The <work-energy theorem> gives $dK=\mathbf F_{\rm net}\cdot d\mathbf r$ for a point particle. For a <conservative force>, $\mathbf F=-\nabla U$ and its work is $-\Delta U$. Force is not generally a scalar derivative of total energy without specifying the displacement and the relevant energy.

Solution

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / Section B / B7 / ii / Solution

 Solution (source code)