A car of mass $ M $ moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature $ R $ and is raised to an angle $ \theta $ from the horizontal. The road is slick, and friction is negligible.

Question

A car of mass $ M $ moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature $ R $ and is raised to an angle $ \theta $ from the horizontal. The road is slick, and friction is negligible.(a) Draw a free body diagram showing all real forces acting on the car as it moves around the circular off-ramp. Clearly indicate a coordinate system in your diagram.
, (b) Derive an expression for the speed of the car as it moves around the circular path. Your answer should be in terms of $ M, R, \theta $ and physical constants as appropriate.
, (c) Calculate the speed of the car as it moves around the banked curve given $ \theta = 20.0^\circ $, $ M = 1150 \; \text{kg} $, $ R = 30.0 \; \text{m} $.
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Jason · Accepted Answer

$v = \sqrt{Rg\tan\theta}$
$10.3\,\text{m/s}$

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