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# CONCEPTUAL PHYSICS LAB PHYS 102N

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This 11 page Class Notes was uploaded by Emery Rippin on Monday September 28, 2015. The Class Notes belongs to PHYS 102N at Old Dominion University taught by Sebastian Kuhn in Fall. Since its upload, it has received 32 views. For similar materials see /class/215334/phys-102n-old-dominion-university in Physics 2 at Old Dominion University.

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Date Created: 09/28/15

PHY SICS 101 102 Conceptual Physics Exam Formula Sheet Units SI Length m 2 meter Time s 2 second Mass kg kilogram Velocity ms Acceleration ms2 Force N 2 Newton 2 kg ms2 Energy J Joule Nm 2 kg mzs2 Power W 2 Watt Js Charge C Coulomb Currents A Ampere Cs Electric Potential V 2 Volt JC Electric Resistance 9 2 Ohm 2 WA Magnetic Field T 2 Tesla Vsm2 210000 Gauss Pre xes kilo k 103 Mega M 106 centi C 10 2 milli m 10 3 micro 14 10 6 nano n 10 9 Amount mol 1 mol 2 NA molecules 2 A gram Where A is atomic mass Pressure Pa Pascal Nm2 z 1100000 atmospheres Temperature K 2 Kelvin C Celsius F Fahrenheit 32 F 2 0 C 2 273 K 212 F 100 C 2 373K Heat J or 1 calorie 42 J 1 food calorie 1000 calories 2 4200 J Useful Constants Speed of Light 0 2998108 ms Gravitational constant G 6671011 Nmzkg2 Avogadro s number N 60221023 moleculesmol Universal Gas Constant R 832 JmolK Gravitational acceleration at surface of Earth g 981 ms2 Distance from Earth 1501011 In Distance from Earth 384108 In Radius 638106 In Mass of Sun 1991030 kg Mass of Moon 735391022 kg Mass of Earth 597391024 kg Elementary Charge e 16021019 C Electron mass me 91091031 kg Proton mass mp 16731027 kg PHY SICS 101 102 Conceptual Physics Permittivity constant 0 88541012 Fm Permeability constant 140 4317107 Hm k electrostatic force constant 2 899109 NmzC2 Earth s magnetic field about 05 Gauss PHY SICS 101 102 Conceptual Physics Average velocity for time interval At t1t2 motion in 1 dimension change in position during the time At xt2 xt1 Ax elapsed time At t2 t1 At av Instantaneous velocity at time t Average velocity for a very short time interval around I Relative velocity addition 17x relative to B 17x relative to A 17A relative to B Acceleration for time interval At t1t2 a change in velocity during time At AV elapsed time interval At E Motion in 1 dimension with constant acceleration vxl va a260quot v1W 0 t1 12 va vxt1 xt 2x0 vxot 12 amt2 Forces some Examples Weight 13 Weight mg in vertical direction g 98 ms2 near Earth s surface Force exerted by spring F51 kx in the direction of the displacement Hooke s Law with k 2 spring constant x displacement from relaxed state of spring Normal force F Equal and opposite to net force perpendicular to a surface Static Friction fsm equal and opposite to net force parallel to a surface 391 st s14 IFtI Kinetic frictionfkm Force opposite to direction of motion lfkml 2 anl Tension T Force along direction of string at the end it is the same as the force exerted by the string on the attachment point PHY SICS 101 102 Conceptual Physics Newton39s First Law When all forces applied to an object balance out to zero cancel each other then this object will not accelerate in an inertial system If at rest it will stay at rest if in motion it will continue to move in the same direction with constant velocity gt 5 0 Newton39s Second Law a Fm acceleration equals force divided by mass More detailed Fresultant Fi m a all forces i1N Newton39s Third Law Forces always come in pairs interaction between two objects A and B 1Action on 1 on Reaction Note Forces add like vectors parallelogram rule Momentum f m 9 Change in momentum impulse j Af 2 13 At System of particle with no external force 2 f i f 1 f 2 conserved Momentum conservation in two particle collision m1V1im2V2i mlvlf m2V2f If collision is completely inelastic m1 m2v2i m1 m2vf Work and kinetic energy Work AW 2 FAX FAS cos only the displacement in the direction of the force counts Kinetic energy of a moving particle KE 2 m2 392 Work Energy theorem A KE 2 AW Power P AWAl F39v PHY SICS 101 102 Conceptual Physics Potential Energy Work done by conservative force stored in form of potential energy U AW fref gt At reference point U r ref 2 0 r M can be chosen for convenience Potential Energy Examples Stretched spring U61 2 k 2 x2 k 2 spring constant x 0 xref for relaxed state of spring Approximate Gravitational Potential near Earth surface Ugr1V mgh h is height above reference point Gravitational Potential Reference point 00 far away Ugr1V GmMr Conservation of total Energy Total mechanical energy E 2 KB U No external dissipative forces present E const AE 0 External forces doing work AE m2 Vf2 m2 Viz AU AWext Other forms of energy Electromagnetic Chemical sound light nuclear HEAT Internal energy least useful for doing work The total sum of ALL these forms of energy is always conserved Motion in a circle Position described by angle 6 radius R Period of revolution T rotational speed in