PHY 101 1nd Edition Lecture 24 Outline of Last Lecture I 8 5 Torque and Angular Acceleration a Moment of Inertia II 8 6 Rotational Kinetic Energy III 8 7 Angular Momentum Outline of Current Lecture IV 9 1 States of Matter a Solids b Liquids c Gases d Plasma e Strange Universe V 9 2 Elastic Moduli of Solids a Elastic Properties Stress Strain Elastic Modulus b Young s Modulus c Shear Modulus d Bulk Modulus Current Lecture Chapter 9 Solids Fluids 9 1 States of Matter Matter a collection of interacting particles atoms Molecules charged particles etc Fundamental states of matter o Solid o Liquid o Gas o Plasma Solids o Have a definite volume shape o Useful models for solids spring ball o Solids exist in 2 distinct forms Crystalline solid ex Diamond These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Amorphous solid ex A silicon o Crystalline solids atoms have a ordered structure Ex Quartz salt diamonds o Amorphous solids atoms are arranged almost randomly Ex Glass Liquids o Has definite volume not shape Takes the shape of its container o For the same material Liquids exist at a higher temp Ex Water vs ice o The molecules wander through the liquid in a random fashion o The intermolecular forces are not strong enough to keep the molecules in a fixed position Gases o No definite volume or shape Can be easily compressed o Ex Air H2 and He gas o Molecules in constant random motion o The molecules exert only weak forces on each other collide occasionally o Average distance between molecules is very large compared to the size of the molecules Plasma o Most abundant form of matter in the universe stars o When gas is heated to a very high temp Many of the electrons are freed from the nucleus Resulted in a collection of electrically charged ions electrons o A star is a massive luminous sphere of plasma held together by its own gravity Strange Universe o All of the aforementioned forms of matter are referred to as normal matter o Normal matter About 5 of universal content o Dark matter About 25 of total matter Cannot be seen optically o Dark energy Responsible for acceleration of the expansion of the universe may be as much as 70 of all matter o Unfortunately we still don t know precisely what dark matter dark energy are 9 2 Elastic Moduli of Solids All solids are deformable Both size and shape can be changed by applying force If the applied force is small or when the forces are removed the object tends to retain its original shape o Elastic behavior A solid may undergo a plastic deformation if the external stress is beyond certain critical value o Objects cannot restore their original shape if they are deformed plastically Elastic Properties Stress Strain Elastic Modulus Suppose some forces are applied to two cylindrical wires Will the amount of deformation be the same o Force alone is not a good measure Stress force per unit area o F A o SI Unit Pascal Pa 1Pa 1 N m2 With an applied stress F A objects ex Rods made of the same materials will have identical strain L L o F A L L o The elastic modulus is the constant of proportionality between stress and strain Stress elastic modulus x strain o Strain fractional deformation dimensionless The elastic modulus measure the stiffness of the material A material with a large elastic modulus is hard difficult to deform There are 3 kinds of deformations o Tensile o Shear o Bulk Correspondingly we have o Tensile modulus Young s modulus Y o Shear modulus s o Bulk modulus B depends on the material NOT on the shape or size Young s Tensile Modulus Elasticity in Length Consider a long bar of length Lo clamped at one end A force F is applied at the other end the bar will deform elongate How large is the deformation elongation L o F A L L F A Y L Lo F A is called the tensile stress L L is the tensile strain Y young s modulus SI Unit Pascal Pa Young s modulus applies to a stress of either tension or compression A solid deforms elastically only within certain maximum stress elastic limit Beyond the elastic limit o it will not return to its original length o it will eventually break when the stress is beyond the breaking point Shear Modulus Elasticity of Shape one force is parallel to one of the object s face the opposite face is fixed shear stress F A shear strain x h ratio of the horizontal displacement and the height of the object o F A x h F A S x h o x relative shift between the top bottom surfaces o S shear modulus Unit Pascale Pa o No volume change for this type of deformation o In shear stress the force is parallel to the cross sectional area o In tensile stress the force is perpendicular to the cross sectional area Bulk Modulus Volume Elasticity Bulk modulus characterizes the response of an object to uniform isotropic squeezing Forces are perpendicular to and act on all surfaces The object undergoes a change in volume without a change in shape o F A v v F A B v v Volume stress F A P also known as pressure v v is volume strain B bulk modulus Unit Pascale Pa A material with a large bulk modulus is difficult to compress The compressibility k is the reciprocal of the bulk modulus o K 1 B Solid s have Young s Bulk and Shear moduli Liquids have only Bulk moduli they DO NOT undergo a shearing or tensile stress