Centripetal Force: Banked Curve

In summary, the problem involves a car of mass 1200 kg traveling around a banked curve with a radius of 150 m and an angle of incline of 42.5 degrees. The length of the ramp is only 55 m. The force of friction on the car is 9000 N. The solution involves finding the normal force and using it to calculate the speed of the car using the formulas Fc= mv^2 / r and FN = (mg + Ffsinθ)/cosθ. However, when using the formula from the website provided, a different result is obtained. It is unclear which calculation is correct and where the mistake may have been made.
  • #1
badsniper
3
0

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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  • #2
How did you apply the 9000N to the equations on the Wiki site?
 

FAQ: Centripetal Force: Banked Curve

1. What is centripetal force?

Centripetal force is a force that acts on an object moving in a circular path, pulling the object towards the center of the circle. It allows the object to continuously change direction without changing speed.

2. How does centripetal force work in a banked curve?

In a banked curve, the centripetal force is provided by the horizontal component of the normal force acting on the object. As the object moves through the curve, the normal force is directed towards the center of the circle, keeping the object on its circular path.

3. How does the angle of the bank affect centripetal force?

The angle of the bank affects the amount of centripetal force needed to keep an object moving in a circular path. A steeper bank requires a greater centripetal force, while a shallower bank requires a smaller centripetal force.

4. What other factors can affect centripetal force in a banked curve?

Other factors that can affect centripetal force in a banked curve include the speed of the object, the mass of the object, and the radius of the curve. A higher speed or a larger mass will require a greater centripetal force, while a larger radius will require a smaller centripetal force.

5. Can centripetal force cause an object to move in a straight line?

No, centripetal force is always directed towards the center of the circle and therefore cannot cause an object to move in a straight line. It only allows the object to continuously change direction while maintaining a constant speed.

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