Question

Demonstre o teorema do trabalho e energia.

Answer 1

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$\sf isolando~\Delta\!~s~na~equac_{\!\!,}\tilde ao~de~Torricelli~temos:\\\sf v^2=v_0^2+2a\Delta\!~s\\\sf2a\Delta\!~s=v^2-v_0^2\\\sf\Delta\!~s=\dfrac{v^2-v_0^2}{2a}$

$\sf sabemos~que~F=m\cdot a~e~que~W=F\cdot\Delta\!~s\\\sf substituindo~temos:\\\sf W=m\cdot \diagup\!\!\!\!a\cdot\left(\dfrac{v^2-v_0^2}{2\diagup\!\!\!\!a}\right)\\\sf W=m\cdot\left(\dfrac{v^2}{2}-\dfrac{v_0^2}{2}\right)\\\sf W=\dfrac{1}{2}m\cdot v^2-\dfrac{1}{2}m\cdot v_0^2\\\sf mas~\dfrac{1}{2}m\cdot v^2=K\\\sf W=K-K_0\\\sf K-K_0=\Delta\!~k\\\Huge\boxed{\boxed{\boxed{\boxed{\sf W=\Delta\!~k}}}}$