Centripetal Force: Banked Curve

AI Thread Summary
The discussion centers on calculating the speed of a car navigating a banked curve, given specific parameters such as mass, radius, angle, and friction. The initial calculation yielded a speed of 54 m/s, while a reference formula suggested a speed of 67 m/s. The user is uncertain about the correct speed and seeks clarification on the application of friction in the calculations. The discrepancy arises from different approaches to incorporating the frictional force into the equations. The conversation highlights the importance of correctly applying the forces acting on the car to determine the accurate speed.
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Homework Statement


A 1200 kg car travels around a curve banked at 42.5 degrees in a circular path of radius = 150m, but the ramp is only 55m long. The force of friction on the car is 9000N, calculate the speed of the car.

So:

radius = 150 m
θ (angle the incline makes with the horizontal) = 42.5
mass = 1200 kg
Friction = 9000 N


Homework Equations



Fc= FNx + FFx

Fc= mv2 / r

The Attempt at a Solution



The car does not move in the y-plane, therefore:

Ff + Fg + FN = 0

FN = (mg + Ffsinθ)/cosθ

Solve for FN and I got 24213.83512 N

Then I used the value of FN to find FNx and added FFx to it.

Then I multiplied by the radius, divided by the mass and took the square root leaving me with 54m/s.

However, when I use the formula found on this page http://en.wikipedia.org/wiki/Banked_turn" I got 67 m/s.

Which one is right? And If I'm wrong, where did I go wrong?
 
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How did you apply the 9000N to the equations on the Wiki site?
 
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