Answer
(a) The length of the stretched spring is 0.290 meters.
(b) W = 0.375 J
Work Step by Step
(a) When two forces are pulling on opposite ends of the spring with a force of 15.0 N, the spring also pulls with a force of 15.0 N. (Be careful: The spring's force is not 30.0 N). We can find the distance $x$ that the spring stretches.
$kx = 15.0~N$
$x = \frac{15.0~N}{300.0~N/m} = 0.050~m$
The length of the stretched spring is 0.240 m + 0.050 m, which is 0.290 meters.
(b) $W = \frac{1}{2}kx^2$
$W = \frac{1}{2}(300.0~N/m)(0.050~m)^2$
$W = 0.375~J$
