Consider a 2-kg block attached to a string with force constant k=8 N/m. The spri

Question

Consider a 2-kg block attached to a string with force constant k=8 N/m. The spring is neither stretched nor compressed at x=0. The block slides on a surface with friction coefficient mu = 0. 61. Suppose the block starts from rest at x = 10 meters. where does the block finally come to rest? How much energy does it have originally? How much energy is dissipated by friction? How much potential energy remains when it has come to rest? Added together, do the answers to (c) and (d) equal the answer to (b)? should they?

Explanation / Answer

Let: m be the mass, g be the acceleration due to gravity, x be the initial drop, k be the spring constant, w be the angular frequency of the SHM. (a) Equating initial PE to PE stored in the spring at full extension: mgx = kx^2 / 2 k = 2mg / x k = 2 * 0.497 * 9.81 / 0.198 = 49.2 N/m. (b) w = sqrt(k / m) = sqrt(2g / x) = sqrt(2 * 9.81 / 0.198) = 9.95 rad / sec.

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