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Final

Conceptual Physics Final Exam Notes.docx

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Department
Physics
Course Code
Physics 1021
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Lara Braitstein

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Conceptual Physics - Final Exam Notes Elastic Materials Pg. 496 – 509 What is an elastic body? Responds with change of shape to external forces  Elasticity: tensile stress and stretching  The response to stretching is stress and strain  Stress: a force exerted per unit area of surface of the extended object, has unit of [Pa]  Strain: relative change of length or size of the object; three types: o Stretching is a change in the length of the object o Twisting is a change in an angle of the extended object o Compression or expansion is a change in the volume of an object  Each type of strain is caused by a different form of stress o Stretching is caused by tensile stress. o Twisting is caused by shearing stress. o Compression or expansion is caused by hydraulic stress. Elastic Deformation Stress will cause deformation of an object. If, after the stress is removed, the object returns to its original shape, the deformation was elastic. Stress and strain are proportional to each other in elastic formation. Linear Response (Hooke’s Law) If stress and strain are linearly proportional to each other, we can write: OR  Near mechanical equilibrium, a linear relation exists between the cause of the deformation (stress) and the response by the extended object (strain)  The linear relation between stress and strain is called Hooke’s law.  The proportionality factor Y is called Young’s modulus with a unit of [Pa]  Large Y means that a large force acting on a material leads only to a small length variation. Materials with a large Y are called strong (hard) materials. Examples are steel and your desk.  Small Y means that a large force acting on a material causes a large length variation. Materials with small Y are called soft materials. Blood vessels and skin are examples of soft materials.  When the response is linear, it is also elastic. Elastic vs. Plastic Deformations  A material is called elastic when it responds to external forces (stress) with a linear deformation (strain). Elastic deformations are reversible (the object resumes its original shape when the stress is removed).  A material is called plastic when it responds to a stress in a non-linear fashion. Plastic deformations are irreversible (the strain does not return to zero when the stress on the material is removed). Elastic Tissue of Blood Vessels  Blood vessels are non-elastic  Combined effect of collagen and elastin (structural protein) result in elasticity of blood vessels  Not included: contractile smooth muscles  Collagen keeps the blood vessel intact (it is due to collagen that the actual blood vessel walls do not show linear stress-strain behaviour, as indicated by the diagram)  Diagram: collagen – blue dashed; elastin – dot dash; solid line – combined effect The elastic force is also called a restoring force. Vibrations Pg.509 – 516 Elastic Potential Energy – kx = m(d²x/dt²)  Elastic potential energy is the energy that depends on the displacement of the object.  A system with a linear restoring force (Hooke’s law) has an elastic potential energy that is proportional to the square of the displacement from the equilibrium position of the system.   Elastic potential energy is not linear in the displacement of the object; elastic potential energy plots are not shown as straight lines are gravitational potential energy plots are, but as curves, where energy is conserved.  Thus, when the displacement from the equilibrium position doubles, the elastic energy increases by a factor of 4. The vibration of an object attached to a spring o For a small displacement Δx = x – xeqhe external force is linearly proportional to the displacement, Δ x from the equilibrium position. (Hooke’s law) o F = F is the force exerted on the object by the spring. The object is at equilibrium. restore elast o Diagram: Observations made from the spring model  The amplitude of the motion of an object attached to a spring is the maximum displacement of a vibrating object.  Simple harmonic motion (when an object oscillates about a point of mechanical equilibrium) and angular frequency Electric Force Pg. 404 – 413, 419 – 420 Properties of Water Large surface tension The water molecule consists of two hydrogen atoms and one oxygen atom connected by covalent bonds (H2O) and arranged at an angle of 104.5. The oxygen end of the molecule carries a partial negative charge and the hydrogen end a partial positive charge. Opposite charges separated by a fixed angle define a dipole.  Water molecules stick to one another as a result of hydrogen bonding; even though hydrogen bonds are weak they hold water strongly at a macroscopic level. This is known as cohesion.  Surface tension is the related measure of how much effort is needed to increase the surface area of a liquid. High specific heat capacity  The amount of energy required for the phase transition of a material from the liquid to the vapour state at its boiling point.  Hydrogen bonds have a large latent heat vaporization because they need to be broken during evaporation.  A large amount of energy is required when water evaporates from a surface.  This effects climate and the heat absorbed by evaporation in oceans. Ice floats on the surface of liquid water ρ ice > ρ liquid water  Water is less dense in solid form than in liquid form  Most materials contract when they solidify but water expands  Floating ice thermally insulates the water below Boiling and melting point Water has a high boiling and melting point Stabilizes salts and polar organic molecules in a solution  Effective solvent in chemistry  Water molecules form a hydration shell – large number of molecules that form a layer around a charged particle – that stabilizes the ions in the solution  The hydration shell is energetically favoured because of an electric interaction between the charged particle and the water molecule All of these features are due to the one microscopic feature of the water molecule – water is an electric dipole.  