Space probes may be attached to their launchers by exploding bolts, which can be used to separate the parts after takeoff. suppose a 4800-kg satellite uses this method to separate from the 1400-kg remains of its launcher, and that a total of 4850 j of energy is supplied to the two parts by the explosion. this process is "perfect" in the sense that the energy is transferred entirely to the motion of the system, rather than any deformations or other internal energy changes.

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.