Mystery of the Physical World
Mystery of the Physical World ISP 209
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To Feel a Force Chapter 11 Spring 2002 Momentum and Energy Chapter 11 Momentum and Energy A Two masses by a spring The transfer of ice potential energy stored in a pES i 1068 1 v0 0 1 1 spring to the kinetic energy of H l KE 0 l q y y y y y y y u u two masses is the starting quotuquot u l Eanh frictionless pomt for the d1scuss1on of another property of motion 1 called momentum As natural length PE S 0 vgt described in chapter 9 and El KE1 mv2 shown in Figure 111 a Em frictionless compressed Spring expanding Figure 111 The potential energy of a compressed spring transferred against a small mass m to a single mass after release transfers all potential energy stored by the spring to the kinetic energy of the mass There is a complete transfer of energy because the spring is attached to the Earth39s huge mass an extreme case that does not move during the expansion As can be determined by equating the initial potential energy PEO kx to the nal kinetic energy KE imvz k the mass attains a nal velocity v x0 m Note that in comparing a spring s potential energy and the kinetic energy of the masses both must be measured in joule units using the equivalence l J lNr m 1 kg m2 s2 The next example has identical masses m at each end of the compressed spring as shown in Figure 112 As the spring expands the spring s potential energy will be transferred in equal portions to the kinetic energy of the two masses Each mass must receive half the initial potential energy and therefore the speed u must be the same for PES 1Ekx3 just released frictionless i 2 natural length x PES 0 L W Figure 112 The potential energy of a compressed spring being split equally between two equal masses 97 To Feel a Force Chapter 11 Spring 2002 Momentum and Energy each mass By equating the initial potential energy PEO kxg to the sum of the nal kinetic energies KE mu2 mu2 one nds that each mass has a nal speed u i 5x0 Comparing this speed with the speed v JEXO when one mass J5 m m takes all the energy as shown in Figure 111 the speed u is lower by not a factor of two but by only a factor of E This occurs because kinetic energy is quadratic in the speed Between the two extremes shown in Figures 111 and 112 there is a third case shown in Figure 113 where m1 is greater than m2 but much smaller than the mass of the earth All energy conservation can say is that the larger of the two masses m1 will have a speed v1 that is smaller than the speed v2 of the smaller mass The speeds of any given masses cannot be predicted without some other constraint on the motion Another just released after release 1 2 KEl Emlvl frictionless Figure 113 The potential energy of the compressed spring splits unequally between two unequal masses quantity associated with the motion of a mass xes the ratio of the speeds Newton called this quantity momentum B Momentum 1n the expansion of the spring as shown in Figure 113 the same force magnitude with average ltFgt acts on each mass For each mass however the displacement s the work done and the kinetic energy change w AKE ltFgts are clear in only the two extreme cases m1 gtgt m2 or m1 m2 discussed above From results of crude experiments similar to the one shown in Figure 113 Newton realized that during any time interval Al FAl would be the same for both masses The quantity ltFAl is called impulse and it causes changes in a quantity called momentum p such that Ap FAt Since force is a vector so are changes in momentum Ap FAl Both masses loose contact with the spring at the same time Al after the release At any time during the expansion the compression force of the ideal spring acts on the 98 To Feel a Force Chapter 11 Spring 2002 Momentum and Energy masses in opposite directions with equal magnitudes The change in the momentum of each mass is Apz ltFgtAt and Apl lt7FgtAt and therefore Apz Ap1 The change in the momentum vectors of the two masses during the expansion will have equal magnitudes but opposite directions It is somewhat involved see box below if you are interested to show that the momentum of a mass m traveling with a velocity v is pmv 111 The direction of the momentum p is the same as the direction of the velocity v Velocity is a vector with a magnitude v speed and a sign i the direction of motion The expression for the momentum of a v0 v mass in terms ofthe mass m and speed F F 7 v can be obtained by analyz1ng the 7 7 i effects of a constant force F acting for a S A Figure 114 A mass with increasing speed caused by tlme Interval Al l to over a the action of constant force acting over a distance displacement s as shown in Figure 114 The velocity change Av v v0 and the average velocity v i are used in the analysis of the momentum change Ap of the mass Ap F us1n A FAt N g P Frs usingFrswAKEmv2 v8mAvrw s vv0 ArvmAvgtv us1n v pltgt ltgt gltgt Al 2 Ap mAv C Momentum conservation The constraint that the momentum changes of the two masses shown in Figure 113 are equal in magnitude but opposite in direction is equivalent to the statement that the VECTOR sum of their momenta pnet p1 p2 at the time of release during and after the expansion must remain the same The momentum of each mass was zero at the start of the expansion however the momentum vector of each mass is no longer zero after the expansion yet the net momentum pnet a vector will remain zero The generalization of this observation is known as the conservation of momentum the vector sum of the momenta the net momentum pnet does not change during the interactions between the masses 99 Chapter 11 MonIElmIluuldElIErgy m 1 lswlmant 112 Ag 0 Ame An exme 1 011212 A Au amend r n AA row As my fame am Am 0 the Ame Am A equal Am oypxne pAnAa rm Am nonofextemlfom wdlmuse AA leuuomenmm m wussnuuou of A EAAAAoA uz AyphES AA Au Mannheim of am A A mmemm omenmm massesevemfeneryls Am unsaved Shdmgfnanomfor Wm we Ame wm mm the AVAuAbxe 1mg mo hetwomasse un becolmervsd Asa gnu WA A gy by the explosion 61M ofthe The AA equal m we hemmmsnexm the mm very Indeefthe energyof ue mer a the gun m A the pmblem of e speeds ofnuequ Ame Ana the epronrA W A wellrwmmhd explosxou am AAA Aow be compbt y solved mngmomelmlm Wmm D Us As momen nucmervznou m wmpbtemmxfero he AAA potenml energy mad AA the m pa 0 we masses a owmg e epronA A gymA AA glne u 5 A x 1 E 3 the lumen emerge of e A WAqu ofenexy am An I I A L m i m2 mmomnq quotM mm 112 My MAuAAAWAAAAWAWAAAWMWWAMS m Ammmm m Ammmmwm mm mm 7 AAA WA AA AAA m w A mm A A2 mm AAA enmvamslla mmamAAAmzmAAmoumemmmormAAA To Feel a Force Chapter 11 Spring 2002 Momentum and Energy just released pnet p1 p20 0 The net momentum after the expansion must also have this value after release pnet p1 p2 0 m1v1m2v2 0 Solving for the speed of mass 1 m v m v 1 1 2 2 115 quot2 V1 quot2 v v or 1 m1 2 v2 m1 116 The speeds of the two masses in the extreme cases where energy conservation was suf cient to determine them are consistent with the values determined using Equation 116 The case of unequal masses can now be fully solved in just a few steps of algebra Squaring both sides of Equation 115 and removing one factor of m from