ENGINEERING APPLICATION, CONTEXT-RICH Your firm is

Chapter , Problem 97

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ENGINEERING APPLICATION, CONTEXT-RICH Your firm is designing a new roller-coaster ride. The permit process requires the calculation of forces and accelerations at various important locations on the ride. Each roller-coaster car will have a total mass (including passengers) of and will travel freely along the winding frictionless track shown in Figure 7-55. Points A, E, and G are on horizontal straight sections, all at the same height of above the ground. Point C is at a height of above the ground on an inclined section of slope angle 30. Point B is at the crest of a hill, while point D is at ground level at the bottom of a valley; the radius of curvature at both of these points is Point F is at the middle of a banked horizontal curve with a radius of curvature of and at the same height as points A, E, and G. At point A the speed of the car is (a) If the car is just barely to make it over the hill at point B, what must be the height of point B above the ground? (b) If the car is to just barely make it over the hill at point B, what should be the magnitude of the force exerted by the track on the car at that point? (c) What will be the acceleration of the car at point C? (d) What will be the magnitude and direction of the force exerted by the track on the car at point D? (e) What will be the magnitude and direction of the force exerted by the track on the car at point F? (f ) At point G a constant braking force is to be applied to the car, bringing it to a halt in a distance of What is the magnitude of this required braking force?