The force f = (-90, 40) n acts on a mass of 8 kg. at time t = 0 s, the mass is initially at rest. what is the magnitude of the force (in n)? what are the (x, y) components of the acceleration vector (in m/s^2)? what are the (x, y) components of the velocity vector (in m/s) after 1 seconds?

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.