## Related questions with answers

A person with a mass of $81 \mathrm{~kg}$ and a volume of $0.089 \mathrm{~m}^3$ floats quietly in water. If an upward force $F$ is applied to the person by a friend, the volume of the person above water increases by $0.0018 \mathrm{~m}^3$. Find the force $F$.

Solution

Verified$\textcolor{#c34632}{(b.)}$ Calculate the upward force $F$ applied to the person at which the volume of the person of above increases by $0.0018\text{ m}^3$.

The force applied is then:

$F_\text{app} = \rho_w g \Delta V_\text{above} \tag{1}$

Entering known values to equation (1), we obtain $F_\text{app}$ as

$\begin{aligned} F_\text{app} & = \left(1000\mathrm{~\dfrac{kg}{m^3}}\right) \left(9.81\mathrm{~\dfrac{m}{s^2}}\right) (0.0018\text{ m}^3)\\ & = 17.66 \text{ N} \end{aligned}$

$\boxed{\therefore F_\text{app} = 17.66 \text{ N} }$

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