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# Conceptual Physics PHYS 101N

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This 48 page Class Notes was uploaded by Emery Rippin on Monday September 28, 2015. The Class Notes belongs to PHYS 101N at Old Dominion University taught by Sebastian Kuhn in Fall. Since its upload, it has received 26 views. For similar materials see /class/215333/phys-101n-old-dominion-university in Physics 2 at Old Dominion University.

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Date Created: 09/28/15

Reminder Acceleration a change in velocity during time At g elapsed time interval At At Can be speci ed by giving magnitude a IAVI Al and sign Positive velocity increasing speed gt positive acceleration a gt 0 Positive velocity decreasing speed slowing down gt negative acceleration deceleration a lt 0 Negative velocity increasing speed gt negative acceleration a lt 0 Negative velocity slowing down gt positive acceleration a gt 0 NOTE Acceleration in an inertial system must have a cause Force See later Examples for accelerated motion Constantly accelerating car Police catching up with speeder Car going around a corner Objects falling down Objects thrown upwards Objects gliding down ramps Objects pulled by a falling weight Motion With constant Acceleration at adv a0 at0 const aav W VoI 0 V0 VI0 gt vtv0at If initial velocity v0 0 vt a t In that case Average velocity during the time interval I 0t is given by vav 0 t 12 0vt 212 0 at12at Constant Acceleration Cont39d 0 Plugging it into expression for position 1261 t vav xt xOt 0 gt xt x0 12at2 0 Typical graph x t 2 0 General case xt 960 vot12at2 t s Police catching up With Speeder Police Catching up with Speeder Velocity Plot 0 Police aP 20 msz W23 VP 5407 f 2 Speeder quotm1 as 0 Police Catching up wichlftpeeder Displacement VS 1 30 mS const 33 x5 I Vs t 122 1000 67 mileshour 37 2007 W 0 0 5 10 15 20 25 30 35 40 Free Fall 0 a g 981ms2 vt gt 0 xtxO 12gt2 0 Example 1 Fall from the Pont du Gard 45 m above water gt t v nal 0 Example 2 Throwing a ball upwards from the top of a building yt m in the absence of air resistance see demo Cart demos 0 Cart rolling down an inclined track 0 Cart being pulled by a falling weight Scalars and vectors 0 Scalars are observables Which can be expressed With a simple number and appropriate units Examples Time mass temperature 0 Vectors are observables Which have both a magnitude a number With units and a direction Examples Displacement velocity force acceleration 0 It is very important to distinguish these two entities use different notation A for scalar A or K for vector and clearly indicate size and direction for a vector result Example Displacement Size actual distance from Point A to Point B don t forget units Direction Describe Which way to go Note Vectors Which have different sizes different units or different directions are different BUT starting point does not matter Specifying a vector 1 By giving its length size magnitude absolute value with units and its direction Examples 1100 rn exactly northeast from here or 017 rn at an angle of 450 above the X aXis in the X y plane 2 You can represent vectors by drawing arrows The length of the arrow represents the size of the vector eg 2 cm represent 2 N and the direction of the arrow is in the direction of the vector Vectors can be added to or subtracted from each other 1 Geometrically See examples Use either tail to head method or parallelogram method 2 Mathematically a bit too advanced for our purpose Example Equilibrium car at rest 0 Equilibrium All forces acting on an object add up to zero vectorially 0 The object Will either be stay at rest or Will move With constant velocity 0 Example Car sitting still on an inclined plane or moving down With constant velocity Friction F y Example Car accelerating down ramp 0 Net force All forces acting on an object add up to a net force along the ramp vectorially 0 The object Will accelerate down the ramp Potential Energy 0 So far Considered all forces equal calculate work done by net force only gt Change in kinetic energy Analogy Pure Cash Economy 0 But Some forces seem to be able to store the work for you when they do negative work and give back the same amount when they do positive work Analogy Bank Account You pay money in ending up with less cash the money is stored for you you can withdraw it again get cash back 0 These forces are called conservative they conserve your workmoney for you Potential Energy Example Car moving up rarnp Weight does negative work AWgrav mgAh Depends only on initial and nal position Can be retrieved as positive work on the way back down Two ways to describe it 1 No net work done on car on way up F Pull 4 2 Pulling force does positive work that is stored as gravitational potential energy AU 2 AWgrav X 1 2 Total Mechanical Energy Dimension Same as Work Unit Nm J Joule Symbol E KE U Specify all external forces acting on a system Multiply displacement in the direction of the net external force With that force AWext F As cosq 3 Set equal