Question

The gravitational field in a region is given by $\overrightarrow{E}=\left(5Nk{g}^{-1}\right)\overrightarrow{i}+\left(12Nk{g}^{-1}\right)\overrightarrow{j}$.
Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).

Answer 1

$\begin{array}{c}\overrightarrow{E}=\left(5Nk{g}^{-1}\right)\overrightarrow{i}+\left(12Nk{g}^{-1}\right)\overrightarrow{j}\\ \because E=\frac{-dv}{dr}\\ {\int }_0^{v}dv=-\int Edv\\ \Delta V=-\left[{\int }_{12}^{0}5dx+{\int }_0^{0}12dy\right]\\ \Delta V=-\left[{\int }_{12}^{0}5dx+{\int }_0^{0}12y\right]\\ \Delta V=-\left[-60+60\right]\\ \Delta V=0\end{array}$