Acar drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 m. at the very bottom, the normal force on the driver is twice his weight. at what speed was the car traveling?

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.