Week 1 Exercise 5 (ENGR5002)

Week 1 Exercise 5Exercise sheetCurrent spec2:28 min

Week 1 Exercises, Exercise 5 (Floating Aluminium Cube)

A cube of aluminium of side $a = 0.4$ m floats in oil as shown in the figure. The relative density of aluminium is $RD_{Al} = 2.70$ , and the relative density of oil is $RD_{oil} = 0.80$ .

Data: $\rho_w = 1000\ \mathrm{kg/m^3}$ ; $g = 9.81\ \mathrm{m/s^2}$ ; $p_a = 101.3\ \mathrm{kPa}$ .

Cube of side a = 0.4 m shown floating in oil with submerged depth D.

Formulas you may need

Buoyancy force: $F_B = \rho_W g V_{displaced}$ (here $\rho$ of the oil) (on the formula sheet)
Gravity force: $F_g = m g$ (on the formula sheet)
Relative density: $RD = \rho/\rho_w$ (on the formula sheet)
Floating equilibrium: $F_B = F_g$ , so $D/a = RD_{body}/RD_{liquid}$ for a uniform prism (learn this)

(a)
Determine whether the cube will float or sink.
weight W =N
max buoyancy =N
(b)
If it floats, calculate the submerged depth $D$ .
D required =m
(c)
What happens in the case of a cube of wood of the same dimension ( $RD_{wood} = 0.6$ )?
D wood =m