Problem 6.08

A highway curve with radius 1000 ft is to be banked so that a car traveling 52.0 mph will not skid sideways even in the absence of friction.
Part A
At what angle should the curve be banked?

θ =

v² / r = g sin(2Θ) / 2

To find the angle at which the curve should be banked, we can use the equation for the banking angle of a curve. The equation is:

θ = tan^(-1)(v^2 / (g * r))

where θ is the banking angle, v is the velocity of the car, g is the acceleration due to gravity, and r is the radius of the curve.

In this case, the velocity of the car is given as 52.0 mph, and we need to convert it to feet per second (fps). There are 5280 feet in a mile and 3600 seconds in an hour, so we can calculate the velocity in feet per second by multiplying 52.0 by (5280 / 3600):

v = 52.0 * (5280 / 3600) fps

Next, we can substitute the given values into the equation to find the banking angle:

θ = tan^(-1)((52.0 * (5280 / 3600))^2 / (32.2 * 1000))

The value of 32.2 is an approximation of the acceleration due to gravity in feet per second squared.

Calculating this using a calculator or a programming language will give you the value of θ in degrees.