Opposite charges separated by a fixed angle define a dipole. Dipoles interact electrically with ions and other dipoles.  The positive end of one dipole and negative end of another attract each other in liquid water.  Water dipoles form hydrogen bridge bonds. Electric Charge and Force  Electric charge is an intrinsic property of the particles that comprise matter in the same fashion as mass is an intrinsic property of the same particles. Because particles carrying single charges are usually very small, the concept of point charge is introduced. A point charge is a charged particle with negligible (insignificant) size.  Mass and charge of a particle are independent from each other.  Only one type of mass exists but two types of charges exist: positive and negative.  Two charges of the same type repel each other and two opposite charges attract each other.  In a system with a large number of charges, the charges are uniformly distributed throughout a given volume and across a given surface. The Magnitude of Electric Force (Coulomb’s Law) We represent charge quantitatively as the force that occurs between separate point charges or the force that charges exert on each other. The magnitude of the electric force between two charged spheres is proportional to the absolute 2 amount of charge on each sphere and is proportional to 1/r where r is the distance between spheres. This is known as Coulomb’s Law:  F e 1 q1q 2 r0 4  0 r2  Coulomb’s law expresses the force a point charge q exerts on a point charge q 1 2  Fels proportional to the absolute values of the two interacting charges q a1d q 2  The force is reduced to ¼ when the distance r between spheres is doubled  The standard unit of charge is C (Coulomb)  The electric force is very strong and reaches very far  The difference between mass and charge is that charge is quantized (no limitations of the amount of mass there can exist; limitations exist for charge as there is a smallest possible charge, known as the elementary charge)  Parallel charged plates allow us to exert an electric force on a point charge that is located between them. The Direction of the Electric Force  Electric force is characterized by magnitude and direction  The direction of the electric force is determined by two factors: 1) The relative positions of the two point charges 2) The signs of the charges of the two interacting particles  Figure 13.5 demonstrates the direction of repulsion between two positive charges and the direction of attraction between opposite charges The Electric Dipole Moment  The product of charge and distance defines the electric dipole moment: µ = q · d  Electric dipole moments characterize the chemical and physical properties of molecules (i.e. water is distinct from other molecules because it’s very large electric dipole moment yields melting and boiling points that are unusually high for such a small molecules)  The electric dipole moment is one way to demonstrate quantitatively the direct relation between the electric properties of the water molecule and its applications as a key ingredient of life processes.  Physically, this relation is established by the direct relation of the electric dipole moment to the strength of hydrogen bonds. Hydrogen Bonds A hydrogen bond between water molecules forms when a hydrogen atom of one water molecule approaches the oxygen atom in another water molecule. The hydrogen bond is therefore a dipole-dipole interaction.  Every oxygen atom is symmetrically surrounded by four hydrogen atoms.  Hydrogen bonds require only 5% to 10% of the energy that is needed to break a covalent bond; however, this energy still exceeds the thermal energy available at sufficiently low temperatures.  The ability to form dipoles varies. In water, oxygen succeeds in drawing electrons from hydrogen to form a strong dipole. This is due to high electronegativity and ionic character. Electric Energy Pg. 422 – 429, 433 – 435 Electric Energy Energy concepts can be as useful in electricity as they were in mechanics. However, we do not measure electric forces directly. Instead, we measure an electric potential difference. The electric potential energy can be combined with kinetic and other forms of energy to determine the total or internal energy of a system. The Potential Energy for Charged Parallel Plates  The plate at the top is charged positively and the plate at the bottom is charged negatively. This leads to a downward-directed electric field.  We assume that a positive mobile point charge moves from close to the positive plate to a position close to the negative plate (i.e. from position y to y ). initial final  Moving a mobile point charge from one equilibrium position to another requires an external force Fextto prevent it from accelerating toward the negative plate. Thus, the external force is positive and the displacement is negative.  A negative work follows from anti-parallel external force and displacement; i.e., the mobile point charge releases work to the source of the external force.  We determine the electric potential energy to specify the magnitude of the electric field.  The electric energy of a mobile point charge in a parallel plate arrangement is a linear function of distance from the plate that carries a charge with opposite sign of the mobile charge.  If you remove the external force that holds the mobile point char
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