# Chapter 6 - Problems - Page 230: 59

(a) $k = 191~N/m$ (b) $U_s = 0.495~J$ (c) $m = 2.38~kg$

#### Work Step by Step

(a) We can find the spring constant: $kx = mg$ $k = \frac{mg}{x}$ $k = \frac{(1.4~kg)(9.80~m/s^2)}{0.072~m}$ $k = 191~N/m$ (b) We can find the elastic potential energy stored in the spring: $U_s = \frac{1}{2}kx^2$ $U_s = \frac{1}{2}(191~N/m)(0.072~m)^2$ $U_s = 0.495~J$ (c) We can find the second mass: $mg = kx$ $m = \frac{kx}{g}$ $m = \frac{(191~N/m)(0.122~m)}{9.80~m/s^2}$ $m = 2.38~kg$

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