Question

1) A car is traveling around a circular portion of road banked at an incline of 20 degrees to the horizonal. If the radius of the turn is 75 m and the coefficient of static friction is 0.75 A) What is the maximum speed the car can take the turn without losing traction? B) At what speed would the static friction be zero?

Answer 1

Here the road is inclined at an ange of 20 degrees to the horizontal, let us call that angle as theta, the radius of the turn is given as r=75m, and the coefficient of static frictio is given as,

Here we will be using the formula for force acting on an object gong around with a speed v around a raius r with a banking theta as given as,

A) For the force to be cmpletely balanced, the force acting on the car due to banking must be exactly equal to its centripetal force, ie,

ie,

Here this v will be the maximum speed that the car can have, otherwise it will run off the road,

........................(1)

Substitutung all the own values,

__________________________

B) To fnd the speed at zero ststic friction, let us substitute the coefficient of stati friction to be zero in equation (1), therefore,

ie,