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solution

You are a civil engineer who has been given the assignment to redesign the curved roadway in Example 6.3 in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a road is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the road is to be 13.4 m/s (30.0 mi/h) and the radius
of the curve is 35.0 m. You need to determine the angle at which the roadway on the curve should be banked.

A 1 500-kg car moving on a flat, horizontal road negotiates a curve as
shown in the overhead view in figure 6.4a. if the radius of the curve is 35.0 m
and the coefficient of static friction between the tires and dry pavement is
a
0.523, find the maximum speed the car can have and still make the turn
successfully.
o
mg
figure 6.4 (example 6.3) (a) the
force of static friction directed
toward the center of the curve keeps
the car moving in a circular path.
(b) the forces acting on the car.
help_outlinefullscreen
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Figure 6.5 (example 6.4) a car
moves into the page and is round-
ing a curve on a road banked at an
angle 0 to the horizontal. when
friction is neglected, the force that
causes the centripetal acceleration
and keeps the car moving in its cir-
cular path is the horizontal com-
ponent of the normal force.

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