Design of looping roller coaster
You are an engineer helping to design a roller coaster that carries passengers down a steep track and around a vertical loop. The coaster’s speed must be great enough when at the top of the loop so that the rider stays in contact with the cart and the cart stays in contact with the track. Riders can withstand acceleration no more than a few “g’s”, where one “g” is 9.8 m/s2. What are some reasonable values for the physical quantities you can use in the design of the ride? For example, one consideration is the height at which the cart and rider should start so that they can safely make it around the loop and the radius of the loop.
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