each will yield m1m1V12 m2m2quot22 mlvf m2v2 117 quot 1 The terms in the brackets of Equation 117 apart from a factor of 12 are just the kinetic energies of the two masses KE1 KEZ 118 quot1 Substituting the left side of Equation 118 into Equation 114 yields PEO KEl KE2 Eq 114 PEO KE2 KE2 KE21amp m1 m1 KE PEO 2 Hg 119 quot1 If the mass m1 is very large like the mass of the earth then the term in the brackets in Equation 119 is equal to 1 and tells us that the potential energy of the spring is transferred entirely to the kinetic energy small mass m2 If the masses are equal the term in the brackets has the value 2 This means that the potential energy in the spring is split equally between the kinetic energies of two equal masses Using conservation of energy and momentum the kinetic energies and therefore the speeds are determined for two known masses of any size propelled by a spring 101 To Feel a Force Chapter 11 Spring 2002 Momentum and Energy storing a known amount of potential energy Momentum conservation alone can also explain many simple phenomena as in the homework that otherwise seem quite mysterious Return again to the process that started this chapter the expansion of a spring attached to the earth against a small mass After the expansion to conserve momentum the earth must have a NONzero momentum but the potential energy of the spring goes entirely into the KE of the small mass Though the speed of the earth must be essentially zero surprisingly its momentum is not The square of the momentum of mass 1 using the relationship between KEI and KE2 of Equation 118 can be related to the kinetic energy of mass 2 0002 m1V12 m1m1V12 2 quot11091 2m1 ampKE2 2m2KE2 quot1 Though the speed of the earth is very small in this process the cancellation of its mass from the expression for its momentum is a consequence of momentum conservation E Time reversal and collisions Combining the steps where energy is rst transferred to potential energy and then back to kinetic energy yields the classic quotcollision problemquot For example a small mass with some kinetic energy hits a wall and bounces off with the same energy it had before the collision A collision such as this one where there is no change in the total energy of the masses is called an quotelastic collisionquot Elastic collisions occur when the contact surfaces of the colliding objects compress and then expand elastically like an ideal spring As discussed at the end of the last section this collision may at first glance seem not to conserve momentum however the momentum of the earth is not zero despite the fact that the kinetic energy of the earth is zero A collision where energy is either lost or gained can be modeled by assuming that the energy difference is stored by a spring that doesn39t fully expand or is partially compressed prior to the collision quotCollisionsquot where an amount of energy is released by the expansion of a compressed spring can for example model an explosion Underlying this discussion is the requirement that there are no external forces acting on the masses in the problem and therefore momentum will be conserved in all interactions between masses Note also that a motion picture of an elastic collision run backward will look like an elastic collision with the directions of each of the masses reversed from the original The collisions don t distinguish one direction of time from another 102 To Feel a Force Chapter 11 Spring 2002 Momentum and Energy The same is not true for inelastic collisions Place some clay on one of the masses so that it absorbs energy in the collision by being squashed It would look rather odd in the motion picture run backward where the clay suddenly becomes undistorted and gives energy back to the masses We know that clay just doesn39t do that Nonconservative forces are involved in making the permanent distortion of the clay and their actions are irreversible This feature of nonconservative forces is related to the 2nd law of thermodynamics that then defines the true direction of time 103 MICHIGAN STATE N IV E R SIT Y Today Announcements 7 HW1 is due Wednesday Jan 16 by 800 am 0 What is science cont d What it time 0 Motion 7 rates of change 0 Special Relativity Time Travel 7 Introduction ISP20958 Lecture 1 717 MICHIGAN STATE N IV E R SIT Y The Scienti c Method creati vity The goal is to find theories that work better no theory is ever proven true deduction induction Example Gravity Aristotle 7 Newton 7 Einstein 7 String Theory experiment ISP20958 Lecture 1 MICHIGAN STATE U N IV E R SIT Y Keep an open mind quotHeavierthanair ying machines are 39 impossible Lord Kelvin pren39dem Royal 0 S clery 1895 In 1912 Alfred Wegener 18801930 39nents Were once and over time they have drifted apart into their current distribution ISP20958 Lecture 1 MICHIGAN STATE U N IV E R SIT Y Pseudoscience not bad just not science 7 The hypothesis is not at risk If data does not agree with the hypothesis then e data is assumed to be Wrong Some facts are ignore 7 Exploit the controversies and inadequacies in a competing theory 7 Portrayed as an underdog being punished by the scientific establishment 7 Reliance on fear and other emotions or reliance on a lack of knowledge 7 People who do pseudoscience usually do not publish in normal peerreviewed scientific journa s ISP20958 Lecture 1 A7 MICHIGAN STATE U N IV E R SIT Y Some Pseudoscience Examples 7 Intelligent DesignCreationism 39 See m and m for an interesting debate btw Darwinists and 7 Cold Fusion 7 Mercury invaccines causes autism 7 Homeo ath 7 Parapsychology ESP and such 7 And many more at httpskepdiccompseudoschtml NOTE Pseudoscience does not always have a crackpot or negative ring to it Some very smaIt physicists might be doing it ISP20958 Lecture 1 757 MICHIGAN STATE U N I V E R S T Y ls String Theory Pseudoscience HILIP W ANDERSON Physicist and Nobel laureate Princeton University ls string theory a futile exercise as physics as I believe it to be My belief is based on the fact that string theory is the first science in hundreds of years to be pursued in preBaconian fashion without any adequate experimental guidance It proposes that Nature is the way we would like it to be rather than the way we see it to be and it is improbable that Nature thinks the same way we do ISP20958 Lecture 1 767 MICHIGAN STATE U N IV E R SIT Y Signi cant Figures In science numerical values as a result of experimenm or models are only known to a certain number of digim which are called signi cant figures If a numerical answer is required for the homework normally you should use 3 significant figures actually the system is not supposed to care To reduce the number of SF round up or down 7 567898 given to 3 SF is 568 r 334997x10392 given to 3 SF is 335x10392 or 335E2 Examples 32 means the real number is between 315 and 324999 Don t sweat the details The important thing is to know that whe ou hear a scientist sa the E is 45 billion years old t means the age is between 445 and 4549999 ISP20958 Lecture 1 7 MICHIGAN STATE U N IV E R SIT Y What is time If nobody asks me I know but if I were desirous to explain it to one that should ask me plainly I know not Augustine of