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 .

A)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?

B)Should the heavy truck go slower than the lighter car?

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

D) 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

The horizontal component of normal reaction is the centripetal force
mv^2 /r = Nsin ?
The vertical component balances the weight
mg = N cos ?
Dividing one by the other
v^2 / r = tan ?
Thus the banking angle does not depend on the mass of the vehicle.
Let v = 61.1mi/h = 27.31m/sec
r = 236 m
tan ? = 27.31^2 / 236
? = 72.19?
--------------------------------------...
For the car the normal reaction N = mg / cos 72.19
= -12787.7N
For the pickup van the normal reaction N = mg / cos 72.19
-25477.4 N

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