A mass m slides down a frictionless plane that is inclined at angle θ. Show, by considering the force of constraint in the Lagrangian formulation, that the normal force from the plane on the mass is the familiar mg cos(θ).
Hint: Consider the Normal force to be the result of a steep constraining potential V(z) confining the mass to the surface of the plane.
The Attempt at a Solution
This question itself can be solved by using the Euler-Lagrange equation to get force along the plane is ##mgsin(\theta)## and simply knowing the total force is mg. But I don't really know what the hint part means. Assuming the normal force is to be the result of a potential, and then add another coordinate that is perpendicular to the surface and have another Lagrangian for it?