Two identical carts are placed on a smooth horizontal track. Cart 1 has mass m and Cart 2 has mass 2m (because it carries an extra load). Starting from rest, each cart is pushed forward by the same constant horizontal force F acting through the same distance d. Neglect any friction.
a. (i) Show that the mechanical work done on each cart by the force F is equal in magnitude.
b. (ii) Using appropriate physical principles, derive the ratio of the final kinetic energy of Cart 1 to that of Cart 2.
c. (iii) Hence obtain the ratio of the final speeds of Cart 1 and Cart 2.