Explanation Consider the block and spring as an isolated system. In this case, the mechanical energy of the system is not conserved because a friction force act on the body. Write the conservation of energy equation for this situation Δ K + Δ U + Δ E int = 0 (I) Here, Δ U is the change in total potential energy, Δ K is the change in kinetic energy and Δ E int is the change in internal energy of system. The total potential energy here is in the form of gravitational potential energy and spring potential energy. Write the expression for change in total potential energy. Δ U = Δ U g + Δ U s Here, Δ U g is the change in gravitational potential energy and Δ U s is the change in spring potential energy. Substitute Δ U g + Δ U s for Δ U in equation (I). Δ K + Δ U g + Δ U s + Δ E int = 0 (II) Write the expression for internal energy of the isolated system under conservative force. Δ E int = f k d (III) Here, f k is the friction force and d is the distance travelled on rough surface. Write the expressioin for friction force. f k = μ k n (IV) Here, μ k is the friction coefficient and n is the normal force acting between the surface and the block. Write the expression for normal force on the block. n = m g Here, n is the normal force acting on the block, m is the mass of the block and g is the accleration due to gravity. Substitute m g for n in equation (IV). f k = μ k m g Substitute μ k m g for f k in equation (III). Δ E int = μ k m g d Since the block is at rest at the initial and final position, hence the change in kinetic energy will be zero. Write the expression for the change in gravitational potential energy. Δ U g = U g f − U g i (V) Here, U g f is the final potential energy and U g i is initial potential energy due to gravitation. Write the expression for the change in spring potential energy Δ U s = U s f − U s i (VI) Here, U s f is the final potential energy of spring and U s i is the initial potential energy of spring

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

9th Edition

ISBN: 9781305932302

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 8, Problem 63AP

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The coefficient of kinetic friction between the block and the rough surface.

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Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

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The coefficient of kinetic friction between the block and the rough surface.

Solution Summary: The author analyzes the coefficient of kinetic friction between the block and the rough surface. The mechanical energy of the system is not conserved because a friction force act on the body.

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