Wednesday, September 4, 2013

A particle of mass 2.5 kg moves in a conservative force field. Its potential energy curve is shown below. From the curve, determine (a) the total...

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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