1) You have a summer job working for a company that designs amusement park rides. Their latest rollercoaster design involves a circular loop-the-loop with a radius of 12 meters. Neglecting friction, what's the minimum energy required for ensuring that the 1440 kg rollercoaster car is able to complete its trip around the loop?
2) One potential design for the rollercoaster involves having the car roll down from the top of a straight ramp (angled at 25 degrees above the horizontal) before it goes into the loop-the-loop. What is the minimum height required for this hill if there is a small friction coefficient of 0.15 for the full length of the hill?
3) An alternative design involves using a power supply to accelerate the car along a straight stretch of track. The power supply can deliver energy at an average rate of 35 kW over the required distance. How long should the straight track be assuming that it can be made approximately frictionless and that the car starts from rest?