Kevin S. Huang

2014: Problem 3

Topic: Fluids
Concepts: Buoyant force, Floating

Solution:

Recall the fraction of an object submerged in water is given by

f_{\text{sub}}=\frac{\rho_{\text{obj}}}{\rho_{\text{water}}}

In our case,

f_{\text{sub}}=1-f_{\text{above}}=1-0.2=0.8

\rho_{\text{obj}}=0.8\rho_{\text{water}}

When the external force $F=3\,\mathrm{N}$ acts on the object, it becomes fully submerged. Balancing forces on the object,

F_B=F+W

\rho_{\text{water}}Vg=F+\rho_{\text{obj}}Vg

Solving for the volume $V$ ,

(\rho_{\text{water}}-\rho_{\text{obj}})Vg=F

Since $\rho_{\text{obj}}=0.8\rho_{\text{water}}$ ,

V=\frac{F}{(\rho_{\text{water}}-\rho_{\text{obj}})g}=\frac{F}{0.2\rho_{\text{water}}g}=\frac{3\,\mathrm{N}}{0.2(1000\,\mathrm{kg/m^3})(10\,\mathrm{m/s^2})}=0.0015\,\mathrm{m^3}=1.5\,\mathrm{L}

so the answer is D.