Suppose a particle moves in space subject to a conservative potential V(r) but is constrained to always move on a surface whose equation is σ(r,t)=0. (The explicit dependence on t indicates that the surface may be moving.) The instantaneous force of constraint is taken as always perpendicular to the surface. Show analytically that the energy of the particle is not conserved if the surface moves in time. What physically is the reason for nonconservation of the energy under this circumstance?