A 1044-kg car and a 2080-kg pickup truck approach a curve on the expressway that

Question

A 1044-kg car and a 2080-kg pickup truck approach a curve on the expressway that has a radius of 236m .

At what angle should the highway engineer bank this curve so that vehicles traveling at 61.1mi/h can safely round it regardless of the condition of their tires?

Should the heavy truck go slower than the lighter car?

As the car and truck round the curve at 61.1mi/h , find the normal force on the car to the highway surface.

As the car and truck round the curve at 61.1mi/h , find the normal force on the truck to the highway surface.

Explanation / Answer

Here ,

speed , v = 61.1 mi/h

v = 27.31 m/s

Here , let the angle be theta

then ,

mg*sin(theta) = mv^2/R

sin(theta) = 27.31^2 /(236 * 9.8)

theta = 18.8 degree

the banking angle must be 18.8 degree

No, the heavy truck can go as fast as the small car

For Normal Force ,

N = mg*cos(theta)

For car

N(car) = 1044*9.8*cos(18.8)

N(car) = 9684.7 N

for Truck

N(truck ) = 2080*9.8*cos(18.8)

N(truck) = 19296 N

the normal force on the truck to the highway surface is 19296 N

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