Question

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 kg/m31030 \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 kg1500 \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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It is given: ρ=1030\rho = 1030 kg/m3^3, m=1500m = 1500 kg, ρw=1000\rho_w = 1000 kg/m3^3. Upward normal force is equal to the difference of hippo's weight and buoyancy:

F=GFB=mgρwVhippogVhippo=mρ=mgmgρwρ=mg(1ρwρ)=15009.81(110001030)=428.6N.\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*}

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