A racetrack has the shape of an inverted cone, as the drawing shows. On this sur

Question

 

A racetrack has the shape of an inverted cone, as the drawing shows. On this surface the cars race in circles that are parallel to the ground, and the surface is at an angle O= 30°. For a speed of 45 m/s, at what value of the distance d should a driver locate his car if he wishes to stay on a circular path without depending on friction?
_____m
My drawings always get distorted when I click on add diagram...sorry.  The arrow is pointing to the car and the two semi-circles were supposed to be different and were to indicate the angles at the bottom of the drawing. 

I need someone to show me how to work this problem and give me the answers please

Explanation / Answer

given speed of   car v = 45m/s angle = 30 car experencies centripetal force directed towads center of circulat path    thi sprovided FN cos60 = ma = mv2/r solving for the radius from the diagram    d= r/ sin60     = mv2/ FN cos60 sin60 ----- (1) the manitude of FN of the normal force can be obtaind by observing   that the car has no vertical acclerations so net force on vertical direction is zero.        the vertical component of the normal force is FN sin60 and teh weigth is -mg      FN sin60 - mg = 0 ----- (2) from the eq (1) and eq (2)         d = mv2/ FN cos 60 sin60            = sin60mv2/ mg cos 60 sin60            = v2/ g cos 60            = (45m/s)^2/ 9.8 cos60           = 413.2m                

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