Serway & Jewett — Conservation of Energy: Problem 25

You are working with a team that is designing a new roller coaster–type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 250-kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 110-m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 50.0 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force for the last 20 m for the empty test car. (b) Find the highest speed reached by the car during the final section of track length 250 m. (c) You are asked by your team supervisor to determine the answers to parts (a) and (b) for a fully loaded car with an upper limit of 450 kg of passenger mass. Find these new values. (d) The required friction force in part (c) is well within design limits. The fastest speed, however, is well below that of current leading rides, so you would like to increase the maximum speed. You can’t make the tower taller above ground, so you decide to include a feature where part of the track goes underground. Determine the depth to which the underground part of the ride must go to increase the maximum speed to 55.0 m/s. Assume the overall length of the first part of the track remains at 230 m and the length of track from the top to the lowest underground point is 150 m. The same 50.0-N friction force acts on the entire 230-m section of track. (e) Is the construction in part (d) feasible?