The question will be on one of the comments on the answers you give just now take the points

In order to place a satellite into orbit, it requires enough fuel to supply the necessary mechanical energy. into what types of mechanical energy does the fuel get transformed?

How will the system respond to a temperature increase?

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.