What’s the kinetic energy of the roller coaster at the top and bottom of the hill? use . a kiddie roller coaster car has a mass 100 kilograms. at the top of a hill, it’s moving at a speed of 3 meters/second. after reaching the bottom of the hill, its speed doubles. the car’s kinetic energy at the bottom is its kinetic energy at the top. the car has joules of kinetic energy at the bottom of the hill.

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.