Solve Banked Curve Problem: tan θ = ν^2/rg

[oreo]

A problem states " For a banked curve, ignoring friction, prove that tan θ = ν^2/rg". I tried to prove but I thought that as the normal force is at right angle to track then how could be the component of normal force provide the centripetal force as my book is saying. Please someone help. I would be greatful.

 

[oreo]

I have solved it but still can't understand how is component of normal force providing centripetal force.

 

[Bystander]

Think about the resultant of the normal force and centripetal force being equal to the gravitational force.

 

[oreo]

I want to confirm this that is centripetal force of curved bank directed towards its center which is perpendicular to normal force or is directed towards the axis of curved road. Please reply

 

[Bystander]

Normal is perpendicular to road surface. Gravity is vertical. Centripetal is in horizontal plane. The road is banked at 45 degrees according to your post.
You caught me, didn't you. Normal would be hypotenuse of force triangle, centripetal would be one leg, and half of gravitational would be other. Best double-check me on that.