Why project the normal force but not weight when banking a curve without friction

[ben_d]

can someone please explain why when banking a curve at an angle so that no friction at all is needed to maintain the car's turning radius , we project the normal into an x and y component and we don't project the weight into an x and y component as we do for problems involving motion over an inclined path ? thanks for any help it will be really appreciated .

 

[Doc Al]

Weight always acts vertically, so it has no x component.

To make the turn, you need some centripetal force (in the x direction). That could be supplied by the normal force or friction or both. If the road is unbanked, the normal force has no horizontal component, so friction is all you have. But if the road is banked, the normal force can supply the horizontal force; for some speeds, you won't need any friction at all to make the turn.

 

[rcgldr]

From Wiki:

http://en.wikipedia.org/wiki/Banked_turn