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section: Conservation laws
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PROBLEM
A particle of mass m moving with velocity V1 leaves a half-space in which its potential energy
is a constant U1 and enters another in which its potential energy is a different constant U2.
Determine the change in the direction of motion of the particle.
SOLUTION. The potential energy is independent of the co-ordinates whose axes are parallel
to the plane separating the half-spaces. The component of momentum in that plane is
therefore conserved. Denoting by 01 and O2 the angles between the normal to the plane and
the velocities V1 and V2 of the particle before and after passing the plane, we have V1 sin 01
= U2 sin O2. The relation between V1 and V2 is given by the law of conservation of energy,
and the result is
sin