The Burj Khalifa in Dubai is the world's tallest building. The structure is 828 m (2716.5 ft) and has more than 160 stories. A tourist is obviously using the elevator to reach their hotel room and after a long ride finally arrives at the correct floor, where the tourist has − 1.97 × 10 5 J of potential energy. If the 89.5 kg tourist has zero potential energy at the top of the building, how high ( h ) is the hotel room from the ground? The acceleration due to gravity is 9.81 m / s 2 .

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.