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DorelXD
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Homework Statement
Prove that the enrgy of a falling body remains constat using the derivate of a function
Homework Equations
We need to prove that:
[tex] \frac{mv^2}{2} + mgh [/tex] is constant, trhat is its derivate equals 0
The Attempt at a Solution
Let the positive direction be downward. Applying Newton's second law we get:
[tex] mg = F = ma [/tex]
Now I differentiated the expression and I got:
[tex] Fv + \frac{dh}{dt}mg [/tex]
If I replace mg with F, I get:
[tex] F(v+\frac{dh}{dt}) [/tex]
Now, how do I show that this equals 0? I don'y get it. I know that probably some elemntary fact is escaping me, but what? Could you please explain me? Thank you very much!