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Unformatted text preview: 44. The magnitude of the acceleration of the car as it rounds the curve is given by v2/R, where v is the speed of the car 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 car and m is the mass of the car, 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 car does not slip, f ≤ μsmg. This means v2 ≤ μs g R v ≤ μ s Rg . Consequently, the maximum speed with which the car can round the curve without slipping is
vmax = μ s Rg = (0.60)(30.5 m)(9.8 m/s 2 ) = 13 m/s ≈ 48 km/h. ...
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