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I'm trying to figure out a method of calculating the work done by friction on an object sliding down a surface with a variable slope, assuming an equation can be determined to fit the line along which the object travels and we have a known coefficient of friction for the surface.

The sticking point for me is that the force of friction is obviously going to vary with the slope of the path of travel since it's dependent upon the normal force. I studied calc and physics extensively, but that was over 10 years ago. I've broken out the calculus book and looked at the section on line integrals in a vector field, but I don't know that the friction could be treated as a vector field opposing the motion of the object like gravity could, for example.

So, I suppose I'm a little lost where to begin. Any hints would be appreciated.