Car on a banket - maximum speed formula derivation

[timarli]

Hi,

This is not related with a specific homework question. I was studying this topic and have noticed that I didn't understand some bits.The car is negotiating a bend with a speed of V.
The slope of the banket is θ
The coefficient of friction is η
Weight of the car if mg
Radius of the bend is R

To find the maximum speed I broke down the weight into two components, parallel and perpendicular to the road surface. So the parallel component + η times perpendicular component should give me the component of the centripetal force that's parallel to the surface. [m*g*cosθ*η + m*g*sinθ] = (m*v^2)*cosθ

But looks like I am wrong because according to the book the force that's perpendicular to the surface is not only from gravity but has a second component coming from 'centripetal force'? This is the actual formula : [(m*g*cosθ + m*v^2*cosθ/R)*η + m*g*sinθ] = (m*v^2)*cosθ

I really don't understand this one because the "centripetal force" itself is the resultant of weight and force applied by the surface on the car. There is nothing else that can cause this central acceleration. So adding a component of the centripetal force to the above formula to find the 'centripetal force itself does not make sense at all :S

Please comment.link to the paper, pages 9-10: http://home.online.no/~orjanbye/fyfazanf1/fysikk/maximum_speed_for_bends.pdfThanks.

 

[utkarsh5]

the centripetal force acts in the direction of centre of the circle in which the the object is moving.in this case,it would be the center of the horizontal circle on which the car moves. so,the centripetal force is not acting parallel to the surface,but instead,horizontally.

 

[timarli]

Thanks a lot utkarsh5. Like you said I was using different axis' where I was simplifying horizontally without realizing that I was introducing a new component.

Thanks again :)