A 1128 kg car and a 2210 kg pickup truck approach a curve on the expressway that

Question

A 1128 kg car and a 2210 kg pickup truck approach a curve on the expressway that has a radius of 272 m. A) At what angle should the highway engineer bank this curve so that vehicles traveling at 72.9 can safely round it regardless of the condition of their tires? B) As the car and truck round the curve at 72.9 mi/hr , find the normal force on the car to the highway surface (in N). C) As the car and truck round the curve at 72.9 mi/hr , find the normal force on the truck to the highway surface (in N).

Explanation / Answer

By safe I am guessing you mean, if there were no friction between the tires and road what should the angle be to stay on the road. There are two forces acting on the vehicle. The downward force due to gravity equal to the weight of the vehicle Fy = mg and the horizontal force (centrifugal) force due to the speed and curvature of the road Fx = m(v^2)/R The road should be sloped so that the vector sume of these forces is perpendicular to the road surface Tan[ang] = Fx/Fy = (v^2)/(R*g) Note the vehicle mass does not appear in the above equation, so the result is independent of vehicle mass Since the forces are perpendicular to the surface. and the two forces are perpendicular to each other. the normal force is Fn = Sqrt[Fx^2 + Fy^2] which you can substitute into. Note, the masses do not cancel here, so the normal force will be proportional to the masses.

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