Frictionless Bank: Normal Force vs. Weight

[Rawr]

Which force is responsible for holding a car in a frictionless banked curve?

The answer is the horizontal component of the normal force. But could anyone explain why that is?

I thought it would be the horizontal component of the weight since normal force is vertical?

 

[Doc Al]

I thought it would be the horizontal component of the weight since normal force is vertical?

The weight acts vertically--it has no horizontal component. The normal force is perpendicular to the road surface; since the road is banked (at an angle) that normal force is not vertical.

 

[civil_dude]

This is a rotational velocity problem. There are two kinda 'normal' forces here. The real vertical normal force to resist gravity, and the horizontal force in the 'normal' directionto accelerate the object along a curve.

 

[Doc Al]

This is a problem involving circular motion and thus centripetal acceleration. There is only one normal force, which is perpendicular to the road surface. That normal force has vertical and horizontal components.