ch06-p041 - 41. The magnitude of the acceleration of the...

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Unformatted text preview: 41. The magnitude of the acceleration of the cyclist as it rounds the curve is given by v2/R, where v is the speed of the cyclist and R is the radius of the curve. Since the road is horizontal, only the frictional force of the road on the tires makes this acceleration possible. The horizontal component of Newton’s second law is f = mv2/R. If FN is the normal force of the road on the bicycle and m is the mass of the bicycle and rider, the vertical component of Newton’s second law leads to FN = mg. Thus, using Eq. 6-1, the maximum value of static friction is fs,max = μs FN = μsmg. If the bicycle does not slip, f ≤ μsmg. This means v2 ≤ μsg R R≥ v2 . μsg Consequently, the minimum radius with which a cyclist moving at 29 km/h = 8.1 m/s can round the curve without slipping is Rmin = v2 (8.1 m/s) 2 = = 21 m. μ s g (0.32)(9.8 m/s 2 ) ...
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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.

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