.

For the more mathematically minded, the actual distances are 5 feet and 545 feet so the energy in the second case is in fact 109 times the energy in the first case.

[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.

[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.

[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.

[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...