Question

Please solve and explain all parts

Many people assume that it is impossible for a car to turn in the absence of friction. If the roadway is banked at exactly the right angle, a car at exactly the right velocity will be put into uniform circular motion and execute the turn successfully.

Here the department of transportation has constructed a roadway that will cause your car to turn in a circle of radius R = 175.00 meters. The roadway itself is banked with an angle of θ = 20.0 degrees. Assume that your car has a mass of m = 950 kg.

Calculate all the following:

The normal force of the road on your car, N

The velocity of your car, v m/s

The time required to make a 90 degree turn, s

Answer 1

Here as shown in the free body diagram of the car in the banked road given,

Here the angle of inclination of the road,

We have have the wieght of the car,

mass of car,

The normal force acting on the car by the banked road,

Here the normal force acts at an angle of with the vertical as shown,

So,We have on resolving the normal foce into the rectangular horizontal and vertical components as shown,

Net vertical force,(Since there is no motion upwards)

ie,

Normal force,

So,The normal force of road on your car,

b)

We have the horizontal component of the normal force,directing towards the centre of the curve of road will provide the neccessary centripetal force for the circular motion through the road.

We have given the radius of the circle of turn,

The maximum permissibe velcoity of the car through the banked road be,m/s

So,

but,normal force,

So,Velocity of the car,so,equation becomes,

So,Velocity of the car,m/s

So,The maximum permissible velocity of the car,

c)

We have the speed of the car throught the banked road is,

Also,the distance of the arc of angle 90^0 is the quarter of the total circumference of the circle,

ie,the distance of the arc,

So,the time taken to travel 90^0 turn,

Time taken to take 90^0 turn,

Please upvote the answer....