Consider again the crates in Problem 45, but now assume the rope has a mass of 2 kg. If th...

Consider again the crates in Problem 45, but now assume the rope has a mass of 2 kg. If the tops of the crates start at the same initial height and the rope has a length of 10 m, what is the final speed?

Problem 45

Two crates of mass m1 = 40 kg and m2 = 15 kg are connected by a mass-less rope that passes over a massless, friction less pulley as shown in Figure P6.45. The crates start from rest, (a) Add a coordinate system to Figure P6.45. (b) What are the initial kinetic and potential energies of each crate? (c) If the crate on the left (m1) moves downward through a distance h, what is the change in the potential energy of m1 and m2? Express your answers in terms of h. (d) What is the speed of the crates after they have moved a distance h = 2.5 m?

Figure P6.45