(a) Consider an extended object whose different portions have different elevations. Assume the free-fall acceleration is uniform over the object. Prove that the gravitational potential energy of the object€“Earth system is given by Ug = MgyCM where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.
(b) Calculate the gravitational potential energy associated with a ramp constructed on level ground with stone with density 3 800 kg/m3 and everywhere 3.60 m wide. In a side view, the ramp appears as a right triangle with height 15.7 m at the top end and base 64.8 m (Figure P9.42).

Figure P9.42