It requires concept from Newton's laws of motion and circular motion. While solving for net force on a body on an inclined plane , we always resolve mg (weight) parallel and perpendicular to the plane but in the banking of road concept, we resolve normal reaction. Why don't we simply resolve weight and then equate it with normal reaction?
As a general rule, resolve force vectors into components that are parallel to and perpendicular to the acceleration of the object. In the case of a vehicle driving around a banked curve the acceleration is horizontal, towards the center so it's the normal force (and friction if any) that you would resolve into components.
What you solve for depends on the coordinate system you choose.
- Choose a tilted coordinate system along the incline, and you must resolve the weight into components (because it is not parallel to any axis) but not the normal force (which is parallel to the y-axis).
- Choose a horizontal/vertical coordinate system, and you don't resolve the weight (it is already parallel to the y-axis) but you do resolve the normal force (since it is not parallel to any axis).
So, it is all about the choice of coordinate system.
People often choose it to fit along the acceleration. Not because it has to, but because it can be easier to handle.
For an object sliding down an incline, the acceleration is parallel to the incline. Thus the choice of tilted coordinate system that follows the incline.
For an object in horizontal circular motion, the acceleration is horizontal towards the centre of the circle (not along the incline). We can then pick the horizontal/vertical coordinate system here.
While solving for net force on a body on an inclined plane, we always resolve mg (weight) parallel and perpendicular to the plane but in the banking of road concept, we resolve normal reaction. Why don't we simply resolve weight and then equate it with normal reaction?
Because the acceleration is horizontal - toward the center of the car's circular path.
A car's tires require friction to turn so you want to allow for various weights of vehicles and varying road conditions.
The angle of the banking can not be changed once it is set (the road construction is completed) thus it is calculated so mass cancels (various vehicle weights are permitted) because friction is assumed proportional to the normal force, which in turn is proportional to mass.
The road can be dry or icy. It is hoped that people will navigate the road at appropriate speeds for the conditions. All those variables are set to allow for the greatest range of reasonable conditions, with vehicle weight and friction of the road being the most variable.
Calculator at hyperphysics.phy-astr.gsu.edu - Maximum speed on banked roadway.
Wikipedia - Superelevation (Bank angle vs. curve radius).
Engineering.stackexchange.com - How are maximum speed limits determined for banked curves?
If you think it would make the problem easier to solve then you can do it any way you want.
However, one reason we might resolve the normal force rather than the weight is because we are usually interested in the resulting centripetal force, which is horizontal. Since the weight is already perpendicular to the centripetal direction resolving the weight would add complication.
protected by Qmechanic♦ May 25 '18 at 18:48
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