Work: Videos & Practice Problems

The gravitational force for large distances from the surface of Earth is given by $F\left(x\right)=\frac{GMm}{(x+R{)}^2}$, where $m$ is the mass of the object in the gravitational field (in kilograms), and $x$ is the distance above the surface of the Earth (in meters). Calculate the work needed to send a probe of mass $1200$ $\text{kg}$ to a height of $3200$ $\text{km}$ above Earth's surface. Use $G=6.7\times {10}^{-11}{\text{ Nm}}^2{\text{/kg}}^2$, $M=6\times {10}^{24}\text{ kg}$, and $R=6.378\times {10}^6\text{ m}$.