rounds per second rps I T Angular velocity u 2339 T 2339 rps 2 WI R linear speed v Ra 231R rps Centripetal acceleration amtr 62 R 602 R gt centripetal force F m a Cm Moment of Inertia I Single Particle at distance R from axis I mR2 Extended Objects I 2 2p mP r13 increases with total mass and average distance rP from axis of that mass Cylindrical Shell radius R I MR2 Solid cylinder I MR22 Solid sphere I 25 MR2 Thin rod axis through center 112 ML2 Thin rod axis through edge 13 ML2 PHY SICS 101 102 Conceptual Physics Angular momentum L 2 la conserved if no external torque is present Torque at point r relative to axis 17 r F AL Al lever arm times force only the part of r perpendicular to F counts No external forces gt no torque gt L is conserved Requirement for equilibrium Sum of all forces AND sum of all torques must both be zero Center of gravity must be above support area Kinetic energy for rotational motion KE 2 12 la 2 Gravitation Gravitational Force of mass M on mass m at distance r F G mMr 2 r is distance from center of mass M to center of mass m Gravitational Force F points back to source of gravitation Tidal force difference across a distance D AF 2 2 GmM Dr 3 Gravitational Potential Energy between two masses at distance D center to center U W GmM D if reference point is at infinite separation Escape speed from planet with mass Mand radius R vesc VZGM R Projectile motion near Earth s surface neglect air resistance Horizontal and vertical motion are independent of each other Horizontal components vx const xl x0 vxl Vertical components vyl vyo gl yl 2 yo vyol 12 glz Total motion is simply combination of horizontal and vertical one Kepler s Laws 1 Orbits of satellites moons planets are elliptical 2 A line from the gravitating body sun planet to the satellite sweeps out equal areas in equal times Conservation of angular momen tum 3 The square of the period T of an orbit around a mass M is proportional to the cube of a T2 0 a3 a 2 major half axis of ellipse and T2 0 1M T 231a3GM 2 gt on a Circular orbit of radius R the velocity is vorbil VGM R PHY SICS 101 102 Conceptual Physics Charge Positive or negative measured in Coulomb C conserved quantized in units of 6 Force between charges COUlomb Force Fon q due to Q at distance r kg k 899109 NmzCz r Alternative Formulation Charge Q or any distribution of such Charges create an electric field E Charge q experiences a force F qE in this field Field lines begin at positive Charges and end at negative ones or go on for ever density of field lines indicates strength of field Conductors Contain huge amounts of free Charges In presence of electric field Charges will flow to counteract field Unless new Charges are constantly supplied current field will be canceled gt no field inside conductors All Charges sit on the outside External field will rearrange Charges such that conductor experiences net force towards external Charge even in absence of net Charge Insulators Contain no free Charges Can pick up a few extra Charges a little net Charge External field can polarize individual molecules such that material ex periences net force towards external Charge Polarization can weaken but never cancel external field Potential Moving Charge q along electric field E does work W F39d qE d Electrostatic forces are conservative gt work stored in electrostatic potential energy Upm Electrostatic potential energy Upot divided by Charge q equals potential V measured in Volt 2 V A Charge q changes its energy by q39AV when moving from a point with potential V1 to a point with potential V2 2 V1 AV 100 V means potential to do 100 J of work per Coulomb PHYSICS 101 102 Conceptual Physics Current Net flow of charge per unit time measured in Ampere A Cs Current in conductor with resistance R requires electric field gt potential dif ference AV RI Ohm s Law Resistance measured in Ohm Q proportional to length of conductor in versely proportional to cross section greater if conductor is hot Currents require return path and non electrostatic pump to keep running Currents heat up conductors power energy transfer per unit time is P Watt AV Volt X I Ampere Typical speed of electrons in wire 106 ms random due to heat but only 01 mms on average in direction of electric force Electric fields that tell the electrons to move travel with nearly speed of light Series Circuit Same current has to go through all elements doesn t matter which one comes first Voltage supplied by battery etc gets divided up among various elements Total resistance is sum of individual resistances The largest voltage drop occurs across the largest resistor Parallel Circuit Current that must be supplied by battery is the sum of the currents to all of the various branches Each branch sees the full battery voltage independent from the other branches Smallest resistor draws the largest current Magnetic elds Due to charges in motion electric currents spinning electrons Field lines can form closed loops but never end or begin Example Permanent dipole solenoid or short coil