A highway curve of radius 833 m is designed for traffic moving at a speed of 82 km/h to be able to traverse the curve without the aid of friction. What is the correct banking angle?

Explanation:

Let model an car moving in the highway curve by using Newton's Laws, whose equations of equilibrium is (x is the axis in the radial direction and y' is the axis perpendicular to the highway ground:

The following expression is derived after manipulating both equations of equilibrium algebraically and trigonometrically:

The banking angle is:

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards