Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $k = 390~N/m$ (b) The spring will be 17.5 cm in length.
(a) The spring stretches by 5 cm. The force with which the spring pulls is equal to the object's weight. We can find the spring constant of the spring; $kx = mg$ $k = \frac{mg}{x}$ $k = \frac{(2.0~kg)(9.80~m/s^2)}{0.05~m}$ $k = 390~N/m$ (b) We can find the amount that the spring stretches with a 3.0-kg object as; $kx = mg$ $x = \frac{mg}{k}$ $x = \frac{(3.0~kg)(9.80~m/s^2)}{390~N/m}$ $x = 0.075~m = 7.5~cm$ Since the unstretched length of the spring is 10 cm, the spring will be 17.5 cm in length.