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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
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Basic Buoyancy• Force on top surface
• Force on bottom surface
• Force difference
• Since h2 > h1 upward
• Side forces cancel
• Buoyant force
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Archimedes' Principal• Buoyant force up:
• Gravity force down:
• Total (+ up)
• Note: if volume filled with same fluid – Total force neutral
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Example 1 – Apparent weight
• Step 1 – empty statue volume of water
• Step 2 – fill statue volume with statue
• Step 3 – total down
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Example 2 - Density
• Apparent vs. real weight
• Mass of displaced water
• Volume of displaced water
1
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Example 2 – Density (cont)
• Volume of crown
• Density of crown
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Partially submerged objects
• Density less than water– (a) Totally submerged – buoyant force > weight– (b) Partially submerged – buoyant force = weight
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Partially submerged objects (cont)• Buoyant force in fluid (partial displaced volume)
• Weight of object (total volume)
• Equating
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Example 3 - Iceberg• The old iceberg problem
• Table 10-1
only 0.11 above water (and that’s just the tip of the iceberg!)
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Example 4 – Hydrometer
• Winemaker’s tool
• Effective density of hydrometer
OK to use g/cm3, since conversion will cancel
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Example 4 – Hydrometer
• Submerged volume ratio
Hydrometer should be 0.9 submerged in waterMark at 0.9 * 25 or 22.5 cm
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Example 5 – Balloon
• Buoyancy in a “pool” of air
• Step 1 – empty balloon volume of air
• Step 2 – fill balloon with heliumadd load weight
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Example 6 – Balloon (cont)
• Buoyancy in a “pool” of air
• Equating up and down forces
• Solving for V