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 gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5 m).

Answer 1

$\begin{array}{c}\overrightarrow{E}=\left(5Nk{g}^{-1}\right)\overrightarrow{i}+\left(12Nk{g}^{-1}\right)\overrightarrow{j}\\ E=\frac{-dv}{dr}\\ {\int }_0^{v}dv=-\int Edv\\ \Delta V=-\left[{\int }_{12}^{0}5xi+{\int }_0^{5}12xj\right]\\ \Delta V=-\left[60+60\right]\\ \Delta V=-120\end{array}$

Gravitational potential energy $=m\times \Delta V$

$-2\times 120$

$-240J$