Ovens cook food by heating up coils which heats up the air inside the oven. Imagine placing cookie dough into an oven that only has coils in the middle of the oven on the bottom. Where would you want to place the cookie dough so that it cooks the slowest? Explain using your knowledge of convection.

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.