Archimedes Principle - Example 8

Example 8:

Figure above shows a copper block rest on the bottom of a vessel filled with water. Given that the volume of the block is 1000cm³. Find the normal reaction acted on the block.
[Density of water = 1000 kg/m³; Density of copper = 3100 kg/m³]

Answer:
Volume of the block, V = 1000cm³ = 0.001m³

Let,
Normal Reaction = R
Weight = W
Upthrust = F


Diagram below shows the 3 forces acted on the block.

All the 3 forces are in equilibrium, hence
$$\begin{array}{l}R+F=W\\ R=W-F\\ R={\rho }_{1}Vg-{\rho }_{2}Vg\\ R=({\rho }_1-{\rho }_2)Vg\\ =(3100-1000)(0.001)(10)=21N\end{array}$$