A 1266-kg car and a 2190-kg pickup truck approach a curve on the expressway that
ID: 1458926 • Letter: A
Question
A 1266-kg car and a 2190-kg pickup truck approach a curve on the expressway that has a radius of 221 m .
A) At what angle should the highway engineer bank this curve so that vehicles traveling at 70.2 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 70.2 mi/h , find the normal force on the car to the highway surface
D) As the car and truck round the curve at 70.2 mi/h , find the normal force on the truck to the highway surface.
Explanation / Answer
Given data
Mass of the car, m = 1266 kg
Mass of the truck is, M = 2190 kg
Radius of the curve is, r = 221 m
Speed of the vehicles, v = 70.2 mi/h
= (70.2 mi / h) ( 1609.344 m /1 mi) (1 h / 3600 s)
= 31.38 m/s
A) The banking angle is,
= tan-1 (v2 / rg)
= tan-1 [(31.38 m/s)2 / (221 m) (9.8 m/s2 )]
= 24.5o
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B) The speed of the vehicle is,
v = r g tan
Since, this relation is independent of mass of the vehicle, there is no
neccesity for the heavy vehicle to go slow than the lighter vehicle.
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C) The forces acting on the car along y axis,
N cos = mg
Along x axis, it is,
N sin = mv2/r
The normal force acting on the car is,
N = (mg)2 + (mv2/r)2
= (1266 kg) [(9.8 m/s2 ) 2+ (31.38 m/s)4 / (221 m) 2 ]
= 1.36 *104 N
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D)
The normal force acting on the truck is,
N' = (Mg)2 + (Mv2/r)2
= (2190 kg) [(9.8 m/s2 ) 2+ (31.38 m/s)4 / (221 m) 2 ]
= 2.36*104 N
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