A roller coaster having a total mass (including passengers) of 500 kg travels freely along a winding, frictionless track. Point A, E, and G are horizontal straight sections, all at the same height of 10 m above the ground. Point C is at a height of 10 m above the on a section of the track that is sloped at an angle of 30 degrees. Point B is at the top of a hill while point D is at ground level at the bottom of the valley. The radius of the curvature at each of these points is 20 m. Point F is at the middle of a banked horizontal curve having a radius of 30 m, and is the same 10 m height above the ground as Points A, E, and G. At point A the speed of the car is 12 m/s.
a) If the car is just barely able to make it over the hill at point B, what is the height of that point above the ground?
b) If the car is just barely able to make it over the hill at point B, what is the magnitude of the total force exerted on the car by the track at that point?
c) what is the acceleration of the car at point C?
d) What are the magnitude and direction of the total force exerted on the car by the track at point D?
e) What are the magnitude and direction of the total force exerted on the car by the track at point F?
f) At point G, a constant braking force is applied to the car, bringing the car to a halt in a distance of 25 m. What is the braking force?