A group of students was discussing whether the concept of magnetic field is just a theory or if magnetic forces can be shown sixes between objects that are not touching. some of the students were convinced that these forces only exist in theory while the rest of the students society to prove that these forces actually exist. how can the students who did the magnetic forces between objects that are not touching each other?

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.