Physics Part 1MECHANICSPhysics 1700

XI. Solid Phase and Elasticity

W. Pezzaglia

Updated: 2013July24

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.

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

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

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

Biggest Mountain on Venus

Maxwell MontesGravity: 0.904 gMountain height 11 km

Consistent with our estimate!

Biggest Mountain on Mars

Gravity 2.66x smaller, so increase maximum height by that factor to 29.9 kmOlympus Mons height 24 km consistent!

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)

C. Scaling

1. Read Book!

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Notes for this section done on board

Notes

• “Scaling” was covered briefly

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