Gravitational Potential and Gravitational Potential Energy
Gravitational Potential Energy
If gravity moves an object it does work on that object. However, the amount of work done does
not depend on the path over which gravity acted, but rather on the initial and final positions of
the object. This means that gravity is a conservative force. We can sketch a proof of this. Imagine
we have a fixed mass
M
and some other mass
m
that is moved from
A
to
B
by the gravitational
force of
M
. It is clear that any two imaginable paths can be broken into infinitesimal steps
perpendicular and parallel to the radius connecting
M
and
m
. Since gravity is a central force, the
perpendicular steps make no contribution to the work, since no force is acting in this direction.
Since both paths progress from
A
to
B
, the sum of their parallelradial segments must be equal.
Since the magnitude of the force is equal at equal radial distance, the work in each case must be
equal.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/09/2012 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.
 Fall '10
 DavidJudd
 Physics, Energy, Gravity, Potential Energy, Work

Click to edit the document details