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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
0.523, find the maximum speed the car can have and still make the turn
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.
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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