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F08_lec15 - P1112 Lecture 15 Oct 1st 2008 For each object...

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P1112 Lecture 15 Oct 1st, 2008
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! L ! R R ! For each object, draw a free-body diagram, and relate the other force(s) acting on the object to its weight w. Conical Pendulum Banking Plane Car on banked curve (no friction)
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Rounding a curve A 1500 kg car is traveling on a flat road that passes through a curve with 35m radius. Assuming the coefficient of static friction is 0.5, what is the maximum speed the car can have to stay on the road without sliding?
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solution Only centripetal force available is friction force, so the maximal speed is given by: W N f s a rad F x = f s " = ma rad a rad = v 2 R f s = μ s N F y " = N # mg = 0 N = mg v max = μ s gR v max = 0.5 " 9.81 m / s 2 " 35 m = 13 m / s
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Banked curve Avoid relying on friction to round a curve: build curve banked at angle α : α
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Banked curve Avoid relying on friction to round a curve. Build curve banked at angle α : • FBD: Calculate the angle you need to round the curve at 25m/s! α α W Ν
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solution F x = N sin " # = ma rad a rad = v 2 R F y # = N cos " $ mg = 0 N = mg /cos " tan " = v 2 gR " = arctan (25 m / s ) 2 9.81 m / s 2 % 35 m & ( ) * + = 60deg
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