How do i even solve this buoyancy question?

An empty box is 11.0 cm per side. It will slowly be filled with sand. Sand has a density of 3.50 g/cm3. What volume of sand will cause the box to sink in water?

1 Answer
A08
Mar 3, 2018

Volume of box#=(11/100)^3=1.331xx10^-3\ m^3#
According to the Archimedes principle buoyant force is equal to volume of fluid displaced.
The box will sink when combined weight of

#w_"Box"+w_"Sand">="Buoyant force"# ........(1)

Now Buoyant force #F_b# is given as

#F_b = rhogV# .........(2)
where #rho# is the density of fluid, #g=10\ ms^-2# is gravity and #V# is volume of fluid displaced.

Setting up the equation by using (2) to rewrite (1) and taking #rho# for water #1000\ kgm^-3 #we get

#w_"Box"+w_"Sand"=1000xx10xx1.331xx10^-3#
#w_"Box"+w_"Sand"=13.31# .......(3)

Let the required volume of sand to sink the box is #V#
Its weight #w_"Sand"=Vgrho_"sand"=Vxx10xx3.50/(1000)xx10^6#

#w_"Sand"=3.50xx10^4V#

Inserting in (3) we get

#w_"Box"+3.50xx10^4V=13.31#
#=>V=(13.31-w_"Box")/(3.50xx10^4)\ m^3#

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