A civil engineer wishes to redesign the curved roadway in the figure below in su

Question

A civil engineer wishes to redesign the curved roadway in the figure below 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 ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 11.6 m/s (25.9 mi/h) and the radius of the curve is 39.0 m. At what angle should the curve be banked? SOLVE IT Conceptualize The figure below shows the banked roadway with the center of the circular path of the car far to the left of the figure. Notice that the horizontal component of the normal force participates in causing the car's centripetal acceleration. Categorize The car is modeled as a particle in equilibrium in the vertical direction and a particle in uniform circular motion in the horizontal direction A car rounding a curve on a road banked at an angle to the horizontal, when friction is neglected, the force that causes the centripetal acceleration and keeps the car moving in its circular path is the horizontal component of the normal force Analyze On a level (unbanked) road, the force that causes the centripetal acceleration is the force of static friction between car and road. If the road is banked at an angle as in the figure, however, the normal force n has a horizontal component toward the center of the curve. Because the ramp is to be designed so that the force of static friction is zero, only the component nx = n sin causes the centripetal acceleration

Explanation / Answer

Master it:

If theta is the angle of banking and mue_s is the coeeficient of static friction,

maximum allowable speed,
Vmax = sqrt(R*g*(mue_s + tan(theta) )/(1 - mue_s*tan(theta) )

= sqrt(39*9.8*(0.42 + tan(19.4))/(1 - 0.42*tan(19.4)) )

= 18.6 m/s

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