(a) A horizontal bridge of length L = 70.0 m and mass Mpridge = 1.00 % 10 kg 1s supported at its ends. The bridge 1s symmetric and 1ts mass 1s uniformly distributed. Vehicle A of mass ma = 1.50 x 10* kg is at a distance of 10.0 m from one end of the bridge, and vehicle B of mass mp = 3.00 x 10* kg is at a distance of 10.0m from the other end of the bridge. (1) Draw a diagram to illustrate the 5 forces acting on the bridge. (11) The bridge is in translational equilibrium. Based on this, write an expression linking the magnitudes of the 5 forces. (111) If the bridge 1s also in rotational equilibrium, determine the torques about the centre of the bridge and hence write a new expression linking the magnitudes of 4 of the forces. (iv) Combine your answers to parts (ii) and (ii1) to evaluate the magnitudes of the forces exerted on each end of the bridge. The mass of Mars is 6.39 x 10?* kg and its radius is 3.39 x 10 m. Assume that Mars 1s a perfect sphere of uniform density, and hence that the planet's moment of mmertia about its central axis 1s equal to 2/5 M R?. The rotational period of Mars about its central axis is 8.86 x 10? s. (1) Calculate the gravitational potential on the surface of Mars. (i1) Calculate the angular momentum of Mars about its central axis