[Phys-L] Re: centripetal force question

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 18:49  -0500 11/14/05, Anthony Lapinski wrote:
> We know that a motorcycle driver leans inward (toward the center of a
> circle) when turning a corner that is UNBANKED. My question is how does
> the FBD look for the driver and cycle? Are both behaving like they are on
> a BANKED curve, or is N still vertical to balance w, and then fs is the
> centripetal force? Or is N slanted inward, and both Nx and fs add to
> provide the centripetal?
>
> It makes sense that the driver FEELS heavier during this turn, like he/she
> would on a banked curve. This means N is more, and then N would be slanted
> inward (like a banked curve), and not upward. However, N is always
> perpendicular to the surface (ground), which is flat. There appears to be
> a contradiction here. Can anyone help me out with this analysis?

Assuming the run is made at constant speed, the forces on the rider
*must* add up to the centripetal force on the rider, which is making
the rider move in a circle. That is true regardless of the banking of
the road. If the rider is on an unbanked road he or she must either
lean the cycle into the turn, or depend on the friction force of the
seat to move the rider in a circle. If the lean angle is correctly
chosen, the force of the seat on the rider will be directed along the
rider's spine, and the vector sum of the seat force and gravity on
the rider will be the centripetal force on the rider. This will be
true whether the road is banked or not, but if the road is banked,
the cycle will not need as much friction force to be able to stay in
the circle, since the "normal" force on the wheels of the cycle will
be slanted toward the center of the circle.

The "normal" force is always just that--perpendicular to the surface
of contact between the two objects. If the road is unbanked then the
normal force of the road is vertical, and all of the centripetal
force must be provided by friction between the wheels and the ground.
The rider banks the cycle so as to get the normal force of the *seat*
directed along the rider's spine, and thus reducing the friction
force needed to keep the rider on the cycle.

If the road is banked, then the normal force is able to provide some
of the centripetal force and tire friction is not so important. But
the situation between the rider and the seat is unchanged. If the
bank angle is not quite right for the speed of the cycle, the cyclist
must bank the cycle to make the seat normal parallel to the rider's
spine. This may end up with the cycle banked relative to the road,
and it may be banked in either direction.

Exactly the same analysis applies to a turning airplane. When in a
"balanced" turn the angle of bank of the aircraft is exactly that
required to make the normal force of the seat parallel to the
passenger's spine, and the angle of the wings will be such that all
of the centripetal force will be provided by lift from the wings. If
the angle of bank is different from that requirement, the turn isw
called "unbalanced," and is very uncomfortable for all concerned.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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