98. Consider that the car is “on the verge of sliding out” – meaning that the force of static
friction is acting “down the bank” (or “downhill” from the point of view of an ant on the
banked curve) with maximum possible magnitude.
We first consider the vector sum
F
→
of the (maximum) static friction force and the normal force.
Due to the facts that they are
perpendicular and their magnitudes are simply proportional (Eq. 61), we find
F
→
is at
angle (measured from the vertical
axis)
φ
=
θ
+
s
where tan
s
=
μ
s
(compare with Eq. 6
13), and
is the bank angle.
Now, the vector sum of
F
→
and the vertically downward pull
(
mg
) of gravity must be equal to the (horizontal) centripetal force (
m
v
2
/R
), which leads to
a surprisingly simple relationship:
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Force, Friction

Click to edit the document details