An ideal spring is hung vertically from the ceiling.When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length.An upward external force is then applied to the block to move it upward a distance of 16 cm.While the block is being raised by the force, the work done by the spring is

Question

Quizplus · Accepted Answer

The work done by the spring is calculated using the formula W = -1/2 k (x_f^2 - x_i^2). The spring constant k is found using Hooke's Law, k = mg/x = (2.0 kg)(9.8 m/s^2)/(0.06 m) = 326.67 N/m. The initial extension x_i is 0.06 m, and the final extension x_f is 0.16 m - 0.06 m = 0.10 m. Substituting these values gives W = -1/2 (326.67) ((0.10)^2 - (0.06)^2) = -1.0 J.

An Ideal Spring Is Hung Vertically from the Ceiling