to change in total energy AE mvaz In2vi2 AU AWext AU vVint We consider all non conservative forces as external plus all forces that we don t want to include in the system Example Gravitational Potential Energy 0 1 Motion in vertical y direction only AU ngv mgAy 0 External force Lift mass m from height yi to height y f Without increasing velocity gt Work gets stored as gravitational potential energy AU 2 mg yf yi mg Ay 0 Free fall no external force Total energy conserved change in kinetic energy compensated by change in potential energy AKE In2 v2 mg Ay 0 Example Throw baseball up With 20 ms accelerate over 05m Maximum height Force needed Here the system consists of Earth plus object Gravitational Potential Energy 11 Important point Potential energy has no absolute zero like kinetic energy does in a given reference frame Depends on choice of reference point You decide Where you want U to be 0 Call that point it 0 De ne potential energy as U mgh gt Total energy E In2 v2 mgh Choice arbitrary other choice means constant offset in de nition of U and E No observable depends on that choice All that counts are differences AU BUT you must specify reference point When quoting E and U l Work on a pendulum an Example Slowly pushing a pendulum bob sideways 1 2 3 Tension does no work perpendicular to motion Pushing force does work equal to potential energy stored by gravitational force After letting go gravitational potential energy gets converted to kinetic energy at the bottom Pendulum cont d On the way up Net work done by external force pushing increases total energy K E U stored in the system grav On the way down No other non grav force gt Total Energy conserved AE 0 AE AKE AU 2 0 gt AKE 2 12122 2 AU 2 mgAh Important points Minus sign negative work done by conservative force increases the potential energy due to that force putting cash into account Potential energy is stored in system pendulum and gravitation wallet and bank account Total energy changes through work done by forces external to system push cash in ux System must be leakproof conserve work return to initial condition gt same potential energy conservative forces Elastic Potential Energy So far Considered system object gravitational eld Potential energy gravitational internal work inside system Now Consider system gt mass attached to spring Potential energy internal work done by spring Call X 0 unstretched position of spring Force exerted by spring F X 40c Work done by spring AW k 2 fo xiz Potential energy stored in spring cart system U AW k2 fo x02 where x0 is the point where we declare U to be U 0 x0 0 gt U k 2 x2 convenient not unique Note U gt 0 stretched and compressed Elastic Potential Energy cont d No other non elastic force gt Total Energy conserved AE 0 AE AKE AU 2 0 gt Am2 v2 2 AU Example Oscillation Non elastic force present gt AE AKE AU 2 AW gt Am2 v2 2 AU AW Elastic and gravitational force present gt E KE Uel Ugravz 12122 k2 x2 mgh several bank accounts Note Elastic forces are conservative because work done only depends on initial and nal position Total Mechanical Energy Final Version 1 Specify all forces acting on an object 2 Separate out all conservative forces Work done depends only on initial and nal position Incorporate them into the system of the object as potential energy U 3 Add all external forces acting on the system all other forces call the result net external force 4 Multiply displacement in the direction of the net force With that force AWext F 39 As F As cosq 5 Set equal to change in total energy 6 AU 2 AWint A 1sz 2 AU Awext Examples Pumpkin falling on spring loaded platform Without and With air resistance bungee jump Other types of Energy 1 Electromagnetic energy see later in the semester Examples Charged capacitors electrostatic energy current carrying coils magnetic energy 2 Chemical energy really a special kind of electromagnetic energy Examples Batteries fuel 3 Sound light nuclear 4 Internal energy heat pressure see next semester PHYS 102 back to Forces Push or pull on an object mass point due to its interaction with something else Cause of changes in motional state acceleration Has both a magnitude strength how hard do we pushpull and a direction which way do we pushpull gt Force is a vector Newton s First Law IF the net force 2 F1 acting on an object is zero its velocity Will not change If it is at rest it Will remain at rest If it is moving With velocity v it Will continue to move With constant velocity v gt IF the velocity changes there must be a force acting Examples Car on Freeway Puck on Ice Spaceship Remember Always add up all forces to get net force You don t need any net force to keep on moving that s the default behavior Newton s Second Law 0 What if there is a net force acting 39 o o gt The object W111 accelerate mass lnertla 0 HOW much Ia N am a l N Um resistance to for given la I need IF I mass change Of mOtiOIl 0 Which direction a points in the direction of F gt a 2Fm aFm Predict acceleration from net force and mass Explain observed acceleration Newton s First LaW follows