Exercise 5.45 A 1177-kg car and a 2170-kg pickup truck approach a curve on the e

Question

Exercise 5.45

A 1177-kg car and a 2170-kg pickup truck approach a curve on the expressway that has a radius of 200m .

Part A

At what angle should the highway engineer bank this curve so that vehicles traveling at 70.3mi/h can safely round it regardless of the condition of their tires

Part B

Should the heavy truck go slower than the lighter car?

Part C

As the car and truck round the curve at 70.3mi/h , find the normal force on the car to the highway surface.

Part D

As the car and truck round the curve at 70.3mi/h , find the normal force on the truck to the highway surface.

Explanation / Answer

By safe I am guessing you mean, if there were no friction between the tires and road what should the angle be to stay on the road.

There are two forces acting on the vehicle. The downward force due to gravity equal to the weight of the vehicle

Fy = mg

and the horizontal force (centrifugal) force due to the speed and curvature of the road

Fx = m(v^2)/R

The road should be sloped so that the vector sume of these forces is perpendicular to the road surface

v= 70.3 mi.hr = 31.4269 m/s

Tan[ang] = Fx/Fy = (v^2)/(R*g) = 0.5033

angle = 26.72 degrees

Part B)
Note the vehicle mass does not appear in the above equation, so the result is independent of vehicle mass .Hence it doesnt matter heavy truck or lighter car .

Part C)
Since the forces are perpendicular to the surface. and the two forces are perpendicular to each other. the normal force is

Fn = Sqrt[Fx^2 + Fy^2]

Hence

Fn for car = sqrt (5812.3^2 + 11546.37^2) = 12926.77 N

Part D

Fn for truck = sqrt(10720 + 21287.7) = 23845 N

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects