Question

A rectangular waterlight box is 560mm long , 420mm wide and 210 mm deep.It weighs 223N.
a) if it floats with its sides and ends vertical in water of density 1030 kgm-3, what dept of the box will be submerged?
b) if the box is held completely submerged in water of the same density, by a vertical chain attached to the underside of the box, what is the force in the chain?

Answer 1

a) For the equilibrium:

$$W=\rho g abh$$

$$h=\frac{W}{\rho g ab}$$

$$h=\frac{223}{(1030)(9.8)(0.56)(0.42)}=0.094 m= 94 mm$$

b)

$$F=\rho g abc-W$$

$$F=(1030)(9.8)(0.56)(0.42)(0.21)-223=276 N$$