A 0.248 kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.148 kg puck moving initially along the x axis with a speed of 2.82 m/s. After the collision, the 0.148 kg puck has a speed of 1.82 m/s at an angle of 25◦ to the positive x axis. Find the fraction of kinetic energy lost in the collision.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.