The final explanation to why kinetic energy is proportional to velocity squaredby Order Tags: energy, explanation, final, kinetic, proportional, squared, velocity 

#55
Nov810, 06:49 AM

PF Gold
P: 2,001

I haven't the patience to read through all responses to this lengthy and ancient thread but surely the question has already been answered.If not here goes:
From the conservation of energy the KE of an object will be equal to the work done in bringing that object from rest to a velocity v(or to bring it from a velocity v to rest) and is independent of the method by which that work is done. Work done=force*distance =mass* acceleration*distance(Mad)....(1) For uniform acceleration from rest to a velocity v in time t, a=v/t and d=(vt)/2 Substitute a and d into equation (1) and we get the well known non relativistic KE equation. 



#56
Nov810, 07:27 AM

P: 697

Without taking away from some of the good answers above, I'll add that Landau and Lifgarbagez answer this question right in the beginning of their famous Classical Mechanics books.
This thread needed only one response. "Go look there and come back with any questions if it's not clear." Their explanation is clear and elegant. "Classics" are classics for the reason that everyone should read them. 



#57
Nov810, 08:23 AM

P: 768

It's because if you want to make something go twice as fast, you have to either push it 4x as hard, 4x as far...or some combination of these. Whichever path you take, you'll get 4x as tired. There's no other way around it.
Since energy is force x distance, it stands to reason that as speed increases then so will the distance. Simple math show exactly how much the distance increases. 



#58
Nov810, 08:45 AM

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P: 2,001





#59
Nov810, 09:23 AM

Mentor
P: 14,435

This begs the question, why define work that way? As is the case with many of the widely used concepts in physics (why is force defined to be mass times acceleration?), the answer is that we use this definition because it is so very useful and so very simple. We physicists are very much enamored with utility and simplicity, particularly when expressed mathematically, and particularly so when it describes some aspect of reality. The concept of energy was an important one even in basic Newtonian mechanics. The concept took on an even bigger role with the developments of thermodynamics and in the development of the Lagrangian/Hamiltonian formulations of Newtonian mechanics. The concept of energy plays a predominant role in quantum mechanics. Noether's theorems pretty much iced the cake. The concept does require a bit of modification with regard to special relativity. With these mods it remains a very important, if not the central, concept of physics. Bottom line: We physicists use the concept of energy because it works so very nicely for us (pun intended). 



#60
Nov810, 01:22 PM

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#61
Nov1010, 08:14 AM

P: 66

if the velocity was raised to any other power except for 2 the formula collapses into the abyss of invalidness  where all the dead ends are All formulae must pass the dimensional consistency test Even the weird ones from quantum mechanics 



#62
Apr1911, 07:30 AM

P: 2

I'm no physicist per se, but I find this subject very interesting.
I am too one of those who are inclined to revise and better understand the basics first, then go into more complicated matters. All people here seem to be quite advanced in the mathematics of physics which I kept avoiding all the time :) When reading this thread, an image kept popping up in my head. The image of getting away from a balance point. Maybe we require more force to accelerate an object from 50 mph to 100 mph (than from 0 to 50) because it's much further from the balance point, and another natural force drags the object backwards (where backwards is opposite to speeding up). Like gravity when we go upwards. Maybe the object needs more force because the balancing force is growing rapidly. Maybe we need to apply then more force, to cope with the backwards balancing force. An interesting logical result (for me at least), is that the object and everything else must be connected somehow. Because forcing a separated object doesn't affect anything else but itself => there would be no need for speed squared in the formula. That's all I have to say for now 



#63
Jul611, 11:31 AM

P: 2

We all know from reality that a car has much more than a double damage when it crashes at 100 km/h instead of 50 Km/h. So speed must be considered more than first power. Let's choose second power: it works! So why don't accept it?




#64
Jul611, 12:06 PM

P: 2

:)
what you say it's like: if you found cause(n1), why bother to know cause(n2) ? why did you bother to find cause(n1) in the first place? 



#65
Jul811, 01:48 AM

P: 2

Just wanted to say it cannot be first power because not enough.
I bother about the topic, I'm still thinking about it and haven't accepted it, to be honest. Sometimes when mathematics goes too far I loose the touch of reality. It's my limit. Alberto 


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