1988M1. A highway curve that has a radius of curvature of 100 meters is
banked at an angle of 15° as shown above.
a.Determine the vehicle speed for which this curve is appropriate if there is no friction between the road and the tires of the vehicle.
On a dry day when friction is present, an automobile successfully negotiates the curve at a speed of 25 m/s.
b.Draw and label all of the forces on the automobile.
Centripetal force = mv^2 / r
(I know how to do the problem, but I'm not sure why what I'm supposed to do is correct)
The Attempt at a Solution
I know that in part a) the centripetal force is provided by the horizontal component of the normal force (Nsin(15)), but shouldn't the gravitational force also play a role? The mgsin(15) component is pushing the car down the ramp, which is pushing the car closer towards the center, albeit at an angle.
For part b) I've been told that the friction force points down the ramp and that its horizontal component contributes to the net centripetal force, but shouldn't it be pointing up the ramp to counteract mgsin(theta)? Furthermore, since friction opposes the direction of motion, shouldn't it be pointing away from the center since that's where the cart is moving towards?