Buoyancy

• Buoyant force vs. Weight• Apparent weight• Apparent weight – Example 10-7• Measuring Density – Example 10-8• Partially submerged objects• Partially submerged Iceberg – Example• Hydrometer – Example 10-9 • Helium Balloon – Example 10-10

Basic Buoyancy• Force on top surface

• Force on bottom surface

• Force difference

• Since h2 > h1 upward

• Side forces cancel

• Buoyant force

Archimedes' Principal• Buoyant force up:

• Gravity force down:

• Total (+ up)

• Note: if volume filled with same fluid – Total force neutral

Example 1 – Apparent weight

• Step 1 – empty statue volume of water

• Step 2 – fill statue volume with statue

• Step 3 – total down

Example 2 - Density

• Apparent vs. real weight

• Mass of displaced water

• Volume of displaced water

1

Example 2 – Density (cont)

• Volume of crown

• Density of crown

Partially submerged objects

• Density less than water– (a) Totally submerged – buoyant force > weight– (b) Partially submerged – buoyant force = weight

Partially submerged objects (cont)• Buoyant force in fluid (partial displaced volume)

• Weight of object (total volume)

• Equating

Example 3 - Iceberg• The old iceberg problem

• Table 10-1

only 0.11 above water (and that’s just the tip of the iceberg!)

Example 4 – Hydrometer

• Winemaker’s tool

• Effective density of hydrometer

OK to use g/cm3, since conversion will cancel

Example 4 – Hydrometer

• Submerged volume ratio

Hydrometer should be 0.9 submerged in waterMark at 0.9 * 25 or 22.5 cm

Example 5 – Balloon

• Buoyancy in a “pool” of air

• Step 1 – empty balloon volume of air

• Step 2 – fill balloon with heliumadd load weight

Example 6 – Balloon (cont)

• Buoyancy in a “pool” of air

• Equating up and down forces

• Solving for V