1) A 1071-kg car and a 2060-kg pickup truck approach a curve on the expressway t

Question

1) A 1071-kg car and a 2060-kg pickup truck approach a curve on the expressway that has a radius of 273 m .

A) At what angle should the highway engineer bank this curve so that vehicles traveling at 57.6 mi/h can safely round it regardless of the condition of their tires?

B) Should the heavy truck go slower than the lighter car? Yes/No

C) As the car and truck round the curve at 57.6 mi/h , find the normal force on the car to the highway surface.

D) As the car and truck round the curve at 57.6 mi/h , find the normal force on the truck to the highway surface.

Explanation / Answer

The solution is as follows:

Centripetal force f = mV²/r = mr²
is angular velocity in radians/sec
1 radian/sec = 9.55 rev/min
m is mass in kg
r is radius of circle in meters
V is the tangental velocity in m/s
f is in Newtons

Now convert mile per hour into meter per second:

57.6 mi/hr = 25.75 m/s
f = mV²/r = m(25.75)²/(273) = 2.43 m
Weight is 9.8m
component of that weight pointing inward, with slope
f = 9.8m(sin)

set the forces equal and solve for . m will cancel.
9.8m(sin) = 2.43m
sin = 0.248
(a) = 14.36º

b) See above, mass is not in the equation hence both heavy and the lighter car should go in the same speed.

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

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]

For (c) and (d), you can simply put the value in the above expressions and get the result.

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