A car having a mass of 1000 Kg is traveling along a track with a banking angle of 10 0 .The radius of curvature of the track is 60 m .If the coefficient of friction between the tires and the road is 0.3 . Determine the maximum constant speed at which the car can travel without sliding up the slope . Neglect the size of the car .

a ) 295.72 m / s
b ) 255.72 m / s
c ) 305.72 m / s
d ) 275.72 m / s

 

Let M be the mass of the car ; NA the normal reaction on the car ;R , be the radius of curvature of the track ; m , the coefficient of friction and v be its maximum constant speed with which it can travel without sliding up the slope .

The equation of motion along the y axis is ,

   NA cos
q - m NA sin q - M g =  0  ;    or
   NA = M g / (  cos q - m sin q )

Substituting the values we get ,


   NA = 10,507.00 N

The equation of motion along the x axis is ,

   NA sin
q + m NA cos q = ( M v 2 ) / R        or
   v 2 = R ( NA sin q + m NA cos q ) / M

Substituting the values and taking the square root on both sides of the equation we get ,

    v = 295.72 m / s.

Hence the maximum velocity with which the car can travel without sliding up the slope is 295.72 m / s .