Chapter 10, Problem 30P

(a)

To determine

To Find: The buoyancy force on the diver in sea water.

Answer to Problem 30P

The value of the buoyancy force is $653\mathrm{N}.$

Explanation of Solution

Given info:

Density of seawater, $\rho =1025\mathrm{kg}/m^3$

Total mass, $m=68.0\mathrm{kg}$

Displaced volume, $v_{dis}=65.0\mathrm{L}$

Formula used:

Buoyancy force is $B={\rho }_{w}gV$

Where ${\rho }_w$ is density of water.

and $V$ is displaced volume of water.

Calculation:

The buoyant force

  $\begin{array}{l}{B}_{\max }={\rho }_{f}g{V}_{dis}\\ =1025\times \left(0.065\right)\times 9.8\\ B_{\max }=652.92=653\text{N}\end{array}$

Conclusion:

The value of the buoyancy force is $653\mathrm{N}.$

(b)

To determine

To Find: whether the driver would sink or float.

Answer to Problem 30P

The sea diver will sink because of $F_{\text{sd}}>B_{\max }$ .

Explanation of Solution

Given info:

Density of seawater, $\rho =1025\mathrm{kg}/m^3$

Total mass, $m=68.0\mathrm{kg}$

Displaced volume, $v_{dis}=65.0\mathrm{L}$

Calculation:

Weight of the diver is

  $\begin{array}{l}{F}_{\text{sd}}=m_{sd}g=\left(68\right)\times \left(9.8\right)\\ =666\mathrm{N}\end{array}$

From the previous part the buoyancy force is $653\mathrm{N}.$

The diver will sink because

  $F_{\text{sd}}>B_{\max }$

Conclusion:

The sea diver will sink because of $F_{\text{sd}}>B_{\max }$ .