# Chapter 2 - Motion Part I - KINEMATICS physics how objects move why objects move how objects interact (environment) KINEMATICS - how objects move (not.

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<ul><li><p>Chapter 2 - MotionPart I - KINEMATICSphysicshow objects movewhy objects movehow objects interact (environment)</p><p> KINEMATICS - how objects move (not why)Description of motion - change in positioncarssports: baseball, football, soccer, etc.world: rotates and revolvesHow to measure position?</p><p>PHYSICAL QUANTITIESdescribe the physical universetwo types of physical quantities:SCALARS - described by a magnitude or quantity how much, how far just describe amountmass, time, volume, length, temperature, density, speed</p></li><li><p>Vectors: magnitude and direction! quantities for which direction is important i.e., where? (displacement - distance and direction)</p><p>velocity, acceleration, force, momentum, magnetic &electric fielddisplacement - like directions on map</p><p> Difference between scalars and vectors20 feet1 step = 2 ftDistance=displacement =</p></li><li><p>How to describe vectors - distance and directionVector variables - A A A A A~~Geometric description - represent with a directed linescale factor - magnitude length - rulerdirection - points along arrow - protractorScale 1 inch = 1miletailheadmagnitude =direction =VECTOR ALGEBRA - adding vectors+=head-to-tail method: head of first to tail of second</p><p> result: from beginning to endmagnitude :direction :displacement from adding displacements</p></li><li><p>Resolution of Vectors - component descriptionBreak vectors into componentsup/down - left/rightscale built incomponents give directionxy=+x-component and y-component specifies vectoreasy component directions (perpendicular)like treasure mapminmilesLooks like two perpendicular rulersVector - TWO SCALAR COMPONENTSCan treat each direction separately as a vector</p></li><li><p>Rectilinear KinematicsMOTION - changes in positionhow objects move without regard to whyone-dimensional motionKinematic physical quantities-how you moveposition, how fast, speed upSCIENTIFIC MODELstraight line - start and endpoint particle- all mass and volume a pointstartendto=0do=0tdtime (t) : use to keep track of the object at a particular instant - synchronize stop watchestime interval or an instant in timestart at t=0 toPosition (d) : rectilinear - displacement, distancewhere the object isstart-position at t=0 do</p><p>stop watch at end time t, position d </p></li><li><p>Speed and VelocitySPEED (scalar) rate of change in positionhow far in a given time how fastAVERAGE SPEED OVER A TIME INTERVAL</p><p>vAVG == d / t</p><p>can speed up or slow down during tripfaster cover more distance in a given time what constant speed to cover a distance in a given timedistancetimeINSTANTANEOUS SPEED AT A PARTICULAR TIMElike looking at speedometer at an instant vmeasure: average speed in a short intervalSpeed of sound uniform motion (constant speed)v = vAVG = 1100 ft/sdHear thunder t=5sSee lightning to=0sLight faster than soundHow far away is the lightning strike?</p></li><li><p>Velocity how fast and what directionVECTOR!Magnitude speedDirection - which way its goingRectilinear speed is magnitude of velocitydirection left/right or up/downxy++--Direction using normal coordinate directionsAVERAGE VELOCITY time interval again</p><p>vavg = = d / tINSTANTANEOUS VELOCITYdisplacementtime20 feetat each instant during the interval -- short piece of time intervalSpeed and velocityt = 10 min.Not same for 2D</p></li><li><p>CHANGES IN VELOCITYspeeding upslowing downchanging direction}acceleration rate of change in velocitycan feel force (cars, elevators,..)VECTOR</p><p>rectilinear change in speed</p><p>Average and instantaneous UNIFORM (CONSTANT) ACCELERATION</p><p>a= = (v-vo)vo =v =Final instantaneous