Question

Enter an expression for the force constant for the floating raft, in terms of L, g, and the density of water, ρ.

Answer 1

Answer:

K = ρL²g

Explanation:

Consider L as the length of the raft inside the water when the raft is displaced through additional distance y;

Then:

F = upthrust ( restoring force) = weight of the liquid displaced.

$F = V_{\omega} \rho_{\omega} g= A y \rho_{\omega} g$

where;

A = L²

$\rho_{\omega} = \rho$

F = ky.

Then,

$Ay \rho g = ky$

$L^2y \rho g = ky$

Divide both sides by y

K = ρL²g