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Conservative Forces and Potential Energy

How does on check a force to see if the force is conservative (using the curl)?

Given a force how does one calculate the potential energy?

Are the following forces conservative

a) F(subx) = axz+bx+c, F(suby) = axz + bz, F(subz) = axy + by

b) F(a vector) = e(sub r) a/r where a, b, c are constants and e(sub r) is a unit vector

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Solution Summary

This solution defines conservative forces and lists their characteristic properties and also instructs on how to calculate potential energy with clear examples. It also distinguishes if Fx, Fz, Fy and F=e are conservative forces.