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I have been given the following question of Newtonian mechanics.

A road has a (horizontal) curve of radius R. The engineer was, however, unclear on the concept, and banked the road (angle Ɵ) in THE WRONG DIRECTION (i.e., reverse banked). The coefficient of static friction between the wheels of a car (mass “m”) and the road surface is 0.80. Find the fastest speed the car can have and still maintain its ability to track (i.e., follow the curve without slipping)

I am not sure about the sentence "The engineer was, however, unclear on the concept, and banked the road (angle Ɵ) in THE WRONG DIRECTION (i.e., reverse banked)", in particular the meaning of "reversed banked". Does it mean the engineer (the designer of the road?) instead of tilting the road towards the inside of the turn made the road inclined towards the outside of the turn?

Could somebody help to clarify this question?

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    $\begingroup$ When you "bank" a road, on a curve, you tilt the road surface so that it slants to the "inside" of the curve. As you guess, he has it slanting outwards instead. $\endgroup$
    – Hot Licks
    May 31, 2018 at 1:29
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    $\begingroup$ This answer, and the links from the DOT at the bottom, is related: physics.stackexchange.com/a/408229/170832 to road design. $\endgroup$
    – Rob
    May 31, 2018 at 1:31
  • $\begingroup$ @Hot Licks Got it! Thanks a lot for the confirmation! $\endgroup$
    – PhysicsMath
    May 31, 2018 at 2:15
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    $\begingroup$ @Rob Thank you so much for referring me to the old question containing very rich relevant material! $\endgroup$
    – PhysicsMath
    May 31, 2018 at 2:17

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Whilst driving a car when you enter a right hand bend then if the road is has a camber (the is banked) to “help” the car go around the bend the left hand side of the road is higher than the right hand side.
This arrangement provides a horizontal component of the normal reaction of the road on the car towards the centre of the bend ie that horizontal component contributes to the force necessary to produce the centripetal acceleration of the car.

Your question is about what is called an “adverse camber” where, when entering a right hand bend, the left hand side of the road is lower than the right hand side with the result that the horizontal component of the normal reaction is in the opposite direction to the required direction of the centripetal acceleration of the car.
This arrangement means that to get around the corner the frictional forces between the tyres and the road must be larger than for a road with a normal camber.

Although at first sight it might appear that the engineer mentioned in your question was incompetent this could well be a false impression as in a number of countries, eg Holland, there is a designed adverse camber at roundabouts in order to deliberately reduce the speed at which vehicles can go around the roundabouts.

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