Hippo I confess I do not believe in time Vladimir Nabokov Time is the accident of accidents Epicurus Time is nature39s way of keeping everything from happening at once Woody Allen Time is a amp 7 Tupac Shakur ISP20958 Lecture 1 787 MICHIGAN STATE U N IV E R SIT Y What is time Time is the thing that is measured by clocks What is a clock We can describe how to make a clock Disclaimer Don t sweat it if the rest of today s lecture is over your head The main point is to show things aren t always as they seem ISP20958 Lecture 1 r97 MICHIGAN STATE N IV E R SIT Y A simple clock 0 A perfectly elastic ball bouncing between two xed walls d1 1 I di t S ance or distance speed time eed One click m SP 2gtltd time for a click speed click 1 2m x 10 ISP20958 Lecture 1 MICHIGAN STATE U N IV E R 5 What happens if the clock is moving Moving clock T i T a Path moving Path not moving Sh ow mov1e ISP20958 Lecture 1 MICHIGAN STATE U N IV E R SIT Y Clicker Question 1 Ifa clock is moving at a modest speed of 1 ms what can we say about the length of a click for a clock in motion relative to one at rest Choose the best answer A They are the same B A click in the moving clock takes longer because the distance traveled is longer C A click in the moving clock is faster because the velocity of the ball is greater Hint This question is ambiguous as We shall see Pretend I m asking this in an ISP209 class 200 years ago Well before Einstein came along ISP20958 Lecture 1 712V 7 MICHIGAN STATE W Motion 0 Position 7 location in space relative to an origin 0 Velocity 7 rate of change of position change in position 7 X xi V conesponding change in time t 7 At Acceleration 7 rate of change of velocity a 7 change in velocity conesponding change in time ISP20958 Lecture 1 7137 m MICHIGAN STATE U N IV E R 5 xample 7 Position of a ball at different times X m t 5 What is the average velocity 0 0 between 1 and 2 s 1 1 7Ax72m71m71m71 mS 2 2 A 271 1 2395 2395 What is the average velocity 30 3 between2and 25 s 30 4 v55 1ms 20 5 I ISP20958 Lecture 1 7147 MICHIGAN STATE U N IV E R SIT Y Example What is the average acceleration at l s 0mS2 a 7amp71m571ms A 1 l l l 1 What is the average 0 acceleration at 4 s l a 7 Av 7 rimgrows 7 A 1 elm2 ISP20958 Lecture 1 7157 MICHIGAN STATE U N IV E R SIT Y Special Relativity Suppose we use a photon of light as the ball in our 0 oc The laws of electromagnetism require that the speed of light be a constant independent of the motion of the clock Einstein s two postulates of special relativity 1 The speed of light is a constant in all inertial reference frames 2 The laws of physics are the same in all inertial reference frames Special relativity deals with nonaccelerating frames of reference General Relativity deals will all cases ISP20958 Lecture 1 7167 MICHIGAN STATE U N IV E R SIT Y Clicker Question 2 If a photon clock is moving to the right at halfthe speed oflight what can we say about the length ofa click for the clock in motion relative to one at rest Choose the best answer A They are the same B A click in the moving clock takes longer because the distance traveled is longer C A click in the moving clock is faster because the velocity of the ball is greater ISP20958 Lecture 1 717V MICHIGAN STATE U N IV E R SIT Y Consequences of Special Relativity Clocks in moving systems run more slowly 7 Equations 3vc 7 7 1 V2 152 7 7 t0 is called the proper time it is the time measure in the inertial reference frame 7 c speed of light 299 792 458 m s 0 The length of moving objects is smaller 7 10 is the proper length LU y 1 0 How do we know y 1 7 Clock in airplanes 7 Lifetime of fundamental particles ISP20958 Lecture 1 7187 MICHIGAN STATE U N IV E R SIT Y Clicker Question 3 Now imagine you are riding along with a photon clock moving to the right at halfthe speed oflight while your friend on the ground has her own photon clock How will your friend s clock on the ground tick according to you Choose the best answer A They are the same B Your friend s clock ticks slower than yours C Your friend s clock ticks faster than yours HINT Don t be afraid of something that seems paradoxical ISP20958 Lecture 1 719V MICHIGAN STATE U N IV E R SIT Y What does this mean 0 Time is relative It depends on the reference frame of the observer ie whether the clock is at rest or in motion relative to the observer 0 If a person were to travel at near the speed of light at a speed corresponding to y for 2 years At when they came back to Earth they would aged by only a few moments Age according for moving person t0 Aty Age according to person on Earth t0 2 years ISP20958 Lecture 1 7207 MICHIGAN STATE N IV E R SIT Y Time Dilation 139 We 7 5 7 c is the speed of light 1 1 100504 1 1 l 2 102062 E l 3 104828 1 l 4 109109 3 5 11547 41 1 1 1 l l 3 6 125 1 7 7 L39 7 140028 Speed 8 16667 Time on Earth for Is on the spaceship 9 229416 The world record vc for electrons is from SLAC 1 00 in California 0999999875 y 20000 can NEVER reach v c for things with mass 72139 MICHIGAN STATE U N IV E R SIT Y What is time Time is the thing that is measured by clocks The more modern view is that time is one of the dimensions in space time general relativity 7 much more about this later 0 If time is a dimension is it possible to move back and forth in time much like we move around in space ISP20958 Lecture 1 7227 MICHIGAN STATE N IV E R SIT Y Clicker Question 4 What do you think Is time travel permitted by the weirdness of time dilation and special relativity A Yes We can go forward and backwards B Sort of We can travel forward in time but not backwards C Sort of We can travel backwards but not forwards D Nope NOTE This is just a survey question Ie all answers get full pains ISP20958 Lecture 1 7237 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 1 Which of the following is a correct statement about entropy A Entropy is a measure of disor er States with a high entropy are more naturally disordered In physical processes like a swingi pendulum entropy ecreases Since energy goes into ran om motion Entropy is measured in Joules I A formula for entropy is temperature divided by heat input ISP20958 Quesuons 717 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 2 A magnetic field is oriented as shown Which way will a bar magnet orient in this field A B I Hint Magnetic field pains from North to South C I D ISP20958 Quesuons 727 MICHIGAN STATE M U N i V E R SIT Y Some Clicker Questions 3 The North geographic pole of the Earth is near a south magnetic pole A True B False ISP20958 Quesuons r37 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 4 The direction of a force on a charge at P is A Up B Down C Left D Right E zero ISP20958 Quesuons Ar MICHIGAN STATE U N IV E R SIT Y Clicker Question What is the electric force on a l C charge When it is very far from other charges A It is not possible to tell B It is in nitely large C It is zero D None of these answers k 2 F k899E9NmC2 Z ISP20957 Lecture 10 MICHIGAN STATE U N IV E R SIT Y Clicker Question If we increase the distance between two charges by a factor of 2 what happens to the electric force between them A It increases by a factor of 2 B It increases by a factor of 4 C It decreases by a factor