Explanation Write the expression for the force along the vertical direction. ∑ F y = 0 N cos θ = m g + f sin θ (I) Here, N is the normal force, m is the mass, g is the acceleration due to gravity, f is the frictional force, θ is the angle of inclination. Write the expression for the force along the horizontal direction. ∑ F x = N sin θ + f cos θ = m v 2 r (II) Write the expression for f . f = μ s N (III) Here, μ s is the coefficient of static friction. Use equation (III) in (I) to solve for N . N cos θ = m g + μ s N sin θ N = m g cos θ − μ s sin θ (IV) Write the expression for circumference of the circumference of the track. C = 2 π r (V) Here, C is the circumference of the track. Use equation (V) to solve for r . r = C 2 π (VII) Use equation (III) and (IV) in (II) to solve for μ s . μ s = ( v 2 g r cos θ − sin θ ) ( cos θ + v 2 g r sin θ ) (VIII) Conclusion: Substitute 2.5 mi for C in equation (VII) to find r

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Author: Giordano

Publisher: Cengage

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Chapter 5, Problem 14P

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