A 1286-kg car and a 2060-kg pickup truck approach a curve on the expressway that

Question

A 1286-kg car and a 2060-kg pickup truck approach a curve on the expressway that has a radius of 272m .

A. At what angle should the highway engineer bank this curve so that vehicles traveling at 66.9mi/hcan safely round it regardless of the condition of their tires?

B.As the car and truck round the curve at 66.9mi/h , find the normal force on the car to the highway surface.

C.As the car and truck round the curve at 66.9mi/h , find the normal force on the truck to the highway surface.

Im a bit confused do you think you can show the equation as well as answer

Explanation / Answer

The horizontal component of normal reaction is the centripetal force

Banking angle is found when the centripetal force = the frictional 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.

converting it in to m/sec
v = 66.9km/h = 29.9m/sec
r = 272m
tan ? = 29.9^2 / 272
? = 72.76(answer for question A)
..
B)For the car the normal reaction N = mg / cos 72.76

=1286-kg*9.8/cos 72.76

=12602.8/-0.875

=-14403.2N
C)For the pickup van the normal reaction N = mg / cos 72.76
=2060*9.8/cos 72.76

=20188/-0.875

=-23072N

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