of 2 D It decreases by a factor of4 E It does not change F L12Q2 k899E9N m2 12 ISP20957 Lecture 10 727 MICHIGAN STATE U N IV E R SIT Y Clicker Question IfI do 10 J ofwork on a baseball during the process of throwing it neglecting air resistance how much does the kinetic energy of the ball increase A280 J B 10J C0 J D 1172x1011 J ISP20957 Lecture 10 V37 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 1 2 V Vol tage 0 2 4 6 8 10 X distance In Place where the electric field is zero A2m B3m C45m D7m E9m ISP20958 Quesuons 717 MICHIGAN STATE U N l v E R 5 Some Clicker Questions 2 V mQLnHLnNLn Voltage 0 2 4 6 8 10 distance In Place where the force on a charge is zero A2m B3m C45m D7m E9m ISP20958 Quesuons MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 3 25 A 2 3 15 g l 05 u 0 H O gt705 0 2 4 6 8 10 distance In Place Where the magnitude of the force on a negative charge is less than zero A 00m B40m c 60m D 90m 50m ISP20958 Quesuons r37 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 4 Electric field is rate of change of potential with distance A Where is the E 3 field zero H 73 B D p or Q Q 4 O m 20 25 30 10 X distance cm ISP20958 Quesuons Ar MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 5 Electric field is rate of change of potential with distance A Where it the 3 electric field in Q the X direction H 4 Q Q 4 O m 20 25 30 10 X distance cm ISP20958 Quesuons 757 i MICHIGAN STATE Kw UNIVERSITY Some Clicker Questions 1 C E D What point on the orbit is the acceleration the largest A B C D E ISP20958 Quesuons 717 i MICHIGAN STATE Kw UNIVERSITY Some Clicker Questions 2 C A sun B E D Which location in the orbit is the planet moving the fastest A B C D E ISP20958 Quesuons 727 MICHIGAN STATE M U N l V E R SIT Y Some Clicker Questions 3 Planet B has 20 times more mass than planet A Which planet has a larger acceleration A B C It is not possible to tell ISP20958 Quesuons r37 MICHIGAN STATE M U N l V E R S I T Y Some Clicker Questions 4 Why is an astronaut in orbit weightless A Because they are always in free fall but constantly miss the Earth B Because gravity from the Earth and moon cancels C Because gravity from the Earth and Sun cancels D Because there is no gravity in space ISP20958 Quesuons Ar MICHIGAN STATE u N 1 v E R s T Y Some Clicker Questions 5 FGL 2G6673E 11N y 2 r kg 1100 km Planet A has a radius ofl km Planet B has a radius of 10 km What distance would we use for r in Newton s formula for gravity Note you must use kg and m for the formula to work A 1000 In B 1000 km C 11110 kmD1111E3 m E 1110E6 In ISP20958 Quesuons 757 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 1 The lightest two elements in nature are hydrogen and helium Where do we think most atoms of other elemenm made A In the Big Bang B In Stars C On planes D In space between stars ISP20958 Quesuons 717 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 2 In the Big Bang what was the in ationary epoch A It was the start of the Big Bang B It was the period when the Universe increased in size by 1050 C It was the period when nuclei were made D It was the period when atoms where made ISP20958 Quesuons 727 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 3 What do we think caused the Big Bang A A Big Crunch B Gravity C A large explosion D The weak force and many neutrinos E We don t know ISP20958 Quesuons r37 28Feb ISP209 Spring 2008 Exercise on Feynman Diagrams Question 1 What is meant by e anti electron with a charge of 1 antielectron with a charge of l 0amp8853 a 5 H o 3 none of these is correct Note We use time as vertical in our diagrams Question 2 What process is described by the following Feynman Diagram A Creation ofan electron and anti electron by a photon B Scattering of an electron by an antielectron C Scattering of two electrons by the EM force D Creation of a quark by the strong force E None of these is correct Question 3 Is it possible for a down quark and an antidown quark to interact to produce two electrons and an antielectron Hint Check that the charge lepton number and baryon number are conserved A Yes B No K MICHIGAN STATE U N IV E R SIT Y Clicker Question If the Sun suddenly became a black hole what would happen to the Earth s orbit A The Earth would start a spiral into the Sun B The Earth would y off out of the solar system C Depending of the mass of the Sun the Earth s orbit would approximately double or be approximately half of what it is now D The Earth would join all the other plants at the same radius from the black hole E Nothing ISP20958 Lecture 717 MICHIGAN STATE U N IV E R SIT Y Clicker Question Which of the following is n0t evidence for the eXistence of Black Holes A The rotation speed of material around a central object B Emission of large amounts of energy C Radio lobes of active galaXies D A blackbody spectrum of photons ISP20958 Lecture 727 MICHIGAN STATE U N IV E R SIT Y Clicker Question What causes QUASARS Which are very bright a 100 times the energy output of a normal large galaxy observed far from Earth A Black holes B ISP209 C The Big Bang D We don t know ISP20958 Lecture 737 MICHIGAN STATE U N IV E R SIT Y Clicker Question What does entropy have to do With time A We think conservation of entropy explains time B It is possible that early in the big bang in ation created a universe with too little entropy Hence all process tend toward increasing entropy and give time a direction C It explains why quasars cause time to increase D We know of no connection whatsoever E The second law says time must always decrease ISP20958 Lecture Ar MICHIGAN STATE U N IV E R SIT Y ISP209 Mystery of the Physical World Prof Brad Sherrill ISP20958 Lecture 0 717 MICHIGAN STATE U N IV E R SIT Y Course Details Course Syllabus Course Schedule 0 Reading Assignments 0 Lecture Notes ISP20958 Lecture 0 727 MICHIGAN STATE 3 E U N l V E R S I T Y What is Physics Physics from the Greek Doomog phusikos quotnaturalquot and 013mg phusis the order of nature is the science of Nature Physicists study the behavior Why didit do thar and properties Wha 139in made of 7 of matter in awide v 39 t of contexts ranging from subnuclear particles from which all ordinary matter is ade particle physics to the behavior of the material Universe as awho e cosmology ttpenwikipediaorgwikiPhysics Physics by Aristotle written in 350 BC When the ob39 cts ofan inquiry in any department have principles conditions or elements it is through acquaintance with these that knowledge that is to scienti c knowledge is attained For we do not think that we know a thing until we are acquainted with its primary conditions or rst principles and have carried our analysis as far as its simplest elements Plainly therefore in the science of Nature as in other branches of study our first task will be to try to determine what relates to its principles 1920958 Lecture 0 3 Fire Air Water Earth Hot Cold Wet Dry MICHIGAN STATE N IV E R SIT Y Far away from Earth what does space look like Deep field 39 1d vith the Hubble Telescope httghubblesiteorg 39 ISP20958 Lecture 0 MICHIGAN STATE U N IV E R SIT Y Hubble Deep Field 7 The stait of what we don t know 0 The Universe is an amazing place 0 The Milky Way Galaxy