Q: Why does normal force do zero work?
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/
As seen in the picture, Normal force is always perpendicular to the contact surface, while the Velocity (Displacement) is always parallel to the surface. Normal force is always perpendicular to Displacement, so the work done by normal force is always zero.
