Why Does Kinetic Energy Depend on the Square of Speed?

[lella]

Why is it that kinetic energy depends on the square of speed instead of simply speed? Is there an example that shows why?

 

[franznietzsche]

Why is it that kinetic energy depends on the square of speed instead of simply speed? Is there an example that shows why?

Its really just because that's the definition of kinetic energy. Momentum is defined as the quantity that depends on the speed linearly.

 

[TiBaal89]

That's a very interesting question - sure its defined that way, but why?

I suppose this isn't truly a satisfatory answer, but we could use dimensional analysis to show that it indeed must be squared:

In SI, we're looking for energy in kg*m^2/s^2

Potentional energy: m*g*h so (kg)(m/s^2)(m) looks good

Kinetic Energy: m*v^2 (kg)(m/s)^2 looks good too!

As far as a "deeper" reason, I don't think I can add anything off hand.

 

[myxinjie]

The guy above is cute. But I have another explanation.
If the mass is M, and at the beginning it rested on the non-fiction ground.
Then we give it a force F.
We know that after S meters' movement, the kientic of the mass will be E=F*S ;
but now we will express it in another way, with the V and M.
we know the acceleration of the mass is a = F/M
and there is the relation S = V^2/(2*a) = V^2/(2*F/M)=MV^2/(2F)
So E = F*S = MV^2/2
it is the kinetic.

 

[drnikitin]

You can get it from the second Newton's law
F=m*dv/dt

According to Work(W)-Energy(E) theorem we have the definition of kinetic energy
dE=dW=F*dx=F*v*dt=m*v*dv=d(m*v^2/2)

From which we get the kinetic energy
E = m*v^2/2

Hope this helps

Prof. Nikitin,
My Quick Online Physics Reference Guide and Help:
http://physics-help.info

 

[Sir_Deenicus]

From a pure foundation and without the benefit of hindsight, the answer of course, is that it is not necessary that kinetic energy be dependant on the square of velocity. This could only have been (and was, by Joule) determined empiracally. The other answer is because momentum, which is the quantity of motion, already does.

Kinetic energy is the energy of motion, it [energy] allows us to note a change of some system's state with respect to time. It also makes sense physically that kinetic energy would depend on the square of velocity since its value does not depend on direction.