Hippos spend much of their lives in water, but amazingly, they don't swim. They have, like manatees, very little body fat. The density of a hippo's body is approximately $1030 \mathrm{~kg} / \mathrm{m}^3$, so it sinks to the bottom of the freshwater lakes and rivers it frequents-and then it simply walks on the bottom. A $1500 \mathrm{~kg}$ hippo is completely submerged, standing on the bottom of a lake. What is the approximate value of the upward normal force on the hippo?

Solution

VerifiedIt is given: $\rho = 1030$ kg/m$^3$, $m = 1500$ kg, $\rho_w = 1000$ kg/m$^3$. Upward normal force is equal to the difference of hippo's weight and buoyancy:

$\begin{align*} F &= G - F_B \\ &= mg - \rho_w V_{\text{hippo}} g \qquad V_{\text{hippo}} = \frac{m}{\rho} \\ &= mg - mg \cdot \frac{\rho_w}{\rho} \\ &= mg \cdot \left(1 - \frac{\rho_w}{\rho} \right) \\ &= 1500 \cdot 9.81 \cdot \left( 1 - \frac{1000}{1030} \right)\\ &=428.6 \, \text{N.} \end{align*}$