physics part 1 mechanics physics 1700 xi. solid phase and elasticity w. pezzaglia updated:...
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Physics Part 1MECHANICSPhysics 1700
XI. Solid Phase and Elasticity
W. Pezzaglia
Updated: 2013July24
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Solids & Elasticity
A. Density
B. Elasticity
C. Scaling
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A. Density
1. Definition, mass density
2. Other Definitions
3. Specific Gravity
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1. Density Definition• Mass Density: mass per volume
– SI unit: kg/m3
– Cgs unit: gm/cm3 = gm/mL
• Density of Water: 1 gm/cm3
– This was originally how the gram was defined as 1 mL (1 cm3) of water
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1b. Density of Water• Density of water depends upon temperature!
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Hence, originally the gram was defined as mass of 1 mL of water at 4C where the density is maximum. The gram has been redefined so now the density of water at 4C is 0.9999720 grams per mL.
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2. Other Definitions• Weight Density: Force per volume
– Pounds per cubic foot
• Molar Density: number of molecules per volume– Molarity (chemistry): moles per liter
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3. Specific Gravity
• Density divided by density of water
• Unitless!
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B. Elasticity
1. Hooke’s Law
2. Stress
3. Strain
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1. Hooke’s Law
This idea was first stated by Robert Hooke in 1675 as a Latin anagram "ceiiinossssttuu" whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force."
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kxF
Spring compressed by “x” will push back with force “F”
Spring constant “k” (units of N/m) describes the stiffness of the spring
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2. Stress
• Types of stress ->
• Units: Pascals (i.e. force/area)
• Breaking stress or “ultimate strength” is the maximum stress at which material fails
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2b. Ultimate Strengths
• Ultimate strengths in table are in MPa (million Pascals)
• Carbon nanotubes are very strong!
• Concrete is rather poor (must use steel reinforcement)
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Substance MPa
Nanotubes 30000
Spider Silk 1000
Steel 250
Granite 100-250
Bone 130
Concrete 3
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2c. Self Stress
• A tall enough column will crumble under its own weight
• For granite, this maximum height would be about 3750 meters for a cylindrical mountain.
• For pyramid shaped mountain the limit would be 3x bigger: 11,250 meters
• Mauna Kea is 10,200 meters tall
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ghP
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Biggest Mountain on Venus
Maxwell MontesGravity: 0.904 gMountain height 11 km
Consistent with our estimate!
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Biggest Mountain on Mars
Gravity 2.66x smaller, so increase maximum height by that factor to 29.9 kmOlympus Mons height 24 km consistent!
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153. Strain
Most substances deform linearly following Hooke’s law up to a point (i.e. will spring back to original shape). Past that point they irreversibly deform (plastic)
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C. Scaling
1. Read Book!
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Notes for this section done on board
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Notes
• “Scaling” was covered briefly
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