Question 10: 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?

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Chapter1: Units, Trigonometry. And Vectors
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Question 10:
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 Ffr represents a friction force?
Transcribed Image Text:Question 10: 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 Ffr represents a friction force?
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