# What force on a floating object displaces 0.6 m3 of water?

May 7, 2018

$F = 5862.36 N$

#### Explanation:

Buoyancy force is equal to the weight of the displaced fluid(liquid or gas) by the object.

So we need to measure the weight of the displaced water by
$F = \textcolor{red}{m} \textcolor{b l u e}{g}$

$F = \text{force}$

$\textcolor{red}{m = m a s s}$
$\textcolor{b l u e}{g = \text{gravitational strength} = 9.8 \frac{N}{k g}}$

but first, we need to find what is $m$
so from density formula

$\textcolor{b r o w n}{\rho} = \frac{\textcolor{red}{m}}{\textcolor{g r e e n}{V}}$

rearrange (solve for m):

$\textcolor{red}{m} = \textcolor{b r o w n}{\rho} \cdot \textcolor{g r e e n}{V}$

$\textcolor{b r o w n}{\rho = \mathrm{de} n s i t y , \text{and density of water is fixed} = 997 \frac{k g}{m} ^ 3}$
$\textcolor{g r e e n}{V = v o l u m e = 0.6 {m}^{3}}$

*if you are given the V in Liters you have to convert it to a cubic meter or cm *

$\textcolor{red}{m = m a s s}$

now substitute

$m = 997 \frac{k g}{m} ^ 3 \cdot 0.6 {m}^{3}$
$m = 598.2 k g$

now find the force

$F = m g$

$F = 598.2 k g \cdot 9.8 \frac{N}{k g}$

$F = 5862.36 N$