Using Archimedes' Principle to find the density of a submerged rock.

Given the tension in a string supporting a submerged object, we use Archimedes' Principle to find the density of the object.

In the first part of the problem, we compute the buoyant force on the rock by doing a vertical force analysis. The tension pulls up on the rock and the buoyant force pushes up on the rock, and these two upward forces are balanced by the downward force of gravity on the submerged rock.

This allows us to quickly solve for the buoyant force in terms of the known weight of the rock and the known tension in the string.

To find the density of a submerged rock, we need the mass and volume because density=mass/volume. The volume is related to the buoyant force because the buoyant force on the rock is equal to the weight of the fluid displaced by submerging the rock: that's Archimedes Principle!

So we express Archimedes' Principle as F_b=rho_water*V_rock*g and solve for the volume of the rock. We already know the buoyant force and the density of water, so we plug in the numbers, get the volume of the rock, then plug into the definition of density to find the density of a submerged rock using Archimedes' Principle.

[juniorcyans]

So many things I need/want to know before I graduate. After I watched this video I realized that I misunderstood the Archimedes’ principle, so I saved the whole playlist of fluid dynamics! Thank you very much!