centripetal acceleration on banked curves

[casrip1@gmx.com]

ok so this concept's been screwing with my mind so much... i get that if there's no bank then a = v^2/r. so we take the object's velocity, and the radius of the curvature and we can find acceleration. but when its banked, the whole friction and the normal etc BS comes into play and it throws me off... could someone please explain to me what forces we have to consider to find out centripetal acceleration and centripetal force on banked curves?

 

please refrain from using equations, instead talk about the actual force you're talking about (i.e. the horizontal component of normal instead of n*cos(theta) or w/e). it makes it easier for me to understand the whole reason why i i'm having issues understanding from my book is they break everything down into equations and then just mish mash them together to come up with a final equation. the problem with that is i don't get the concept of what forces were involved and how they arrived at that equation.

 

PS: is the normal force on a banked curve greater than the force of gravity? or am i looking at it wrong

[swansont]

The centripetal acceleration is ALWAYS v^2/r

 

Centripetal acceleration (or force) is the acceleration (or force) required for uniform circular motion. Centripetal force is not a new kind of force, such as the normal force, or friction, or gravity, etc. Whatever forces you have, they must add up to whatever the centripetal force is, if you have uniform circular motion.

 

Adding a bank just means there is another force to add in to the problem. The mv^2/r part is the same

[casrip1@gmx.com]

The centripetal acceleration is ALWAYS v^2/r

 

Centripetal acceleration (or force) is the acceleration (or force) required for uniform circular motion. Centripetal force is not a new kind of force, such as the normal force, or friction, or gravity, etc. Whatever forces you have, they must add up to whatever the centripetal force is, if you have uniform circular motion.

 

Adding a bank just means there is another force to add in to the problem. The mv^2/r part is the same

 

but what components of the forces contribute to that centripetal acceleration? i gather its the horizontal component of static friction, horizontal component of the normal. but what about gravity? since the obj is on a bank would the horizontal component of gravity also contribute to the centripetal acceleration?

[Vay]

When a car drives in a circular motion around a center of reference, friction exists between the tire of the car and the road such that the car accelerates toward the center of circular motion. On a flat plane, friction is enough to contribute to centripetal force or acceleration.

 

In a banked situation, ignoring friction, gravity contributes to the horizontal component of normal force which affects the centripetal force on the car. The normal force is caused by the weight of the car, or gravity. Normal force is perpendicular to the plane of inclined bank surface. Because inclined normal force has a inward, horizontal component, then an inclined plane in the absence of friction, is enough to provide centripetal acceleration and force.

 

In the case of banking, depending on the direction of banking, gravity contributes in different ways. If the banking is inward, as in a 'U' toward the center, then gravity pulls down on the car, conversely the opposite when it banks in an 'n' because gravity would be pulling the car away from the center of circular motion(not centripetal).

 

If the road is banked inward, ignoring friction, then the tilt of the bank by itself is sufficient enough to give a car driving around the banked plane a centripetal acceleration and force. Then centripetal force is -(normal force)*sin(theta) = -(centripetal force) = m((-(v^2)/R). -(normal force)*sin(theta) finds the inward horizontal component of the normal force. Since the equation uses normal force, that means you must take into account the effect of gravity on the car. If friction exists, you must find the horizontal component of kinetic friction parallel to the horizontal component of normal force on the banked road in order to find net centripetal acceleration and force inward.

 

In conclusion, the banking incline of a plane and kinetic friction both contribute to centripetal acceleration and force of a car driving around the fore-mentioned incline plane. Both scenarios use the normal force, thus factoring in effects of gravity. ((Kinetic friction) = (coefficient of kinetic friction) * (normal force))

Edited April 7, 2013 by Vay