velocityinitial instantaneous velocitychange in speedtimetaTwo types of problems:Uniform motionUniform acceleration</p></li><li><p>Tools for 1D Uniform Acceleration - formulaeDEFINITIONS : vavg = d / ta = (v-vo)/ t</p><p>DERIVATIONS : not magic use math to rearrange definitionsUNIFORM ACCELERATION FORMULAd=vot + at2v=vo + atvavg= (v+vo)/2vavg=d / tcan find out how objects move Only works for constant acceleration.Fill out line diagram and apply formulaHow to pick right formula-pick two with variable of interest (v, t, a, d)-find variable you dont care aboutIdentifies when acceleration begins</p></li><li><p>1D uniform acceleration - examplesAn airplane starts from rest and reaches the final take-off velocity in 50 s. What is its acceleration?</p><p>2. Space shuttle rocket accelerates 2 m/s2. a) What is the velocity 90 s after lift-off?</p><p>b) How far did it go? Finish description</p><p>3. A car travels 75 ft/s east and slams on brakes. a) If it stops in a distance of 200 ft, then how long did it take to stop?</p><p>b) What is the acceleration?</p><p>4. Car accelerates on I-10 uniformly along ramp. The speed is 30 ft/s at one instant and 5 s later it is going 110 ft/s. What is the acceleration of the car?</p></li><li><p>2D Motion (planar) - projectilesUnnatural motion to Aristotlefour elementsnatural state rest (he said so)medium adds resistance to speedslow / fast depends on object</p><p> unnatural medium pushes objectDEMO weight vs. crumpled paperARISTOTLE RIGHT?Galileo scientific methodmeasure the motion - kinematicscompare quantitatively</p><p>inclined planeall objects fall the samerate: ay = - g = -10 m/s2 (ay = - g g = 10 m/s2)natural state constant velocity</p><p> everything we need to treat complex 2D motion projectile motion :objects projectedsupported by Church 2000 yrs</p></li><li><p>Planar Motion</p><p>two dimensional motionin the plane of paper x and y graph describe vector position - vector velocityEXAMPLESUniform Circular Motion: ball on a stringMoves at a constant speed in circle</p><p> At time t : position given by x and yProjectile Motion: cannonball, arrowvoProjectile: - projected (thrown) with initial velocity - falls in earths gravity</p></li><li><p>VERTICAL DIRECTIONGalileo: ALL objects fall the same ay= -g g =10 m/s2 approx.</p><p>HORIZONTAL DIRECTIONNo acceleration if no force (friction)ax=0 (ignore air resistance)Projectile motion thrown in the earths gravityseparate into component directions (x,y)work with each component separately!ay= - g =-10 m/s2ax=0</p></li><li><p>Two Cases We Will Deal With:Vertical Projectile - Jump ball FREE FALL - freely falling in gravitythrown straight up-fall straight down</p><p> rectilinear - y directionaya) time to highest point?b) how high?EXAMPLES A baseball is thrown straight up with a speed of 35 m/s. a)How long does it take to reach the highest point? b) How high does the ball go?</p><p> An egg is thrown straight downward with aspeed of 12 m/s. What is its speed 3 seconds later? </p></li><li><p>Horizontal projectile - cannonball, soccer, gunProjected with a horizontal velocity -no initial velocity in vertical (y) direction -must work in two directions - separate ! -time connects the directionsSeparate componentsvertical free fallhorizontal uniform motiontwo rectilinear problems12 mvo=40 m/srangea) How much time to hit ground? what direction?</p></li><li><p>B) What is the range of the projectile? direction?</p><p>time connects position for fall in both directions: how far does it go in x-direction in the time it takes to fall?NOTE: time of fall has nothing to do with x-direction! falls same independent of horizontal speed!!!!