Question

A rectangular scow 150 ft long and 15.0 ft wide weighs 50,000 lb. Find the depth of

fresh water required to float it.

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Answer 1

Given:-

length of scow, L=150 ft=45.72 m

width of scow, b=15 ft=4.572 m

weight of scow, W=50000 lb=222411.08 N

To Find:-

depth of fresh water required to float the plate.

Explanation:-

Since, body is floating. Therefore, we will apply principle of flotation on the body.

$\Rightarrow\text{Weight of the body, W}=\text{Buoyancy Force, }F_{b}\\\\\Rightarrow W=V_{fd}\times\rho_{f}\times g \text{ where},\\\\V_{fd}=\text{volume displaced by the scow}\\\\\rho_{f}=\text{density of fluid}=1000kg/m^{3}\\\\\Rightarrow 222411.08=1000\times9.81\times V_{fd}\\\\\Rightarrow V_{fd}=22.67m^{3}$

Let 'h' be the height of the scow submerged in the fluid

$\Rightarrow L\times b\times h=22.67\\\\\Rightarrow h=\dfrac{22.67}{45.72\times4.572}=0.108m=10.8cm$