Question

A scientific mission uses a submersible to collect a rock sample from around the smoker. The
rock is taken back to the lab for examination and its density is measured using Archimedes
principle. The rock is found to weigh 900 N in air and 600 N in water.Calculate the density of the rock.

I understand the theory Archimedes principal, and when it's explain to me it makes total sense. But come to calculations, I don't even know where to begin! :( Full working please??

Answer 1

Okay I actually just worked out the correct answer (3000kg/m^3) but I don't understand what I was doing. Help??

Answer 2

The fact that it "weighs" something when completely submerged should first tell you that this object is denser than water (because it doesn't displace it's weight in water). Now, the difference between it's weight in air and in water is the net upward force it experiences underwater i.e. the buoyant force.
\[\large F_{b}=300N\]
We should calculate the volume of water displaced (which is the same volume as the rock) so that we can find the rock's density by dividing it's mass (known) by it's volume.
The archimedes principle says that this force of 300N is equal to the weight of the water the rock displaced. Now you say "what volume of water weighs 300N?"
300=mg
=\(\large (\rho_{water}V)g\)
\[\begin{align} \Large \Rightarrow V&= \frac{300}{\rho_{water}g}\\
&=\frac{300}{1000\times 10} \\
&=0.03m^{3}.\end{align}\]
The volume of the rock, therefore, is also 0.03m^3.
The mass of the rock is 900/10=90kg.
The density is therefore
\[\large \rho_{rock}=m/V=90/0.03=3000kg/m^3.\]