</p></li><li><p>Motion - Part 2: Dynamics (MECHANICS)-Why objects move!not unnatural motion* force not required to keep object going* well-defined laws of motionSir Isaac Newton - 1st theoretical physicist Great mathematician bubonic plague sent him home to orchard developed theories in 18 months-algebra, calculus, motion, gravitation fluid motion, optics (Principia, 1687) looked at results of others---Galileo, Keppleron the shoulders of great menNewtons Laws explain events in everyday life!Newtons First Law of MotionA body in uniform motion will remain in uniform motion unless acted on by an external forcenew natural state - uniform motionchange motion with force - acceleration</p></li><li><p>inertia - tendency of an object to remain in uniform motion LAW OF INERTIADecelleration turning a curve PROJECTILE MOTIONso objects travel in a straight line at a constant speed unless force (push or pull) acts natural stateGalileo knew but Newton publishedNewtons Second Law of Motion (Force Law)The acceleration of a body is proportional to theforce and inversely proportional to the mass a=F/m m proportionality constant (inertial) mass (kg) resistance to a change in uniform motion-or force-ability to remain in uniform motion</p><p> big mass small accelerationsmall mass accelerates easilytrain vs. bicycle</p></li><li><p>Example:How much force is required to accelerate a 1 kg block at 1 m/s2?F=?a=1 m/s2m=1 kgF= ma = (1 kg)(1 m/s2) = 1 kg m/s2SI force: kg m/s2 = 1 Newton = 1 N</p><p>MODELF=ma not whole truthF=ma vector equation direction 2N left gives 2 m/s2 leftAlso talk about net force add all forces on objectFnet=Fpush + (-Ffriction)friction opposes motion</p></li><li><p>Second Law Examples:m=1000 kg1.F=?a=1 m/s2m=1000 kg2. two peopleF1=500 Na=?F2=800 NFnet =m=1000 kg3.a=?F1=500 NF2= 800 NDirection be careful!!!</p></li><li><p>Weight and massMass intrinsic property of matter- doesnt change-always resistance to forceWeight force of gravity on an object- depends on location-difficulty in lifting an object-weightless in space, but F=ma stillno effort to lift!weight force of gravity W= F = ma = mg on Earth surface g=10 m/s2 acc. due to gravity Surface gravity : depends on gsurfaceMoon gmoon=1/6 gearth =1.66 m/s2M=100 kgWearth= 1000 NWmoon= 166 NWspace= 0g=0 weightlessF=ma still</p></li><li><p>Newtons laws good for more than 200 yearsNO DISCREPANCIESTribute to Newton 20th century-new observationsmeasurement techniques improvedfailures in F=maJet planes, rockets very very fast scaleEinsteins Theory of Special Relativity</p><p>E-Microscope, scattering very very small scaleQuantum Mechanical Theory (Bohr, Scrodinger)</p><p>Telescopy (BH, Neutron stars) very very massive scaleEinsteins Theory of General RelativityALL theories reduce to F=ma in the scale of everyday experience:- use Newtons 2nd law for our purposes- F=ma valid for cars, buildings, etc.less complicated math!!!!- use other theories when needed.</p></li><li><p>Forces of Nature: accelerate objectsGravitational force between massessuns, planets, peopleElectromagnetic force between chargesopposites attract-likes repelcontact forceStrong Nuclear nucleus of an atomkeeps atom together likes repelWeak Nuclear nuclear decay gamma rays, beta-decay, nuclear reactionsUNIFYING THEORY binds all forces together at times beginning-all forces have same form HOLY GRAIL</p></li><li><p>Newtons Third Law of Motion (Action-Reaction)If one body exerts a force on a second, then the second exerts a force back on the first which is equal in magnitude and opposite in directionEasy statement:How objects push on one another- Forces exerted in pairs-Always exerts force back-Large mass, small acceleration</p><p>pendulum toyleaning on wallwalkingFhandFwall</p></li><li><p>Application of Newtons Laws: Circular MotionUniform Circular motion object traveling in a circle of constant radius at uniform speedR Like planet motionOr a ball on a string1st law inertial movementconstant speed in straight line - velocity2nd law forced falls in toward center direction