Confusion about centripetal force

[Rick16]

I have run into some serious confusion with a seemingly very simple problem: A car is going around a circular track, the road is banked, and there is no friction. For this case all texts state that the centripetal force is caused by the normal force, i. e. by the radial component of the normal force. Now, here is my problem:

When the car sits still on the banked road surface, the normal force acting on the car is clearly less than the car’s weight. When the car is moving, the normal force acting on the car is greater than the car’s weight. What causes this increase in the normal force? It would seem that the circular motion causes the increase. This increased normal force then causes the centripetal acceleration which causes the circular motion. So, which was first, the hen or the egg? I am really confused here.

 

[Merlin3189]

... When the car sits still on the banked road surface, the normal force acting on the car is clearly less than the car’s weight. ...

The car can't be stationary on a banked surface if there's no friction!
If it is stationary on a flat surface, then N=mg.
Once it starts moving (rocket propulsion say) it will move up the (probably curved) banking until the banking is sufficient to provide the appropriate centripetal force.

When the car is moving, the normal force acting on the car is greater than the car’s weight. What causes this increase in the normal force?

The rocket is pushing the car into the surface. If the vertical component of the surface were not there, the car would slide in a straight line across the horizontal surface. The vertical component of the surface (the banking) pushes on the car to stop it going in a straight line. This is the extra normal force.

It would seem that the circular motion causes the increase.

I would say not. The normal force causes the circular motion. If there were no change in the normal force, the car would go in a straight line. The car can't move in a circle until a centripetal force is provided.
In fact the car does not at first move in a circle. It moves in some curve which takes it up the banking until it is steep enough to provide the right centripetal force. (And I'm not at all sure that it ever reaches a circular path on a frictionless surface.)

This increased normal force then causes the centripetal acceleration which causes the circular motion. So, which was first, the hen or the egg? I am really confused here.

I think generally we say objects continue to move in a straight line unless acted on by a force. So the force causes the change in motion.

The normal force is often called the normal reaction, because it is a Newton's third law force. The road pushes the car because the car pushes the road. Equal and opposite. Simultaneous.
If a car driving along a flat road comes to a hill (ascending), the normal force increases to push the car up the hill. It increases because the car pushes harder against the road. Both forces increase and decrease together.

 

[Rick16]

Thanks a lot. I forgot to consider the force that makes the car move. The situation seems perfectly simple now and I feel pretty stupid to have asked this question.

 

[Merlin3189]

No need to feel stupid. A lot of things seem obvious once you understand them or see them in another way.

Some questions invite you to be mistaken by making odd conditions, like the frictionless banked track. This is sufficiently unusual that you need to check any intuitive assumptions are valid.

In Physics (and probably all science) you'll get on much better by asking questions, even "stupid" ones, than by glossing over doubts and uncertainties.

And you gave me some pleasant gentle exercise for the little grey cells trying to answer you. So welcome to PF and feel free to ask all the questions you want.