has about 200 billion stars in it 0 There are approximately 200 billion other galaxies in the Universe 0 We don t know if there are other Universes 39 0 We don t know how man dimensions our universe has 4 at least 0 We don t know what most of our universe is made 0 ISP20958 Lecture 0 757 MICHIGAN STATE N IV E R SIT Y The iClicker System You must purchase and bring your iclicker to each lecture How to read your clicker number under UPC code by the battery case 0 Register your clicker ISP20958 Lecture 0 767 MICHIGAN STATE U N IV E R SIT Y Scienti c Notation The Universe appears to be described by mathematics example Newton s Universal Law of Gravity Power output of the Sun 382700000000000000000000000 Watts 3827XlO26 W in LONCAPA we would write this 3827E26 W The biggest and smallest physical numbers 7 Largest There are about 108 protons in the Universe 7 Smallest Plank Length 103935 meters ISP20958 Lecture 0 7 MICHIGAN STATE U N IV E R SIT Y 0 10000 10 X 10X 10X 10 1041104 10X 10X ntimes 10H 0 To multiply add axponents 7 10000 X 100000 1000000000 7 104X 105 1045 109 0 345 0345 X 101 000345 X 103 ISP20958 Lecture 0 MICHIGAN STATE U N IV E R SIT Y More About Large Numbers 100000000010000 100000 109104 10910394 109 105 To divide subtract exponents 345 345 X 1013450 X 10393 1000100 103102 103392 101 10 0 Anything to the rst power equals itself Example 31 3 ISP20958 Lecture 0 r97 MICHIGAN STATE U N IV E R SIT Y Exponent of 0 gives 1 0 100100 102102 102392 100 1 0 Anything to the zero power equals 1 ISP20958 Lecture 0 7107 MICHIGAN STATE U N IV E R SIT Y Does Anybody Need Really Big Numbers 10100 googol 1010100 lOg g l googolplex Statistical Physics calculations involving a mole of gas 1 mole has 60221023 atoms 7 Need to know the total number ofpossible energy states Roughly 10numba39ufmulecules 10m23 7 Not a googolplex but respectable Some String Theories predict there may be 10500 parallel universes The symbol for infinity is 00 ISP20958 Lecture 0 7117 To Feel a Force Chapter 6 Spring 2002 Gravity and the body Chapter 6 Gravity and the body A The unit mass In objects with mass such as our bodies tension or compression forces are not necessarily constant throughout as they are in massless ideal springs Humans tend to use our bodies as detectors for forces and it is the perception or detection of forces that lies at the heart of most force misconceptions Before discussing the structure of our bodies a simple model of an object with mass is constructed that closely reproduces most effects of gravity and elastic forces on them A unit mass combining a thin mass attached to a massless ideal spring is shown in Figure 61 This unit separates elasticity and mass the two important properties of matter that govern its reaction to forces Figure 61 The unit mass Objects having mass can be modeled as a sequence of unit masses with the spring of one unit attached to the mass of the next as shown in Figure 62 The behavior of this Figure 62 A series ofunits modeling an object with mass attachment springs and masses is rst described in a horizontal orientation where gravity can be ignored in preparation for the more dif cult case where gravity also affects the stack of masses An object subjected to a pair of compressing forces F applied slowly generates compression forces C in each spring as shown in Figure 63 The compression forces Figure 63 The reaction ofthe series ofunits to being compressed by a force F have the same magnitude as the applied force C F Two forces with equal magnitude and opposite direction act on any one of the masses Thus balanced forces act on each mass and cause no part of the object to change its motion In this case the masses start and remain at rest Each mass is compressed by a pair of compression forces generating reaction forces of the same magnitude the mass is too thin to show these forces within the mass To Feel a Force Chapter 6 Spring 2002 Gravity and the body Before considering the effects of gravity on this stack of masses consider a single spring compressed by the weight of one mass and an identical spring compressed by the weight of ve of these masses are shown in Figure 64 Between the earth and the single mass m a gravitational force Fl mg pulls the Figure 64 One mass and ve masses compressing the masses together to compress the spring same Sprng betweenit andthe Emh Between the earth and larger mass 5m there is a gravitational force F5 5mg compressing its ideal spring a distance that is ve times larger Since the masses are at rest each compressed spring must be applying a balancing compression force on the earth and on the supported mass with a magnitude equal to the corresponding gravitational force C1 F1 and C 5 F5 B A quiz Now consider the stack of 5 masses m and 5 springs Use your common sense in solving a quiz regarding the gravitational force Consider the identical mass amp spring units arranged as shown in Figure 65 in three vertical stacks with a all springs having their natural length b each spring compressed the same amount and c the bottom spring compressed ve times as much as the rst Quiz Decide which state represents 1 the stack resting on the ground 2 the StaCk 1 fncnonless free fall Figure 65 Three states of compression a uncompressed and equal compression c increasing compression 3 the masses of the stack affected by additional forces other than gravity and the spring forces How can you tell which of the states is the one sitting on the ground Use a process of elimination It can t be state a because the bottom spring must be 56 To Feel a Force Chapter 6 Spring 2002 Gravity and the body compressed if the stack is sitting on the ground as it was in Figure 64 The choice is between state b and statec for the one sitting on the ground Each spring in state b is identical and compressed an equal amount The top spring must support only one mass while the bottom spring must support all ve masses above it as if a massless box lled with 5 masses and 5 springs sat on the bottom spring The bottom spring must compress ve times that of the top The compression of the springs in statec are consistent with the stack being placed on the ground For the freeifalling object the choice is between state a and state b State b can be eliminated because in freeifall there would be nothing pushing upward on its bottom spring yet it is compressed This leaves only state a The lowest spring doesn t push upward on the lowest mass and therefore the second spring cannot compress and so on None of the springs compress all springs have the natural length The gravitational force makes each mass fall but alone cannot compress the springs It follows that the equal compression seen in state b cannot occur without additional forces acting on the masses Without masses between the springs a stack of springs sitting on the ground supporting only a top mass will result in equal spring compressions If a mass is inserted between springs as in state b the springs will no longer be compressed an equal amount by gravity C Forces on and in a mass Moving downward through stack c the compression forces produced by the springs increase in magnitude At rst this seems to contradict Newton