change - accelerationCentripetal (center-seeking) acceleration - FORCEacceleration required to keep object on circletoo fast, spirals in too slow, spirals outac=v2 / Rdepends on particular circle and speedVelocity tangentAcceleration - radial</p></li><li><p>Another Application: MOMENTUMmomentum difficulty in stopping an objectp = mv linear momentummass and velocityvector direction!BASEBALLm=0.2 kgv=40 m/sp=mv=(0.2 kg)(40 m/s) = 8 kg m/s SI unitskg m/s is almost NTRAINm=100,000 kg v=1 m/sp=mv=(100,000 kg)(1 m/s) = 100,000 kg m/sHeavy or moving fast harder to stop!no motionno momentumYou can change the motion by changing momentumaccelerate-fell the force from momentum changes fastball hurts more than slider</p></li><li><p>DERIVATION: ImpulseSecond lawdefinition:accelerationFext=maa= (v-vo)/ t F=ma=m{(v-vo)/ t}I = Ftc = mv-mvo Impulse-change in momentum tc contact time -during which force applied external force accelerates as long as force appliedIMPULSE-MOMENTUM THEOREMConsequences: sports tennis golf baseballHit ball as hard as possibleandFollow-through (increase tc)}safety (cars) -- metal dash padded dash airbagsSAME IMPULSE-increase tc}Io=Ftc</p></li><li><p>IMPULSE force applied for a timeexternal force produces accelerationaccelerates for time tcaImpulse momentum theorem includes accelerationI= F tc = mv-mvoEXAMPLE:A baseball is initially pitched toward the batter at 40 m/s, and the batter hits it straight back to the pitcher at 30 m/s. What impulse is imparted to the ball?What is the force on the bat?</p><p>The bat applies the external force which changes the motion of the ballexternal connected to body connected to ground - etc</p></li><li><p>Conservation of Momentum - COLLISIONSMomentum important in collisionsCOLLISION MODELm1m2v1v2m1m2m1m2v1v2IsolatedSystemNo external forcesF12F21internal forces3rd lawaction-reaction pairindividual impulses cancel equal & oppositeDURINGBEFOREAFTERMomentum exchanged : I is change in momentumI12=-I21 one gains, other loses momentumaccelerated</p></li><li><p>Conservation laws conserved same before as afterconstant if assumptions trueConservation of momentumptot=m1v1+m2v2 if no external forcesINTERACTING OBJECTSFor collisions, conserved before and after collisionptot= (m1v1+m2v2)before</p><p>=(m1v1+m2v2)after</p><p>ISOLATED FROM OUTSIDE FORCESNo momentum losttransferredEXAMPLE:Internal forces transfer momentumperfectly inelastic stick together after colliding</p></li><li><p>Newtons Law of Universal GravitationNewton described how a gravitational force would actMOTIVATION:ASTRONOMY circular motionEarthinertial- - linearMOONcentripetalFalls toward center of earthWhat caused moon to fall?APPLES and the MOON fall due to same force -- gravityLAW OF UNIVERSAL GRAVITATIONAll objects with mass attract all other objects with mass-attractive force-smallest force in nature-universal (all objects the same) falling apples-orbiting planets-satellites Moon falls like appleEXPLAINED Heliocentric Model!</p></li><li><p>Gravitation Model picture to understandm1m2dpoint mass-centersF=G m1m2 / d2m1, m2masses (kg)dseparation (m)Guniversal constantsame for everythingGmust be measuredNewton couldnt do that, but he could: 1. explain motions of planets around Sun(satellites, comets) 2. explain the tides from moon 3. explain why g changes w/ altitude(distance from center of earth) 4. orbital perturbations deviations from predicted path</p></li><li><p>Cavendish experimentEstablished the universal gravitation constant GG = 6.67 x 10-11 N m2/kg2Can do things like:- calculate forces between ordinary objects- weigh the earth- predict new planets (perturbations)- put man-made satellites into orbitcentripetal force equals gravity force</p><p> TV, mapping, weather, spygeosynchronous same period as earth</p></li></ul>

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