Answer
The spring constant is $12.5~N/m$
Work Step by Step
We can find the mass $M$ of the block:
$M = \rho~V$
$M = (800~kg/m^3)(0.040~m)^3$
$M = 0.0512~kg$
We can find the weight of the block:
$weight = Mg = (0.0512~kg)(9.80~m/s^2) = 0.5018~N$
The weight of the block is $0.5018~N$
According to Archimedes' principle, the buoyant force is equal to the weight of the displaced water. We can find the buoyant force:
$F_b = m_w~g$
$F_b = \rho_w~V~g$
$F_b = (1000~kg/m^3)(0.040~m)^3(9.80~m/s^2)$
$F_b = 0.6272~N$
We can find the spring force $F_s$ when the block is submerged in water:
$\sum F = 0$
$F_s+Mg-F_b = 0$
$F_s = F_b-Mg$
$F_s = (0.6272~N)-(0.5018~N)$
$F_s = 0.1254~N$
We can find the spring constant:
$kx = F_s$
$k = \frac{F_s}{x}$
$k = \frac{0.1254~N}{0.010~m}$
$k = 12.5~N/m$
The spring constant is $12.5~N/m$
