Rounding a Curve - Rounding a Curve Friction is critical if...

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Rounding a Curve Friction is critical if we want to round a curve while driving a car or bicycle. This can be easily understood if we consider the forces that act on a car while it is making a turn. Suppose that the car in question make a turn with radius R and velocity v. Figure 6.12 shows the forces acting on the car. There is no motion in the vertical direction and the net force in this direction must therefore be equal to zero. This requires that the normal force N is equal to the weight of the car: N = m g When the car rounds the curve it carries out uniform circular motion. The corresponding centripetal acceleration of this motion is given by In order for the car to carry out this circular motion there must exist a radial force with a strength equal to This force can only be supplied by the static friction force and therefore we require that The static friction force f s has a maximum value equal to u s N and this limits the velocity and the radius of curvature of the curve that the car can take: We conclude that the car will be able to make a turn with radius R and velocity v if the coefficient of static friction between the tires and the road is Figure 6.13. Forces acting on a car while rounding an banked curve. If the road is frictionless (u s = 0) because of a cover of ice, the car will not be able to round any curve at all. In order to avoid problems like this, curves on highways are usually banked. The effect of banking the curves can be easily understood. Figure 6.13 shows the forces acting on an
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automobile when it is rounding a curve on a banked highway. We assume that there is no friction between the tires and the road. The normal force N has components both along the radial and the vertical axes. Since there is no motion along the vertical direction, the net force along the vertical axis must be zero. This requires that and fixes the normal force N
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