if net force is zero acceleration Will be zero gt constant velocity Valid only in Inertial Frames of Reference Include all forces including friction normal force weight ropes and sticks Only include external forces Only include forces actually acting on the body mass point under consideration Explains Why all objects fall With same acceleration g Fma Operational de nition of Force Unit must be kg ms2 2 N Newton How much net force do I need to accelerate a known mass m with acceleration a Example roller coaster If I observe a known mass m accelerate with acceleration a how much force can I infer to be acting on it All bodies fall with acceleration g in Earth s gravity eld gt Gravity Force must be IF gm mg This is the weight of mass m Warning The expression m a is not a force itself It is equal to the net force mFal Inertia net force applied acceleration achieved Can be used to determine mass Use known force and measure acceleration Compare ratio of accelerations for 2 different masses and same net force m1 m 2 a 2 a1 Use gravity to determine mass Measure weight in Newton divide by known g automatically done by most scales Depends on location Note this is not the de nition of mass that is given by comparison with standard 1 kg mass But can be used for that comparison Important Hints for Problem Solving Take all external forces into consideration Take their directions into account ma is not aforce Don t confuse mass and weight Newton s 2nd Law is only valid in Inertial Frames of Reference In an accelerating car there is no force pushing you into the seat instead the seat is exerting an accelerating force on you In a falling elevator there is a force weight acting on you even if you don t feel it You don t actually feel gravitational force pulling on you you feel the normal force holding you up Work and Energy 0 Newton showed momentum p mv is an important concept Relevant for collisions momentum is conserved Can tell you about the change in motional state during collision Change in momentum Impulse F X At 0 Leipnitz proposed 12 mv2 as relevant quantity Compare distance needed to stop moving object 2X the velocity gt 4X the distance average v X time to get v to zero Nowadays called kinetic energy Change in energy 2 WORK 2 F As force time distance Many other forms of energy the sum of all of them is conserved Momentum tells you oomph energy tells you ouch O syst 0 Ene Work and Energy Work The total effect a force F has on an object mass point closed em after some change in its position Given by Force times Displacement see later Changes motional kinetic state or internal state mechanical state Can be positive or negative Can be transferred from one object to another but no object can have work Analogy Transfer of cash rgy The ability to do work Property of the object mass point closed system Changed by work done on object Can be exchanged between objects systems but can not be created or destroyed energy conservation Analogy Net Worth Work and Kinetic Energy I 0 Prototype example free fall starting at rest Force mg Acceleration g Velocity vt gt Distance fallen As 12 gt2 Work done after time t AW FAS mg12 gtz 12mgt2 12mvt2 2 KB I 0 In general CHANGE of kinetic energy of some object A K E Alva2 EQUALS Work done on that object AW 2 FAS 1 2 3 Work and Kinetic Energy 11 Dimension Displacement times Force Unit Nm 2 J Joule Specify a force acting on an object Multiply displacement in the direction of the force with that force AW 2 F AS cosq 0 If F is in the direction of As then positive work is done on object 0 If F is in opposite direction of As then negative work is done on object 0 If F is perpendicular to direction of As then no work is done at all Add work done due to all external forces acting on object AW EFi 39 As 2 EAWZ 4 Set equal to change in kinetic energy Examples Pushing car up incline car rolling down demo Catching a ball ball bouncing off wall ball getting stuck in wall Work and Kinetic Energy Example Car rolling down ramp Gravity does work normal force doesn t gt only displacement in vertical direction counts Final velocity same as for free fall 12 mv2 mgAh Car moving up ramp Weight does negative work AW 2 mgAh Slows down car or I have to supply additional work F Pull a Important Notes Even if EFi 0 Work done can be zero No displacement Holding a book pushing against a wall Direction of displacement perpendicular to Force Moving sideways constant height in gravity eld circular motion constant speed Normal forces and static friction never do work but tension can and kinetic friction can too always negative Kinetic energy is a scalar quantity unlike momentuml KB 2 In2 v2 W 0 gt v always positive Independent of direction circular motion at constant speed doesn t change kinetic energy Depends on system of reference Everything I said only valid in Inertial System of Reference Gravitation 0 Objects on the surface of Earth fall down With acceleration a rad g 981 ms2 Earth s radius is REarth 6380 km 0 Moon circles the Earth once every 273 d 236106 s gt 60 26610396s Moon is D 