What is the Net Force on a Banked Curve?

From an outside observer's perspective, there is no need to include the centrifugal force as it is canceled out by the centripetal force. However, from the perspective of the rotating object, the centrifugal force is present and equal in magnitude to the centripetal force. In summary, when deriving the formulas for cars on banked curves, the net force in the Y direction is zero because the centrifugal force, mv^2/r, cancels out the normal force. However, in the X direction, there may be a net force if considering the ground inertial frame. From the perspective of the car's accelerated reference frame, there is an additional inertial force, the centrifugal force, that needs to be taken into account
  • #1
Abu
I understand why when deriving the formulas for cars on banked curves, the net force in the Y direction is zero. However, when I google how to derive them, people say that there is a net force greater than zero in the X direction. This is not what my professor says in his explanations however: he says that the net force in the X direction is also zero, and that this is because there is a centrifugal force equal to mv^2/r pointed to the left that cancels Fnsintheta..

I will attach the following diagram to better explain my question. Note the mv^2/r that is pointing to the left, where typically other diagrams do not include that.
question1.PNG


All in all, why is the net force in the X direction for my professors explanation equal to zero, where other explanations say it is not?
 
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  • #2
This depends on which reference frame you consider. If you consider the ground inertial frame, there is a net force. If you consider the car's accelerated reference frame there is an additional inertial force, the centrifugal force.
 
  • #3
Orodruin said:
This depends on which reference frame you consider. If you consider the ground inertial frame, there is a net force. If you consider the car's accelerated reference frame there is an additional inertial force, the centrifugal force.

Oh okay, so let's say there is a string tied to rock spinning in a vertical motion. If I am looking at the scenario as an outside observer, the forces include the tension that acts as the centripetal force and the force of gravity (depending on where the rock is in its rotating motion), there is no centrifugal force that needs to be included. But if I am looking it at as if I am the rock, then there is a centrifugal force that will be equal to the tension? Am I correct in this regard?
 
  • #4
In essence, yes.
 

1. What is the net force on a banked curve?

The net force on a banked curve is the sum of all the forces acting on an object as it moves along the curve. It is the combination of the centripetal force (directed towards the center of the curve) and the normal force (perpendicular to the surface of the curve).

2. How is the net force on a banked curve calculated?

The net force on a banked curve can be calculated using the formula: Fnet = (mv2)/r, where m is the mass of the object, v is its velocity, and r is the radius of the curve.

3. What factors affect the net force on a banked curve?

The net force on a banked curve is affected by the mass of the object, the velocity at which it is moving, and the radius of the curve. Additionally, the angle of the banked curve and the coefficient of friction between the object and the surface of the curve can also impact the net force.

4. How does the angle of the banked curve affect the net force?

The angle of the banked curve affects the net force by changing the direction and magnitude of the normal force. A steeper angle will result in a larger normal force, which in turn will decrease the required centripetal force and therefore decrease the net force. On the other hand, a shallower angle will result in a smaller normal force, requiring a larger centripetal force and increasing the net force.

5. Why is the net force on a banked curve important?

The net force on a banked curve is important because it determines the stability and safety of an object moving along the curve. If the net force is too high, the object may lose control and slide off the curve. Therefore, understanding the net force can help ensure the safe design and operation of banked curves in various applications such as racetracks and highways.

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