s 3rd law If compression forces can change from one side of a mass to the other Newton s 3rd law will not be violated Using a magni ed view of the top mass in F i8 8 66 Forces Wgt Cb aetng on the mass the stack as shown in Figure 66 we see that no and Cm aetng onthe Spring forces act on the top surface leaving that surface uncompressed The gravitational force W mg pulls the entire mass downward compressing the bottom surface against the spring causing two compression forces C m produced by the mass acting downward on the spring and C1 produced by the spring acting upward onto the mass Only two of the forces shown in Figure 66 act on the mass W and C1 while the third force C m acts only on the spring The forces acting on the mass are balanced therefore C1 W By Newton s 3rd law where the mass and spring meet the magnitude of the two compression forces must be equal C m C1 Therefore all forces shown in Figure 66 have a magnitude equal to the weight of the supported mass 57 To Feel a Force Chapter 6 Spring 2002 Gravity and the body Massless objects have a uniform compression throughout but within a mass the compression can change with position At any level within the mass shown in Figure 66 the magnitude of the compression force is equal to the weight of the portion above it Any mass is itself a series of thin masses connected by microscopic and massless springs We now use these concepts on the second mass from the top of stack c A detail as shown in Figure 67 on the left identi es forces that act on the mass and on springs in contact with it Also shown on the right are the compression forces C1 mg that Figure 6 7 Forces acting across the second mass in the stack WOUId eXISt If an Idea Spnng were le and for an ideal spring mthe same location placed at this position instead of a mass For the mass in addition to the compression force C1 its weight W mg is a source of compression C m W acting on the lower spring The mass does not distinguish between the two sources of compression and creates atotal force C2 C1 Cm 2mg as shown in Figure 68 By Newton s 3rd law the compression force in the lower spring must also have this value C 2 2mg The compression at the bottom of the second mass of stackc therefore corresponds to the weight of the two masses supported above that point As an exercise take the next lower mass within the stack shown in Figure 68 and identify those forces that act on the springs and those acting on the mass You should nd three forces acting on the mass and one each on springs The two compression forces generated by the mass each act F 13987 68 The forces across the second mass 13911 the stack on a spring To Feel a Force Chapter 6 Spring 2002 Gravity and the body The forces acting on each mass in stackc are shown in Figure 69 The compression force in any spring is equal to the weight of all the masses above it This pattern is repeated for each mass until the lowest spring which is compressed by the full weight WTotal 5mg By compressing each spring and mass pass the weight of the masses above on to the next mass At a contact point between a spring and mass forces consistent with the 3rd law are generated The force labeled Cm in Figure 67 is a compression force within the mass due to gravity acting independently on each of it39s thin sections The weight of these sections will compress the mass only if the bottom surface presses against another object The removal of all spring forces results in a relaxation within the mass removing the internal compression but the gravitational force remains and the mass instead of compressing falls This discussion illustrates the one feature that Figure 69 Forces on a StaCk 0f Ve distinguishes the behavior of an object with mass from a massless ideal spring Forces of different magnitude can act on opposite ends of a massive object Gravity and an elastic force acting on an object with mass can create a compression in the object that varies from the top to the bottom in Figure 67 the forces are C1 mg at the upper boundary and C1 Cm 2mg at the lower boundary of the mass The situation is more dramatic for the top mass where no force acts on the top surface while C1 mg acts from below and gravity acts throughout External forces acting on opposite sides of a massless object eg an ideal spring must be equal in magnitude However external forces acting on opposite sides of a mass can differ The most obvious example of this has just been described near the surface of the earth a stationary mass it remains at the same place for a period of time has a gravitational force pulling down and an upward force of equal magnitude usually an elastic force supporting from below The upward force creates compression in the mass at the lower surface that equals its weight The compression force at an intermediate point within the mass equals the weight of the mass above that point To Feel a Force Chapter 6 Spring 2002 Gravity and the body Gravity and an elastic force can create a state of varying compression or tension within a stationary mass lf balanced elastic forces act on a stationary mass no gravity a uniform compression or tension is created within it However generating an imbalance of elastic forces acting cause the mass to begin to move does not remain stationary and compression or tension will vary within the mass There are two ways to generate a varying tension or compression within a mass a gravitational force opposed by an elastic force as seen in the stack of masses shown earlier or in the absence of gravity an imbalance of elastic forces acting on the surface of an object In Figure 69 the stack of ve equal masses m separated by ideal springs can be considered as a single object with a mass of 5m The lower part of this object must support all of the mass that lies above it and compression forces change linearly in ve steps through the object Any object with a uniform distribution of mass placed on the ground will have compression forces within it that change linearly from zero at the top to the full weight on the bottom Using a model of a massive elastic object consisting of a series of small masses connected by massless ideal springs an understanding of any quothiddenquot internal forces within objects can be obtained If one is only interested only in the motion of an object without regard to internal forces then there are techniques that make it unnecessary to go into this detail However using our bodies to perceive the presence of forces as we often do internal elastic forces cannot be ignored D The body paradigm The concepts developed in the head previous sections provide the tools needed neck to construct a model of the human body useful in understanding the human torso perception of forces A highly schematic model of a human body is shown on the left waist in Figure 610 On the right each body part rump is modeled either by a rigid mass or by an pelvis ideal spring massless connecting the masses The natural length of the springs legs joints in your body are small but they are knees shown much larger exaggerate the changes in feet length used to measure the magnitude of the 501 compression forces acting at that joint The two