find the angle of bangking highway curve of 90m radius designed to accomodate cars travelling at 160 kph, if the coefficient of friction between tires and the road is 0.60.
To find the angle of banking for a highway curve, we need to consider the forces acting on the car. These forces include the gravitational force and the frictional force.
First, let's calculate the frictional force acting on the car:
Frictional force = coefficient of friction * Normal force
The normal force is the force exerted on the car perpendicular to the surface of the road. In this case, it is equal to the gravitational force acting on the car:
Normal force = mass * gravity
To find the normal force, we need to know the mass of the car and the acceleration due to gravity. Since these values are not given in the question, we'll assume a standard mass of 1000 kg and a gravity of 9.8 m/s^2.
Normal force = 1000 kg * 9.8 m/s^2
Next, we can calculate the frictional force:
Frictional force = 0.60 * (1000 kg * 9.8 m/s^2)
Now, let's consider the forces acting on the car while it is traveling on the curve. The gravitational force has two components: one acting vertically downward and the other acting perpendicular to the surface of the road. The vertical component cancels out the normal force, leaving the horizontal component as the centripetal force:
Centripetal force = Frictional force
The centripetal force can be calculated using the formula:
Centripetal force = (mass * velocity^2) / radius
Velocity is given as 160 km/h (convert to m/s by dividing by 3.6):
Centripetal force = (1000 kg * (160,000/3600)^2) / 90 m
Now we can equate the centripetal force with the frictional force:
(1000 kg * (160,000/3600)^2) / 90 m = 0.60 * (1000 kg * 9.8 m/s^2)
Simplifying the equation, we can find the unknown angle:
Angle = arctan(((160,000/3600)^2 * 1000) / (90 * 9.8))
Using a scientific calculator, you can evaluate this expression to find the angle.