p0272 - 184 CHAPTER 2. PARTICLE KINEMATICS 2.72 Chapter 2,...

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184 CHAPTER 2. PARTICLE KINEMATICS 2.72 Chapter 2, Problem 72 Problem: A man is driving his classic 1957 Corvette on a circular path of radius R . The Corvette’s distance along the path’s circumference is s = R ( t/ τ ) 2 ,whe re t is time and τ is a characteristic time scale. Determine the magnitude of the car’s acceleration, | a | ,inte rm so f R , t and τ . Compute R if τ =10 sec and | a | =10 m/sec 2 when t =2 τ . Solution: For natural coordinates, the acceleration vector is a = v 2 ρ e n + dv dt e t Hence, noting that the radius of curvature is equal to the radius of the circular path, R ,wehave | a | = ± v 4
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