Acivil engineer plans to design a curved ramp such that a car may not have to rely on friction to round the curve without skidding. the roadway is tilted toward the inside of the curve. suppose the designated speed is v and the radius of the curve is r. at what angle should the curve be tilted?

Explanation:

let \theta be the inclination at which curve is tilted

v is the speed of car and R is the radius of curve

m is the mass of car

Suppose R is the reaction offered by road to car

Resolving R in x and y direction we get

will balance weight and will provide the necessary centripetal Force

thus  ------------1

 ----------------2

Divide 1 & 2 we get

overcharge is the right answer system

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