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Derivation of Kinetic Energy

by francescopadormo
Tags: derivation, energy, kinetic
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francescopadormo
#1
Feb18-06, 05:38 AM
P: 5
Hi,

I've always tken for granted that KE=(mv^2)/2, but never seen the derivation! I think it probably comes from U= - inegral of the force, but I can't see which force to use. Any help anyone? Maybe dimensional analysis was used?

Thanks!
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Doc Al
#2
Feb18-06, 06:29 AM
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I suspect you are thinking of the "work-energy" theorem, in which one integrates the net force on an object over the distance traveled to obtain the change in KE.

Start with Newton's 2nd law:
[tex]F = m \frac{dv}{dt}[/tex]

[tex]\int F dx = \int m \frac{dv}{dt} dx = m \int \frac{dx}{dt} dv = m \int v dv[/tex]

I'll leave the last step to you.


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