legs and feet have been Flgme 63910 MOdGIOfthe human bedy 60 To Feel a Force Chapter 6 Spring 2002 Gravity and the body merged in this version of the body but it is easy to divide those forces and spring constants by two if desired For simplicity the compression is shown as if each body part had a similar mass The compression of the neck waist pelvis knees and soles exhibit a progressively increasing compression indicating the increasing internal compression forces acting at these locations The lower springs must support the weight of all the mass above it A person is generally unaware of these compressions An injury to one of the lower springs joints however will cause pain when standing In many joint injuries bone parts normally supported in the damaged area compress nerves sending pain signals to your brain The pain is a warning to you to be very careful with that part until the damage heals If you ignore the pain the two body parts not normally in contact can be further damaged or they can interfere with the healing process When standing the soles of your feet are compressed between you and the earth by a gravitational force a force better known as the weight of your body An average adult has about a mass m 70 kg resulting in an approximate weight W 700N about 150 1b compressing the soles of the feet by an amount close to 5 mm You may be unconvinced that soles of your feet are compressed by about this amount but after viewing a picture of the bottom of a person s feet when standing on a piece of glass you would no longer have any doubts The bottom of the foot looks mashed or crushed showing the effects of the compression The spring constant if the feet behave like an ideal spring for combined effect of the soles of both your feet acting together is easily calculated using Hooke s law F 700 N x 05cm l400Ncm This is quite a strong spring lts spring constant approaches values comparable to the spring in an automobile although limited in its allowable compression and it is 1400 times stronger than our standard spring with its spring constant of lNcm E Altered states of the body Any time the compression of the body is changed from that normally experienced standing sitting or lying down the body informs your brain that something unusual is occurring lf instead of standing on solid ground a person is holding onto and hanging from abar all of the lower body parts are in tension The feeling we have when hanging from our hands is caused by tension in joints that are most often in compression On the other hand if placed in a situation where your body is compressed in the same way as when standing on the earth you would have no way of knowing you weren t on earth from the messages your body was sending to your brain Your sight 61 To Feel a Force Chapter 6 Spring 2002 Gravity and the body might give you ahint that something else was happening but your body would be saying that you were on the earth A scene in the movie 2001 shows a crewrnember trotting around the walls of a circular room The appearance of arti cial gravity is created by the rapid rotation of the room as seen from outside of the ship The walls of the room are pushing inward against the crew s feet which allows the crew to rotate with the room The invward force on the feet causes compression forces within the body that duplicate and simulate the effects of gravity when standing on the earth We will now consider the unusual situation where a person who is sky diving for the rst time hopefully with a parachute has just left the airplane and is in ee fall feet rst toward the earth You may remember that we discussed a similar situation in the previous section There we determined that in a state of freeifall there is a complete loss of compression in the springs Here the argument is the same there is no force acting on the bottom of the skydiver s feet to create the compression of the soles Following this feature upward through the body we nd that although the gravitational force is acting on each body part there is no compression of the skydiver s body You can imagine that in this state the body would inform the brain that something unusual is happening here Experienced skydivers know and like this feeling but incorrectly associate it with their bodies being weightless The skydiver always has weight The gravitational force on each body part is still there and each body part still has weight The state of the body that the skydiver calls weightless is really a misnomer this state should be called compressionless Thus far most of our examples have been for objects that were at rest however the feeling of being weightless in the presence of a gravitational force on the body can be understood as the lack of one of the two forces needed to compress the body Falling motion will be discussed at length in upcoming chapters MICHIGAN STATE U N IV E R SIT Y Clicker Question Suppose that normal living tuna contains a certain nucleus that has a halflife of 10 years Once canned the nuclei begin to decay If we find a can that has half the expected amount of the nucleus how old is the can A We can not tell B 1 year C 10 years D 20 years E 12 year ISP20958 Lecture 717 MICHIGAN STATE U N l v E R SIT Y Clicker Question After three halflives What fraction of the original material is left A 12 B 121212 18 C 1212 14 D 121212 121212 164 E 23 8 ISP20958 Lecture 727 MICHIGAN STATE U N l v E R SIT Y Clicker Question The equation for fraction remaining is A 1 f B 2 Which letter in the above equation is the number of halflives A A B B C C ISP20958 Lecture 737 K MICHIGAN STATE U N IV E R SIT Y Clicker Question DATA Take the halflife of l4C to be 6000 years If we nd a sample of old bone that has 116 the normal amount of l4 C found in living bone how old is the bone A 6000 years B 12000 years C 24000 years D 116 years E 160004 years ISP20958 Lecture Ar MICHIGAN STATE U N IV E R s ISP209 Mystery of the Physical World Prof Brad Sherrill ISP20958 Lecture 0 717 MICHIGAN STATE U N IV E R 5 Course Details 0 Course Syllabus Course Schedule Reading Assignments 0 Lecture Notes ISP20958 Lecture 0 727 WWWre What is Physics Physics from the Greek oomKog phusikos quotnaturalquot and Wang phusis the order of nature is the science of Nature Physicists study the behavior Why didit do that and properties Wha fr it made of of matter in awide variety of contexts ranging from subnuclear particles from which all ordinary matter is made particle physics to the behavior of the material Universe as awhole MICHIGAN STATE U N IV E R SIT v u n o m E S o httpenwikipediaorgwikiPhysics Physics by Aristotle written in 350 BC When the objects of an inquiry in any department have principles conditions or elements it is through acquaintance with these that knowledge that is to sa scientific knowledge is attained For we do not think thatwe know a thing until e are acquainted with its primary conditions or first principles and have carried our analysis as far as its simplest elements Plainly therefore in the scienc Nature as in other branches of study our first task will be to try to determine what relates to its principles 1920958 Lecture 0 737 Frre Air Water Earth Hot Cold