Spring 1997
Due: Friday April 18, 1997
In this problem we derive the principle of conservation of Energy. The kinetic
energy of a particle moving with speed v is . For a
conservative vector field
with potential function f(x,y,z) (in the
physicist's sense) so that
. The potential energy of a
particle at position
is
. The Conservation of Energy
Principle says that the expression
is constant for a particle moving in the field with position vector
and velocity vector
. Let P and Q be two points in space and
let C be a path from P to Q parameterized by
,
, where
and
.