i) Derive a relation between a conservative force (F(x, y, z)) and the poten- tial energy...

   

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i) Derive a relation between a conservative force (F(x, y, z)) and the poten- tial energy associated with this force U(x, y, z). ii) What is the result of the following integral, explain your answer briefly: where F and dr represent the conservative force and the infinitesimal dis- placement vector, respectively, and the integral is a line integral along a closed path. iii) What can you say about the sign of work done by a friction force? iv) What can you say about the result of the following integral: where F represents a friction force? dr i) Derive a relation between a conservative force (F(x, y, z)) and the poten- tial energy associated with this force U(x, y, z). ii) What is the result of the following integral, explain your answer briefly: where F and dr represent the conservative force and the infinitesimal dis- placement vector, respectively, and the integral is a line integral along a closed path. iii) What can you say about the sign of work done by a friction force? iv) What can you say about the result of the following integral: where F represents a friction force? dr