Q: The driver steps on the brake, so the car skids downward to a full stop on a slope. What forces have done non-zero work in the slowing down motion? Is the work done by each force positive or negative?
I had included the negative work done by kinetic friction. The solution includes the positive work done by gravity, but I thought the work done by gravity was zero. Why is it positive?
A: Work is the dot product of Force vector and Displacement vector. See my post about the operations of vector for dot product on https://www.physicsdoable.com/posts/2020-11-06-highlights-of-questionanswer/
The sign of the work done by each force in this problem can be determined based on the diagram (in the attached picture). Work of normal force: zero, work of friction: negative, and work of gravity (weight): positive. The work done by a non-zero force would be zero only if either the displacement is zero or the displacement is perpendicular to the force.
