A110. g wooden block is initially at rest on a rough horizontal surface when a 12.8 g bullet is fired horizontally into (but does not go through) it. after the impact, the block–bullet combination slides 6.5 m before coming to rest. if the coefficient of kinetic friction between block and surface is 0.750, determine the speed of the bullet (in m/s) immediately before impact.

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.