A spring and block are in the arrangement of the figure, when the block is pulle

Question

A spring and block are in the arrangement of the figure, when the block is pulled out to x = +4.0 cm, we must apply a force of magnitude 370 N to hold it there. We pull the block to x = 14.0 cm and then release it. How much work does the spring do on the block when the block moves from x.-+ 5.0 cm to (a) x = +3.0 cm, (b) x =-30 cm, (c) x-.5.0 cm and (d) x--9.0 cm? Block attached to spring x positive F negative F x negative positive (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

x = +4.0 cm = 0.04m, F = 370 N

F = Kx, so K = F/x = 9250 N/m

Work done by the spring on the block when the block moves from xi to x is

(1/2)Kxi^2 - (1/2)Kx^2 = (K/2)*(xi^2 - x^2) = 4625*(xi^2 - x^2)

(a) E = 4625 (0.052 – 0.032) = 7.4J

(b) E = 4625 (0.052 – (-0.03)2) = 7.4J

(c) E = 4625 (0.052 – (-0.05)2) = 0J

(d) E = 4625 (0.052 – (-0.09)2) = -25.9J

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