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?

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Quizlet Admin · Accepted Answer

It is given: $ho = 1030$ kg/m$^3$, $m = 1500$ kg, $ho_w = 1000$ kg/m$^3$. Upward normal force is equal to the difference of hippo's weight and buoyancy: 
$$
\begin{align*} F &= G - F_B \ &= mg - ho_w V_{	ext{hippo}} g \qquad V_{	ext{hippo}} = \frac{m}{ho} \ &= mg - mg \cdot \frac{ho_w}{ho} \ &= mg \cdot \left(1 - \frac{ho_w}{ho} ight) \ &= 1500 \cdot 9.81 \cdot \left( 1 - \frac{1000}{1030} ight)\ &=428.6 \, 	ext{N.} \end{align*}
$$

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