11.2 Worked Example - Car on a Banked Turn

A car of mass \(\displaystyle m\) is turning on a banked curve of angle \(\displaystyle \phi\) with respect to the horizontal. The curve is icy and friction between the tires and the surface is negligible. The curve has a radius \(\displaystyle r\). What is the speed \(\displaystyle v\) at which the car can turn safely? Express your answer in terms of \(\displaystyle g\), \(\displaystyle r\), and \(\displaystyle \phi\).

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