PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics
Action and Symmetry, Ch Constraints, generalised coordinates and Lagrange's equations twice over
Problem
A block of mass 1.2kg rests on a rigid, frictionless plane inclined at α=25∘ to the horizontal, and is constrained to slide only along the line of steepest slope. Let x, measured along the incline surface from some fixed point on it, be the block's single generalised coordinate, taken as increasing up the slope. A steady horizontal force of magnitude F=4.0N, directed horizontally in the uphill sense, acts on the block in addition to gravity.
((a)) State the dimension and shape of the configuration space of this block.
((b)) Find the generalised force Qx due to the horizontal push alone, and state its units.