Re: Banked road

[Rick Tarara <rbtarara@SPRYNET.COM>]

Let me expand a little on this.

N = mg/cosA is only true for the frictionless solution of the moving car.
For example, if the car is at rest on the incline then we have a frictional
force which will have a vertical component and thus will change the value of
N.  One of the things to remember about the two formulations for N, is that
one is done in a coordinate system that has one axis parallel to the incline
surface, while the other is in the normal vertical/horizontal configuration.

Rick


----- Original Message -----
From: "Rick Tarara" <rbtarara@SPRYNET.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, November 04, 2001 12:12 PM
Subject: Re: Banked road


> Here's my take.  Look at the second situation.  N = mg/cosA is only true
if
> the object is in equilibrium.  That is not generally true if the object is
> at rest--take the surface to be frictionless for example.  That is, the
> object (usually a car) has to be moving around the banked road so that the
> horizontal component of N will produce the needed centripetal
acceleration.
> In effect the car is trying to drive in a straight line but the road is
> pushing it towards the center point of the curve.  This INCREASES the
normal
> force to be greater than the weight of the car.  This is one I think you
> have to visualize in 3 dimensions to understand.  That is, you have to
'see'
> the straight line path versus the actual path of the car in 3D.
>
> Rick
>
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> Richard W. Tarara
> Professor of Physics
> Saint Mary's College
> Notre Dame, IN 46556
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> ----- Original Message -----
> From: "Ludwik Kowalski" <kowalskiL@MAIL.MONTCLAIR.EDU>
> To: <PHYS-L@lists.nau.edu>
> Sent: Sunday, November 04, 2001 11:48 AM
> Subject: Banked road
>
>
> > The normal force with which an inclined plane is acting on an
> > object is N= m*g*cosA, where A is the angle of inclination.
> > Students use this approach to calculate accelerations (with or
> > without friction) or to solve equilibrium problems.
> >
> > But in dealing with banked roads they are suddenly asked to
> > accept that N=mg/cosA. How can this be explained?
> > Ludwik Kowalski