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Question

In deriving the work-energy theorem , we used the chain rule to Calculate the derivative $d E / d t$. This is actually a rather subtle point because $E$ is a function of three variables, $E\left(p_x, p_y, p_z\right)$, and the relevant form of the chain rule is

$d E=\frac{\partial E}{\partial p_x} d p_x+\frac{\partial E}{\partial p_y} d p_y+\frac{\partial E}{\partial p_z} d p_z$

where the three derivatives are partial derivatives. Use this equation to fill in the details.

Solution

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The net force $\vec{F}$ acting on a body is equal to the change in momentum $\vec{p}$ of the body.

$\begin{aligned} \vec{F}=\frac{d\vec{p}}{dt} \end{aligned}$

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