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**Particle movement in matter**

What happens when a particle moves in another matter?

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Approach: Solids Deformations Stress Strain Elasticity Fluids Pressure

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**Matter Anything that occupies space and has mass.**

Volume Mass Density Exhibits gravitational attraction Has inertia

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**States/Phases of Matter**

Solid Liquid Gas Plasma Supersolids Superfluids

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**Some properties of solids**

Elasticity Malleability Ductility Plasticity Strength Hardness Flexibility

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**Elasticity vs. Plasticity**

Elastic and plastic materials are both deformed when subjected to force Difference: Elastic: material returns to its original dimension when force is removed Plastic: deformation is permanent Elastic materials may exhibit plasticity. When and how?

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**Malleability vs. Ductility**

Both are determined by the crystal lattice of the metal, and the strength of the bond between molecules of the metal Copper is malleable and ductile. Aluminum is malleable but not as ductile as copper.

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Hardness vs. Strength In the general use, they are the same; the ability o a material to resist deformation Concrete is hard but it may not be as strong as metal. Hardness … deformation due to compression Strength … deformation due to tension

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**Hooke’s Law Also known as Law of Elasticity Robert Hooke**

For relatively small deformations, the magnitude of deformation is directly proportional to the deforming force.

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**Limitations Conditions that fall under Hooke’s Law**

Relatively small deformation Deformation is within the elastic limit The material returns to its original dimension when the force is removed

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**Illustration for Hooke’s Law**

Greater deformation requires greater force. The ratio of these too defines the elasticity of the material

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**Deformation Quantified**

Deformation will now be called strain in our analysis, and the deforming force will be represented as stress. Note: However do not think that stress is a force.

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**Young’s Modulus of Elasticity**

Also called ELASTICITY OF LENGTH Describes the stiffness of materials; resistance to compression and tension in one axis High value of Y means high resistance

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**Shear Modulus of Elasticity**

Also called elasticity of shape or modulus of rigidity High value of S means high rigidity

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**Bulk Modulus of Elasticity**

Also called elasticity of volume Its reciprocal is called compressibility Higher value of K means the material is harder to compress.

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**Typical Values for Elastic Moduli**

Substance Young’s Modulus (GPa) Shear Modulus Bulk Modulus Aluminum 70.0 25.0 Bone 18.0 80.0 - Brass 91.0 35.0 61.0 Copper 110 42.0 140 Steel 200 84.0 160 Quartz 56.0 26.0 27.0

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Exercises A wire 2.50 m long has a cross – sectional area of 2.00x10-3 cm2. When stretched by a force of 80.0 N it elongates by 5.00x10-2 cm. Determine the tensile stress the tensile strain the Young’s Modulus of this kind of wire. If this material has twice the cross-sectional area with the same length, what must be the magnitude of deformation when subjected to the same force?

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Exercises A certain metal can withstand a maximum shear stress of 8.65 GPa. What magnitude of force is required to puncture a hole of 3.00 cm radius on a metal bar that is 4.00 cm thick?

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Exercises How much is the decrease in the volume of 5.00 cubic centimeter of aluminum when submerged in the sea at a depth where the pressure is 2.35 MPa?

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Seatwork A vertical steel beam in a building supports a load of 6.00x104 N. If the length of the beam is 4.00 m and its cross-sectional area is 8.00x10-3 m2, find the distance it is compressed along its length.

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Seatwork A solid sphere of volume m3 is dropped in the ocean to a depth of about 2,000 m where the pressure increases by 2.00x107 Pa. Lead has a bulk modulus of 7.70 GPa. What is the change in the volume of the sphere?

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Seatwork What magnitude of force is required to puncture a square hole, 3.00 cm on each side, on a steel bar of 5.00 cm thickness? The maximum stress that steel can withstand is approximately 85.0 GPa

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**Assignment Prepare for seatwork on Elastic Moduli**

Answer the following questions in your LNB. What is the atmospheric pressure at sea level (standard atmospheric pressure)? Differentiate gauge pressure and absolute pressure. State Pascal’s Principle on hydrostatic pressure. Illustrate and explain Pascal’s Principle using Pascal’s vases and hydraulic press.

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ENGR 225 Section 3.1 - 3.8.

ENGR 225 Section 3.1 - 3.8.

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