Particle movement in matter

What happens when a particle moves in another matter?

Approach:

Solids› Deformations› Stress› Strain› Elasticity

Fluids› Pressure

Matter

Anything that occupies space and has mass.› Volume› Mass› Density

Exhibits gravitational attraction Has inertia

States/Phases of Matter

Solid Liquid Gas Plasma

Supersolids Superfluids

Some properties of solids

Elasticity Malleability Ductility Plasticity Strength Hardness Flexibility

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?

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.

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

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.

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

Illustration for Hooke’s Law

Greater deformation requires greater force.

The ratio of these too defines the elasticity of the material

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.

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

Shear Modulus of Elasticity Also called elasticity of shape or

modulus of rigidity High value of S means high rigidity

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.

Typical Values for Elastic Moduli

Substance Young’s Modulus(GPa)

Shear Modulus(GPa)

Bulk Modulus (GPa)

Aluminum 70.0 25.0 70.0

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

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?

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?

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?

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.

Seatwork

A solid sphere of volume 0.500 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?

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

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.