Question

The gravitational field in a region is given by →E=(5 N kg-1) →i+(12 N kg-1) →j. (a) Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin. (b) Find the potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin is taken to be zero. (c) 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). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).

Answer 1

Explanation:

It is given that the gravitational field in a region is $E=(5 N k g-1) \rightarrow i+(12 N k g-1) \rightarrow j$.

(a) The magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin:

$F^{\rightarrow}=m E^{\rightarrow}=(10 N)(\lfloor)+(24 N) S$

Therefore, the magnitude of $F^{-1}=26 N$.

(b) The potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin zero:

$\mathrm{V}=-\vec{E} \cdot \vec{r}$

Potential at (12m, 0) = $=-60 j / k g$

Potential at (0, 5m) = $=-60 j / k g$.

(c) 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):

The change in gravitational potential energy can be defined as initial potential subtracted from final potential. The potential at origin is zero and the final potential is potential at (12, 5).

$V=-\vec{E} \cdot \vec{r}$

This implies that V = -240 J.

(d) The change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m):

The change in potential can be written as $\Delta V=-\vec{E} \cdot \Delta \vec{r}$  .

$\Delta \mathrm{v}=-(10(1)+125) \cdot(12(1)-5 \mathrm{J})=0 \mathrm{J}$.