Question

On a highway, why are sharp turns banked more steeply than gentle turns?

Answer 1

I will be happy to critique your thinking.

Answer 2

Sharp turns are banked more steeply because when turning the vertical component does not matter, however it is the horizontal component should be balanced otherwise the car skids on in the horizontal direction??

Answer 3

On a banked curve, the force of gravity tends to make the car slide downward (into the curve). This provides some of the force necessary to make the car turn inward, friction on the tires doing the rest. Turning inward is necessary if the car is to move along the curved road.

Answer 4

You want the weight component down the slope to exactly result in mass times centripetal acceleration component down the slope.
Call bank angle up from horizontal road = T
then m g sin T = m (v^2/r)cos T

tan T = (v^2/rg)
for a given v, as r goes down (tighter turn), tan T and therefore T goes up.