Explanation Write down the equation for energy of a system. Δ E = − f k d (I) Here Δ E is the energy in the system, f k is the force due to friction and d is the displacement. Rewrite (I) Δ E = E f − E i = − f k Δ x (II) Here E f is the final energy and E i is the initial energy in the system. Initially the body will have only potential energy and, as it slides downward, the potential energy decreases and the final energy is only kinetic energy. Write down the equation for initial energy E i = m g h (III) Here E i is the initial potential energy of the body, m is the mass of the body, g is the acceleration due to gravity and h is the height of equilibrium position. Write down the equation for final energy. E f = 1 2 k x 2 (IV) Here E f is the final energy, k is the spring constant and x is the displacement of spring from equilibrium position. Write down the equation for force due to friction. f k = μ m g (V) Here f k is the force due to friction, μ is the coefficient of kinetic friction, m is the mass of the body, g is the acceleration due to gravity

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Chapter 7, Problem 71P

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Principles of Physics: A Calculus-Based Text

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