Question

A 1025 car and a 2150 pickup truck approach a curve on the expressway that has a radius of 246 m. At what angle should the highway engineer bank this curve so that vehicles traveling at 71.9 mph can safely round it regardless of the condition of their tires? Should the heavy truck go slower than the lighter car? As the car rounds the curve at 71.9 mph, find the normal force on the car due to the highway surface. As the truck rounds the curve at 71.9 mph, find the normal force on the truck due to the highway surface.

Answer 1

Given data

Mass of the car, m = 1025 kg

Mass of the truck is, M = 2150 kg

Radius of the curve is, r = 246 m

Speed of the vehicles, v = 71.9 mi/h

v = (71.9 mi / h) ( 1609.34 m /1 mi) (1 h / 3600 s)

v = 32.14 m/s

A)

The banking angle is,

                   = tan^-1 (v²/r*g)

                   = tan^-1 [(32.14)² / (246)*(9.8 )]

                   = 23.17^o

B)

The speed of the vehicle is,

v = sqrt(r*g*tan)

Since, this relation is independent of mass of the vehicle, there is no

necessity for the heavy vehicle to go slow than the lighter vehicle.

C)

The forces acting on the car along y axis,

N*cos =  m*g

Along x axis, it is,

N*sin = m*v²/r

The normal force acting on the car is,

                          N = sqrt[ (mg)² + (mv²/r)² ]

N = sqrt[ (1025*9.8)² + (1025*32.14²/246)² ]

N = 1.09*10⁴ N

D)

The normal force acting on the truck is,

   N = sqrt[ (Mg)² + (Mv²/r)² ]

N = sqrt[ (2150*9.8)² + (2150*32.14²/246)² ]

N = 2.29*10⁴ N