Consider the system shown below. The upper pulley is fixed. The lower pulley is hanging. Both pulleys arc massless and frictionless. If it helps, you may assume both pulleys have radius R and string length I. (a) Explain how we can use just two coordinates x and y despite there being three masses. (13) Write expressions for the kinetic energy and potential energy ofthc system and show that the Lagrangian is given by: 1 1 1 L = m1(33+3:')2 +Em2(i?)2 +5313)? +mlg(x+y) m2g(yx) m3gx If you ignore any terms in getting to your Lagrangian, briey explain why you can do so. (c) Find the equations of motion. (d) Solve your equations of motion to determine the accelerations if and j? for the special case where an + m2 = m3. Express your answer in terms ofms and dim = m2 m1. (e) Suppose m] = 3m, m2 = m and m; = 4m, obtain .1? and y. (1) Use your results to note down which directions m I, m; and 1113 move