Problem # p027

2-D motion, Normal-Tangential Coordinates

A car is travelling at constant velocity v = 10 m/sec over a hill ( from left to right ) which has the shape of a parabola :

y = c · x2     c = 0.02 m-1

  1. Determine the radius of curvature at the top of the hill (x=0).
  2. What is the value of the tangential and normal acceleration at the moment the car reaches the very top of the hill (x=y=0) ?

  3. How big is the force of the road onto the car if the car has a mass of 1000 kg and is at the very top of the hill ? ( assume zero friction, g=9.81 m/sec² )

  4. What is the maximum velocity the car can travel without loosing contact with the road ?