A 1266-kg car and a 2280-kg pickup truck approach a curve on the expressway that

Question

A 1266-kg car and a 2280-kg pickup truck approach a curve on the expressway that has a radius of 300 m .

a) At what angle should the highwat engineer bank this curve so that the vehicles traveling at 72.1 mi/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 72.1 mi/h, find the normal force on the car to the highway surface.

d) As the car and truck round the curve at 72.1 mi/h, find the normal force on the truck to the highway surface.

Explanation / Answer

a) v = 72.1 mph = 72.1 x 1609 m / 3600s

v = 32.22 m/s

in horrizontal,

Nsin@ = m v^2 / r .......(i)

in vertical,

Ncos@ = mg   ........(ii)

(i) / (ii)

tan@ = v^2 / rg   = 32.22^2 / (300 x 9.81) = 0.353

@ = 19.43 deg

b) tan@ = v^2 / rg

@ is independent of mass of vehicle.

hence speed will be same.

c) Ncos@ = mg

for car :

Nc cos19.43 = 1266 x 9.81

Nc = 13169.48 N

d) for truck :

Nt cos19.43 = 2280 x 9.81

Nt = 23717.55 N

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