Wet Dry MICHIGAN STATE U N IV E R SIT v Far away from Earth what does space look like 39 l Dee J fieli tudy with the 39 Hubble Telescope htt hubblesiteor MICHIGAN STATE U N IV E R SIT Y Hubble Deep Field 7 The start of what we don t know 0 The Universe is an amazing place 0 The Way Galaxy has about 200 billion stars in it 0 There are approximately 200 billion other galaxies in the Universe quot 0 We don t know if there are other Universes 39 0 We don t know how man dimensions our universe has 4 at least 0 We don t know what most of our universe is made 0 ISP20958 Lecture 0 757 The iClicker System MICHIGAN STATE UNIVERSITY You must purchase and bring your iclicker to each lecture How to read your clicker number under UPC code by the battery case 0 Register your clicker ISP20958 Leemre 0 MICHIGAN STATE U N IV E R SIT Y Scienti c Notation The Universe appears to be described by mathematics example Newton s Universal Law of Gravity Power output of the Sun 382700000000000000000000000 Watts 3827X1026 W in LONCAPA we would write this 3827E26 W 0 The biggest and smallest physical numbers 7 Largest There are about 1080 protons in the Universe 7 Smallest Plank Length 103935 meters ISP20958 Lecture 0 7 arge and Small Numbers 7 Scienti MICHIGAN STATE U N IV E R SIT Y c Notation 0 10000 10X 10X 10X 10 104 1104 0 10X 10X ntimes 10H 0 To multiply add exponents 7 10000 X 100000 1000000000 7 104 X 105 1045 109 0 345 0345 X 101 000345 X 103 ISP20958 Leemre 0 Hooke s law Fkx Weight W FG mg g 981Nkg on Earth TorquegFJJ m Fr39 Work w s Potential Energy PES ikx2spring PEG mgh gravity on Earth 7 2 Kinetic Energy KE 7 mv Energy Conservation KE PE KEO PE0 wNCF Momentum p mv 2 law 1F const1 p p0 Ft No Fextemal Sump Sumpo Homework 11 Solutions Before L V2 0 Collision use V s After 31 2 Collision use MS Picture for Problems 13 Two hockey pucks masses m1 and m 1 moving with a speed v1 and 2 at rest collide headon with energy conserved an elastic collision 1 What are the expressions for the kinetic energies and momenta of the each puck before the collision and after the collision Before collision KEl izmlvlz n mlvl KEZ 2 p2 Q AftercollisionKE1 mluf p1 mlul KEz m2 22 p2 M 2 What are the expressions for the total momentum and the total energy ptot P1 P2 5 and Em KEI KE2 of the two pucks before and after the collision Before collision ptot mlvl After collision ptot m1u1 mZuZ Before collision Etot Lzml v12 After collisionEtot E m1u127 m2u 3 Momentum conservation and energy conservation can now be used to solve for the two speeds M1 and Mg in terms of the masses and the initial speeds To simply the problem first consider the two masses to be equal m1 and m m and find the solution for the two speeds M1 and Mg hint square the momentum equation Does the solution make sense to you Momentum Conservation m1 m1 n m2 v1 ul u2 now square it v12 u12u Zulu2 Energy Conservation 1 2 1 2 1 2 Erhv1irfu1irfuz V12 u12ug Combine results u12 M22 Zuluz ulz Mg Zulu2 0 u must be zero it stops 2 v hit puck gets all the momentum Before a Collision use V s use MS Picture for problems 47 The same two hockey pucks collide again but this time they stick tightly together when they make contact 4 What is the expression as in 1 above for the total momentum vector in the system before and after the collision Before collision ptot mlvl After collision ptot m1m2u 5 Use momentum conservation to determine the speed u of the two masses stuck together in terms of the masses m1 and m2 and the initial speed v1 7711 m2 m1V1 m1 V1 ml m2 6 What is the total mechanical energy KE and PE not heat of the masses before and after the collision in terms of the masses and the initial speeds 2 Before collis1onEtot Etot m1 v1 2 m 2 After collis1on Etot i m1 m2u 1 1 m1 v1 2 2 7711 m2 7 Did the total mechanical energy in the system change YES some energy was lost Explain why this makes sense This makes sense because the lost energy went into heating the sticky stuff pgt p469 Before hitting the wall After hitting the wall peanh A mass with momentum vector p hits a wall attached to the earth and bounces off with momentum vector 7 p opposite direction see section D and E of this chapter 8 Is the momentum of the small mass alone conserved Why not Momentum of just the small mass is not conserved An external force the force of the wall against the mass acted on that one obiect to reverse its direction 9 What is the other objects involved in this collision the Earth 10 What is the momentum vector of the other objects to conserve momentum Before pm p Afterptot pemh p pemh p p pearth a 11 Is this collision elastic see the last section for its de nition Collision is elastic because the energy of the small mass remains the same and the earth get verV little energV but does have 39 SOON lOON person backpack ice 1 shore 10m Picture for problems 12 and 13 A person weight SOON wearing a backpack filled with CDs weight lOON is standing on a frozen lake that is too slippery to walk on but the shore is just 10m away 12 Which direction should the backpack be thrown to get the person to the shore Throwing the CDs on the ice to make a path to the shore is not the answer Left Backhack s is to the left and the person s will be to the right MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 1 What happens to a star if its surface temperature is increased and is size remains the same A It only gem brighter B It only gem more red C It gets brighter and more blue D It only gem dimmer E It gem dimmer and more red ISP20958 Quesuons 717 MICHIGAN STATE U N IV E R SIT Some Clicker Questions 2 g 3 5 E Q ll 10 l 1039 10 l 01 10 10 10 10 10000 5000 3000 Surface Temperature kelv39in Luminosity is relative to our Sun The line in the HR diagram indicates the main sequence What determines if a star lies on the main sequence A It is blue B It is red C How it produces energy D Is temperature B What the surface is made out of ISP20958 Quesuons 727 MICHIGAN STATE U N l v E R SIT Y Some Clicker Questions 3 C 1quot D Where do we find 1 White Dwarfs on 1 7 the HR diagram Luminosity 1 J A 101 A 10000 5000 3000 Surface Temperature kelvin Luminosity is relative to our Sun ISP20958 Questions 737 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 1 Which of the following is a correct statement about entropy A Entropy is a measure of disor er States with a high entropy are more naturally disordered In physical processes like a swingi pendulum entropy ecreases Since energy goes into ran om motion Entropy is measured in Joules I A formula for entropy is temperature divided by heat input ISP20958 Quesuons 717 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 2 A magnetic field is oriented as shown Which way will a bar magnet orient in this field A B I Hint Magnetic field pains from North to South C I D ISP20958 Quesuons 727 MICHIGAN STATE M U N i V E R SIT Y Some Clicker Questions 3 The North geographic pole of the Earth is near a south magnetic pole A True B False ISP20958 Quesuons r37 MICHIGAN STATE U N IV E R SIT Y Some Clicker Questions 4 The direction of a force on a charge at P is A Up B Down C Left D Right E zero ISP20958 Quesuons Ar
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