Calculating Normal Force Acting on Car at Point B

AI Thread Summary
To calculate the normal force acting on a car at point B, the mass of the car (1190 kg) and its speed (78.2 km/h) are essential. The equations of motion indicate that the normal force (N) must balance gravitational force (mg) and the centripetal force required for circular motion. At point B, where the curvature is relevant, the correct formulation is N - mg = mv^2/r, indicating that the normal force is adjusted based on the car's speed and the radius of curvature (155 m). The confusion arises from understanding the role of curvature in determining the forces acting on the car, particularly in distinguishing between scenarios at the top of a hill versus in a valley. Properly applying these principles will yield the correct normal force at point B.
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Homework Statement


A car with a mass of 1190 kg is traveling in a mountainous area with a constant speed of 78.2 km/h. The road is horizontal and flat at point A, horizontal and curved at points B and C. The radii of curvatures at B and C are: rB = 155 m and rC = 120 m.

Calculate the normal force exerted by the road on the car at point B.


Homework Equations


Forces...
x = f = mv^2/r
y = -mg + n = 0

The Attempt at a Solution


If n = mg then where does the radius come into play? I must have something set up wrong in the forces but I don't know what.
 
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I think the curves are supposed to be the tops of hills right?

So N - mg = mv^2/r (during a valley because the center of curvature is towards the top)

mg - N = mv^2/r (during a hill because the center of curvature is towards the bottom)
 

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