A child on a sled has a combined mass of 54 kg. At the top of a 2.7 meter hill, the sled has a velocity of 6 m/s. Assuming there is no friction, what would the velocity of the child and sled
be when they reach the top of a different 0.6 meter 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.