Answer
(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:
$mg = kx$
$m = \frac{kx}{g}$
$m = \frac{(191~N/m)(0.122~m)}{9.80~m/s^2}$
$m = 2.38~kg$