384000 km away gt a rad 2 Da 2 000272 ms2 3600 times smaller D is 60 times bigger than R Earth gt Gravitational force must be falling off like lr2 D Newton s Law of Gravitation All masses are accelerated With the same acceleration at the same distance from Earth gt F M m since a F m Newton s 3rd laW gt Earth is attracted to any mass With force proportional to M gt F M m M The force is proportional to the distance squared F M lr2 Need proportionality constant G gt F G m M r 2 Universal constant gt Universal force laW for any two bodies With masses m M at distance r Measure G using torsion balance gt G 67 103911N m21g2 Plug in numbers on the surface of earth g F m G M R Earthz gt M 5971024 kg Important points d d m m Fon m2 at r2 due to m1 at r1 GH fz po1nt1ng from m2 to m1 2 r1 0 Universal lr2 force law describes not only gravity but also electromagnetism 0 Valid not only for point masses but for spherical extended masses as well measure r from the center 0 G can be measured with torsion balance but it s hard because it is so small gt Value 6673103911N m2lg2 0 Force always acts on center of gravity of an object roughly equal to center of mass 0 Force always points to center of gravity of attracting mass along distance vector 0 Mass m exerts equal and opposite force on mass M as that exerted by M on m 0 Superposition Gravitational forces add Example I 39 Gravity on the surface of rnoon Radius of Moon 1740 km 273 of Earth s radius roughly 14 IF density were the same Mass of Moon z 164 Mass of Earth really 181 123 Gravitational acceleration on Moon z 18O142 15 2 ms2 really 162 msz Example 11 Project Lagrange Point Put a satellite between Sun and Earth Where the net gravitational force is zero Satellite can be stationary looking at Earth Where to put MEanh 61024kg MSW 21030kg DES 151011m Require OmitIEmhr2 GmMSunD E s r2 gt D E s r 577 r gt r DB s578 259000 km Example 111 0 Two steel balls oating in space initially at rest Masses M 10kgm5kg d 01 m apart Initial gravitational attraction F G m Md2 33410397N on each Initial acceleration 33410 8 ms2 for M 66810quot8 ms2 for m After 60 s rst one has moved 006 mm Second has moved 012 mm Center of mass remains at same point 13 of the way from rst to second mass Motion The change in position relative to some xed point There is no such thing as absolute motion only motion relative to something else Examples Motion of bouncing ball relative to me my motion relative to train train s motion relative to ground Earth s surface Earth s motion relative to sun and other xed stars sun s and other stars motion relative to galaxy How do we measure position How do we measure motion Example Speedometer relative to ground GPS relative to satellites subtract motion of ground relative to satellites What is the cause of motion You don t always need one Example Astronaut oating freely in International Space Station passenger jumping up inside an airplane There are some reference systems called inertial systems where uniform motion in a xed direction doesn t require any cause it s the natural state In such systems objects at rest tend to stay at rest and objects in motion tend to continue to move or coast NEWTON S FIRST LAW Forces Push or pull on an object mass point due to its interaction with something else Cause of changes in motional state acceleration see later Has both a magnitude strength how hard do we pushpull and a direction which way do we pushpull gt Force is a vector Units m kg s 2 N Examples 0 Contact Forces Push Normal force pressure pull tensional force adhesion carry along stickiness static and dynamic friction shear T 0 Forces at a distance Gravity mg near surface of Earth more complicated form for general case of one mass attracting another 0 Forces at a distance Electric and magnetic forces Electromagnetism gt 2nd part of semester 0 On the subatomic level all force strong force QCD l Ultimately all due to electrostatic forces Principle of Superposition The effect of several different forces acting on the same mass point is equal to that of the single force which is their vector sum Example Holding up an object gravity and normal force cancel Can generalize for many forces gt Fresultant 2 F1 F2 quot39 FN all forces i1N If all forces add up to zero gt equilibrium no change in motional state in an inertial system object remains in its previous state of motion or rest Another way to determine an unknown force balance it with known forces Newton s First Law IF the net force 2 F i acting on an object is zero its velocity will not change If it is at rest it will remain at rest If it is moving it will continue to move with constant speed along a straight line gt IF the velocity changes there must be a force acting Examples Car on Freeway Puck on Ice Spaceship Remember Always add up all forces to get net force If an object is in contact with another object there usually are frictional forces between them including friction in air You don t need any net force to keep on moving inertia does it

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