Lesson 2.6 - Gravitational Potential Energy

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CONSIDER NEWTON'S UNIVERSAL GRAVITATION

If we consider an object of mass \( m \) on the surface of the earth, \( r_1=R_E \) is raised to a new altitude of \( r_2=R_E+h \). How much work is done to raise the object?
We know that it is acted on by a gravitational force given by the following formula.


Using the work formula


DERIVING GRAVITATIONAL POTENTIAL ENERGY (CALCULUS NONSENSE)


GRAVITATIONAL POTENTIAL ENERGY

Therefore the work required to move an object from \( r_1 \) to \( r_2 \) abover a planet with mass \( M \) (and thus the change in gravitational potential energy) is given by:


ESCAPE ENERGY

If we consider an object on the Earth it requires a certain amount of energy to be completely removed from the influence of Earth's gravitational pull. We need to go to a point infinitely far away from earth since the \( \vec{F}( \vec{r}) \rightarrow 0 \) as \( r \rightarrow \infty \).

This is the energy required to escape the pull of Earth's gravity. We can call this the escape energy.


ESCAPE VELOCITY

To escape the pull of gravity we need to have enough kinetic energy to begin with to overcome this escape energy. Therefore



How can 

And


Are these equivalent for small changes in \( r \)? See if you can show that these are equivalent. 


Last modified: Monday, 19 May 2025, 9:31 AM