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. 6-1), we find F→is at angle (measured from the verticalaxis) φ= θ+ swhere tan s= μs(compare with Eq. 6-13), and is the bank angle. Now, the vector sum ofF→and the vertically downward pull (mg) of gravity must be equal to the (horizontal) centripetal force (mv2/R), which leads to a surprisingly simple relationship:
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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.