Field lines can be described as if emanating from North pole and converging towards South pole but connect through the interior of the dipole Earth has a magnetic dipole field with magnetic north pole close to geographic south pole Field of straight wire circles around it falls off like lr PHY SICS 101 102 Conceptual Physics Magnetic materials Most materials are non magnetic or react only slightly to magnetic fields Exceptions Iron Cobalt Nickel and some Rare Earth compounds Magnetic properties due to electron spins aligned within domains Normally random orientation of domains no net magnetism External field can orient domains strong magnetic response polarization leading to attraction towards other magnets For some alloys domains can keep orientation indefinitely permanent magnets Permanent dipoles can attract unlike poles or repel like poles net force on dipole is zero in homogeneous magnetic field but torque tends to align dipole with field direction Magnetic forces Acts only on moving Charges Proportional to q v and Bperp the part of B perpendicular to v Acts perpendicular to both v and B right hand rule Typical motion in homogeneous field Circle of radius R mVqB with an gular velocity 0 qBm neither speeding up nor slowing down no Change in kinetic energy gt magnetic forces don t do work on moving Charges Force on wire LB LzLength sideways perpendicular to field and wire Induction Wire moving in magnetic field gt magnetic force pushing a current along wire Magnet moving relative to a wire gt same force but cause is electric field induced by changing magnetic field Induced field E is proportional to area filled with magnetic field and how much the magnetic field changes per unit time Coil with several loops in changing magnetic field Induced voltage differ ence is proportional to number of loops Transformers Output voltageInput voltage 2 of secondary coil loops of primary coil loops Lenz law Effects of magnetic field Change oppose that Change PHY SICS 101 102 Conceptual Physics Second Semester PHYSIOZ Atomic structure of matter Size of typical atoms about 1 Angstrom 10 10 m Atomic Mass 2 Mass of Atom Mass of 12C atom 12 2 approximately ZN number of protons and neutrons in nucleus H 1 He 4 C 12 O 16 Molecular Mass 2 Sum of atomic masses of all atoms in the molecule H2 2 Oz 32 H20 18 1 mol of a compound 2 as many grams as molecular mass 1m0112C 12 g 1 mol 13C 13 g 1 mol of anything contains NA 60221023 molecules or atoms Deformation of solids Elongation or compression ALL 0 F tension inversely proportional to cross section and strength Young s modulus Hooke s law F kx Bending beam Outside layer elongated inside layer compressed Density p massVolume kgm3 39 Air z 125 kgm3 at sea level decreases continuously with height 50 at 56 km Water 1000 kgm3 ice a little less Iron 7874 kgm3 Iridium 22650 kgm3 Pressure P 2 force surface area Nm2 2 Pa Hydrostatic pressure A pgAh Air pressure at sea level 101000 Pa weight of 1 kg 10 N on 1 cm2 Buoyant force Equal to weight of displaced fluid upwards g39V0bjp uid Pascal s Principle Change pressure somewhere in liquid gets transmitted to all other parts modulo hydrostatic pressure difference Boyle s Law Pressure and density are proportional in ideal gases PV const for constant amount of gas and constant temperature Bernoulli s principle Pressure is lower in faster flowing fluid PHY SICS 101 102 Conceptual Physics Internal Energy All types of kinetic energy of particles making up an object that are random and undirected no overall motion of the object Heat internal energy transferred from one object to another through direct contact conduction flow convection or radiation Measured in J or calo ries 1 calorie warms 1 gram of water by 1 C Temperature Measure of proportional to average internal energy per particle per degree of freedom measured in Kelvin Celsius or Fahrenheit thermometer tends to even out between different objects or systems over time by transfer of heat from warmer to colder object Heat transfer Conduction Convection and Radiation Heat capacity C amount of energy needed to increase temperature of an object by l0 C Specific heat capacity c amount of energy needed to increase temperature of 1 kg of a substance by 10C Eg water has specific heat capacity C 4200 JkgOC 1 calg 0C Newton s Law of coolingheating Heat transfer rate proportional to tem perature difference Phase Change Change in internal energy Without Change in temperature solid gtliquid gtgas gtplasma gt Example Water gt Latent heat of melting 80 cal 335 J melts 1 g of ice at 0 C Latent heat of evaporating 540 cal 2255 J convert 1 g of water to vapor at 100 0 C Evaporation can occur at any temperature if vapor pressure at that temperature exceeds partial pressure of surrounding vapor else conden sation Boiling vapor pressure equals or exceeds air pressure Vapor pressure increases with temperature and is 1 atm 105 Pa at 100 C Triple point All 3 phases exist together 001 C 600 Pa

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