A 1072-kg car and a 2000-kg pickup truck approach a curve on the expressway that

Question

A 1072-kg car and a 2000-kg pickup truck approach a curve on the expressway that has a radius of 238 m. Part A At what angle should the highway engineer bank this curve so that vehicles traveling at 63.6 mi/h can safely round it regardless of the condition of their tires? Part B Should the heavy truck go slower than the lighter car? Part C As the car and truck round the curve at 63.6 mi/h, find the normal force on the car to the highway surface. Part D As the car and truck round the curve at 63.6 mi/h, find the normal force on the truck to the highway surface.

Explanation / Answer

Part D) Ntruck = m_truck*g/cos(theta)

tan(theta) = v^2/(r*g)

v = 63.6 mi/h = 63.6*0.44704 = 28.43 m/s

then tan(theta) = 28.43^2/(238*9.81)

theta = 19.1 degree

then N_truck = 2000*9.81/(cos(19.1)) = 20762.7 N

Part A)

theta = 19.1 degrees

Part B) No

Part C) N_car = m_car*g/cos(19.1) = 1072*9.81/cos(19.1) = 11129 N

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