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I have read about the motion of a car on a banked road.

  1. I read that the maximum possible speed of a car on a banked road is greater than that on a flat road. I know the formula for finding velocity in each case. But I am unable to figure out the reason by comparing the equations.

  2. I read about the ideal speed when friction is zero. I cannot understand how can the speed determine the frictional force. Frictional force should only depend on the nature of surfaces in contact. How is it possible that at a certain speed the frictional force is zero.

  3. Also I cannot understand that if the velocity is greater than the ideal velocity then what will be the change in the motion of the car.

Please provide me the answers. Thank you very much.

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  • $\begingroup$ Can you tell us where you read this? Point 2. does not sound right. $\endgroup$ – Void Apr 8 at 9:11
  • $\begingroup$ I have read it in many books that there is a velocity given by v=[R.g.tan( theta)]^1/2 where frictional force is not needed to provide the necessary centripetal force. $\endgroup$ – Ashok Sharma Apr 8 at 9:20
  • $\begingroup$ @AshokSharma If we're neglecting friction, then we're not strictly talking about a car on a banked road (which can use the static friction exerted on the road by the wheels to accelerate even around flat, non-banked curves). We're talking instead about a wet bar of soap sliding around a banked bathtub; the intuition from that scenario is far more helpful here (for example, the soap cannot turn on non-banked curves at all due to the lack of friction, and the normal force is the only thing that allows it to change direction). $\endgroup$ – probably_someone Apr 8 at 9:54
  • $\begingroup$ Perhaps it's best to refer to physics.stackexchange.com/questions/106405/… and then decide if you still have questions left. $\endgroup$ – Dlamini Apr 9 at 1:17
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  1. The higher the speed at which a car takes a bend, the greater the centripetal force that is required to keep the car following the curve of the bend. On a flat bend the normal force from the road surface is $mg$ and the whole centripetal force is supplied by the friction between the car's tires and the road surface, which is usually assumed to be proportional to the normal force. On a banked bend a component of the normal force acts towards the centre of the curve, and so provides part of the centripetal force.

  2. Speed does not determine the frictional force. In the "ideal" (or simplest) case there is assumed to be no friction (at any speed) - the road surface is assumed to be perfectly smooth. This simplifies the analysis of forces.

  3. If there is no friction and the car's speed is higher than the ideal speed then it will move away from the centre of the curve i.e. up the bank.

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