Question

An oak block had the following dimension, 2 cm by 2 cm and 5 cm in height. A copper block had the same dimensions. The copper block was on top of the wood block and both blocks were submerged tightly inside a water container.Required:Find the average density of the composite block.

Answer 1

Answer:

ρ_body = 1000 kg / m³

Explanation:

This is an exercise in fluid mechanics, specifically we must use the Archimedean principle, which states that the thrust is equal to the weight of the dislodged liquid.

In this case let's start by finding the volume of our body

oak block

      v = l to h

       v = 0.02 0.02 0.05

       V = 2 10⁻⁵ m³

cooper block indicate that it has the same dimensions so its volume is the same, the total volume of the body is

        V_total = 4 10⁻⁵ m³

as they indicate that the body is fully submerged there is a balance between weight and thrust

          B - W = 0

the push is

          B = ρ_fluid g V_total

the body weight is

         ρ_body = M / V_total

          M = ρ_body V_total

         W = Mg

          W = ρ_body V_total g

we substitute

          ρ_fluid g V_total = ρ_body V_total g

        ρ_body = ρ_fluid

in this case the body is in equilibrium in the fluid, in case the density of the body is greater than that of the fluid, the body sinks

Therefore the average density is equal to the density of the fluid, since since it is water the density is

              ρ_body = 1000 kg / m³