Hello! I'll answer the first part of your question.
Total energy of a particle is kinetic energy plus potential energy
The force field is conservative so the potential energy depends only on the position
of a particle. Total energy of a particle has the same value for any
because of energy conservation law.
a) at the potential energy is
as we see from the graph. The...
Hello! I'll answer the first part of your question.
Total energy of a particle is kinetic energy plus potential energy
The force field is conservative so the potential energy depends only on the position
of a particle. Total energy of a particle has the same value for any
because of energy conservation law.
a) at the potential energy is
as we see from the graph. The kinetic energy is
so the full energy is
b) a particle escapes a force field if its can be arbitrary large. Denote the total particle's energy as
and consider the equation
From it we obtain From the graph we see that
as
Also recall that the displacement is the integral of the velocity (the velocity is the derivative of the displacement with respect to time).
b1) if then
cannot be arbitrary large (
will become negative which is impossible), and a particle won't escape.
b2) if then
Therefore
So a particle will escape.
b3) if then the answer may be different for different
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