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 .

Let M be the mass of the car ; N_A 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 ,

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

Substituting the values we get ,

   N_A = 10,507.00 N

The equation of motion along the x axis is ,

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