Archimedes Principle - Example 6

Example 6:

A metal block that has volume of 0.2 m³ is hanging in a water tank as shown in the figure to the left. What is the tension of the string? [ Density of the metal = 8 × 10³ kg/m³, density of water = 1 × 10³ kg/m³]

Answer:
Let,
Tension = T
Weight = W
Upthrust = F

Diagram below shows the 3 forces acted on the block.

The 3 forces are in equilibrium, hence
T+F=W T=WF T= ρ 1 Vg ρ 2 Vg T=( ρ 1 ρ 2 )Vg =(80001000)(0.2)(10)=14,000N

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