Re: Banked road

[Bob Sciamanda <trebor@VELOCITY.NET>]

In the static case, all I really had to say was that here the acceleration
is given as zero.  Therefore ANY component of the net force must be zero.
N=mgCosA simply applies this to the direction perpendicular to the plane.
Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Ludwik Kowalski" <kowalskiL@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, November 04, 2001 5:05 PM
Subject: Re: Banked road


> Thanks to all who responded. I was puzzled but
> now all is clear. Unfortunately, most authors do
> not discuss this "quazi-paradoxical" situation.
> Ludwik Kowalski
>
>
> Bob Sciamanda wrote:
>
> > Both cases involve an object accelerating under the influence of two
> > forces : mg(down) and N(normal to the plane).
> > These problems are solvable only because it is assumed that the
direction
> > of the acceleration (and therefore the net force) is known from the
> > statement of the problem (the ocurring motion is stated-or implied).
The
> > acceleration is along the plane in one case, and toward the center of
the
> > circular trajectory in the other case.
> >
> > The equations you quote for N simply state that the net force (the
> > resultant of mg and N) must have zero component perpendicular to the
known
> > direction of the acceleration.
> >
> > In the static case, a third (frictional) force is involved.  Here
although
> > the acceleration is zero the rigidity of the plane still demands that
the
> > net force into the plane be zero.  The Normal force adjusts to make
this
> > so (so long as the structure is capable!).
> >
> > Bob Sciamanda
> > Physics, Edinboro Univ of PA (em)
> > trebor@velocity.net
> > http://www.velocity.net/~trebor
> > ----- 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