A roller-coaster car having a total mass (including passengers) of 500 kg travels freely along the winding frictionless track in Figure .Points A, E, and G are horizontal straight sections, all at the same height of 10 m above ground. Point C is at a height of 10 m above the ground on a section sloped at an angle of 30°. Point B is at the top of a hill, while point D is at ground level at the bottom of a valley. The radius of curvature at each of these points is 20 m. Point F is at the middle of a banked horizontal curve of radius of curvature of 30 m, and at the same height of 10 m 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 brakingforce?

Transcribed Image Text:

v= 12 m/s D. 30