Calculating Normal Force Acting on Car at Point B

[BuBbLeS01]

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.

 

[learningphysics]

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)

 

[m2003]

As a scientist, it is important to start by clearly defining the problem and any given parameters. In this case, the problem states that a car with a mass of 1190 kg is traveling at a constant speed of 78.2 km/h in a mountainous area. The road is horizontal and flat at point A, and horizontal and curved at points B and C, with radii of curvature of 155 m and 120 m, respectively. The goal is to calculate the normal force exerted by the road on the car at point B.

In order to solve this problem, we can use the equations for forces in the x and y directions. In the x direction, the only force acting on the car is the centripetal force, which is given by mv^2/r. In the y direction, we have two forces: the weight of the car, mg, acting downwards, and the normal force, n, acting upwards. These two forces must balance each other out for the car to maintain a constant speed and not accelerate in the y direction.

Using the given values, we can plug them into the equations and solve for the normal force at point B. It is important to note that the radius of curvature comes into play in the x direction, as it is the distance from the center of the curve to the point where the normal force is acting.

Therefore, the correct setup for the forces at point B is:

x direction: mv^2/r = n
y direction: -mg + n = 0

Solving for n, we get:

n = mv^2/r + mg

Plugging in the given values, we get:

n = (1190 kg)(78.2 km/h)^2 / 155 m + (1190 kg)(9.8 m/s^2)

n = 48,439 N

Therefore, the normal force exerted by the road on the car at point B is approximately 48,439 N.