Your firm is designing a new roller-coaster ride. The permitprocess requires the calculation of forces and accelerations atvarious important locations on the ride. Each roller-coaster carwill have a total mass (including passengers) of 800 kg and willtravel freely along the winding frictionless track shown in thefigure below. Points A, E, and G are on horizontal straightsections, all at the same height of 10 m above the ground. Point Cis at a height of 10 m above the ground on an inclined section ofslope angle 30°. Point B is at the crest of a hill, while point Dis at ground level at the bottom of a valley; the radius ofcurvature at both of these points is 20 m. Point F is at the middleof a banked horizontal curve with a radius of curvature of 35 m andat the same height as points A, E, and G. At point A the speed ofthe car is 11.1 m/s.
(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?
__ m
(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 onthe car at that point?
__kN
(c) What will be the acceleration of the car at point C?
__ m/s2
(d) What will be the magnitude and direction of the force exertedby the track on the car at point D?
__ kN directed 5 ---Select--- upward downward
(e) What will be the magnitude and direction of the force exertedby the track on the car at point F?
__ kN directed 7° upward from the horizontal.
(f) At point G a constant braking force is to be applied to thecar, bringing it to a halt in a distance of 30 m. What is themagnitude of this required braking force?
__ kN
Your firm is designing a new roller-coaster ride. The permitprocess requires the calculation of forces and accelerations atvarious important locations on the ride. Each roller-coaster carwill have a total mass (including passengers) of 800 kg and willtravel freely along the winding frictionless track shown in thefigure below. Points A, E, and G are on horizontal straightsections, all at the same height of 10 m above the ground. Point Cis at a height of 10 m above the ground on an inclined section ofslope angle 30°. Point B is at the crest of a hill, while point Dis at ground level at the bottom of a valley; the radius ofcurvature at both of these points is 20 m. Point F is at the middleof a banked horizontal curve with a radius of curvature of 35 m andat the same height as points A, E, and G. At point A the speed ofthe car is 11.1 m/s.
(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?
__ m
(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 onthe car at that point?
__kN
(c) What will be the acceleration of the car at point C?
__ m/s2
(d) What will be the magnitude and direction of the force exertedby the track on the car at point D?
__ kN directed 5 ---Select--- upward downward
(e) What will be the magnitude and direction of the force exertedby the track on the car at point F?
__ kN directed 7° upward from the horizontal.
(f) At point G a constant braking force is to be applied to thecar, bringing it to a halt in a distance of 30 m. What is themagnitude of this required braking force?
__ kN
