When you kick a soccer ball, you apply a force f1 to the ball. what force f2 does the soccer ball exert on your foot? 1. there is no force f2. 2. f1 = f2, acting in the same direction 3. f1 = f2, acting in opposite directions 4. f2 < f1 5. f1 < f2?

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.