Data

Object Masses

ObjectSymbolMass (kg)
Metal Cylinder0.2245
Wooden Block0.0322

Experimental Tension Values

ObjectScenarioTension (g)SymbolTension (N)
Metal CylinderSubmerged211.6
Wooden BlockSinker Submerged85.5
Wooden BlockSinker & Block Submerged34.75

Free Body Diagram

Calculations

Weight of Metal Cylinder

Tension in string with Metal Cylinder submerged

Multiply the reading of the balance in kg by gravity to determine tension in N

Experimental Buoyant Force on Metal Cylinder

Newton’s first law:

There is no acceleration:

General Scenario:

Specific Scenario with proper symbols:

Solve for B:

Substitute:

Theoretical Volume and Buoyant Force for Metal Cylinder

Apparently the thing is tungsten

Substitute:

Equation for Buoyant Force

Substitute:

Error % In Buoyancy

Block Density


Find buoyant force, which can be combined with mass to find density later:

Just sinker submerged:

Block and Sinker submerged:

Combine equations:

Relate buoyant force, volume:

Substitute and solve for volume:

Relate density mass, volume:

Substitute:

Solve for :

Substitute real values: