Newtonian Mechanics - Banked curves

[SeReNiTy]

Hi, I'm having some trouble determining the formulae for banked curve problems, could somebody give me a general guideline on how to tackle these type of problems.

My main problem is resolving the Normal reaction in terms of the angle of the inclined plain. Like i know that Ncos(angle) = (m(v^2))/r

But how did they resolve to find this, a diagram if you can will be truly helpful guys!

 

[Nenad]

draw out a free body diagram of the situation. Then make Fnet on the car = 0.

Regards,

Nenad

 

[thepatientmental]

Banked curves involve the motion of an object along a curved path with a banked surface, such as a race track or a banked road. In order to understand the motion of an object on a banked curve, we need to consider the forces acting on the object. These forces include the normal force, the gravitational force, and the centripetal force.

To find the formula for the normal force in terms of the angle of the inclined plane, we can use the concept of equilibrium. In a banked curve, the normal force is the component of the weight of the object that is perpendicular to the surface. This normal force helps to balance out the centrifugal force, which is the force that keeps the object moving in a circular path.

To resolve the normal force in terms of the angle of the inclined plane, we can use trigonometric functions. The formula you mentioned, Ncos(angle) = (m(v^2))/r, comes from resolving the normal force into its components along the x and y axes. The x component of the normal force is Ncos(angle), which is equal to the centrifugal force, mv^2/r. This can be derived using basic trigonometry and Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration.

A diagram can definitely be helpful in visualizing this concept. In a banked curve, the normal force is perpendicular to the surface, while the centripetal force is directed towards the center of the curve. The angle of the inclined plane can be represented by the angle between the surface and the horizontal. By drawing a right triangle and using trigonometric ratios, we can derive the formula for the normal force in terms of the angle.

In summary, to tackle banked curve problems, it is important to consider the forces acting on the object and use basic principles of equilibrium and trigonometry to derive the necessary formulas. A diagram can be useful in understanding the concept and visualizing the forces involved. I hope this helps in tackling your banked curve problems!