The international space station has a mass of 1.8 × 105 kg. a 70.0-kg astronaut inside the station pushes off one wall of the station so she accelerates at 1.50 m/s2. what is the magnitude of the acceleration of the space station as the astronaut is pushing off the wall? give your answer relative to an observer who is space walking and therefore does not accelerate with the space station due to the push.

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.