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Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in salt water if its body density is 1015 kg/m3?

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opudodennis

Answer:

[tex]Fe=-10N\dot j[/tex]

Explanation:

Buoyant force is given by the equation:

[tex]F_B=M_{disp\ water}g[/tex]

Given  [tex]m_g=85.0kg, \rho_b=1015kgm^3, g=10m/s^2[/tex]

We also know that:

[tex]V_g=V_d_w=\frac{m_g}{\rho_b}\\\\=\frac{85}{1015}\\\\=0.084m^3[/tex]

Knowing that:

[tex]\rho_w=1000kg/m^3\\\\F_B=w_{dw}=m_{dwg}\\=\rho_wV_{wg}\\=1000\times 0.084\times10\\ \\ =840N[/tex]

then:

[tex]F_e=F_B-w_g\\=840N-850\\=-10N[/tex]

Hence, the 85.0kg needs a to exert a 10N   force to stay submerged.

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