Chapter 1Interactions and Motion1.1 Kinds of matter 21.2 Detecting interactions 41.2.1 Change of direction 41.2.2 Change of speed 51.2.3 Change of velocity: change of speed or direction 51.2.4 Uniform motion 61.3 Newton’s first law of motion 61.4 Other indicators of interaction 81.4.1 Indirect evidence for an interaction 91.4.2 Summary: changes as indicators of interactions 91.5 Describing the 3D world: Vectors 91.5.1 3D coordinates 91.5.2 Basic properties of vectors: magnitude and direction 101.5.3 Equality of vectors 101.5.4 Drawing vectors 111.5.5 Vectors and scalars 111.5.6 Magnitude of a vector 111.5.7 Mathematical operations involving vectors 121.5.8 Multiplying a vector by a scalar 131.5.9 Direction of a vector: Unit vectors 131.5.10 Vector addition 151.5.11 Vector subtraction 151.5.12 The zero vector 161.5.13 Change in a quantity: The Greek letter ∆ 161.5.14 Relative position vectors 161.6 SI units 171.7 Velocity 171.7.1 Average speed 171.7.2 Vector velocity 181.7.3 Determining average velocity from change in position 191.7.4 Scaling a vector to fit on a graph 201.7.5 Predicting a new position 201.7.6 Instantaneous velocity 221.7.7 Connection to calculus 231.7.8 Summary of velocity 241.8 Momentum 241.8.1 Changes in velocity 251.8.2 Approximate formula for momentum 261.8.3 Direction of momentum 271.8.4 Change of momentum 281.8.5 Average rate of change of momentum 291.8.6 Rate of change of momentum along a curving path 301.9 *The principle of relativity 331.10 Summary 371.11 Review questions 391.12 Problems 431.13 Answers to exercises 49Copyright 2005 John Wiley & Sons. Adopters of Matter & Interactions by RuthChabay and Bruce Sherwood may provide this revised chapter to their students.2 Chapter 1: InteractionsChapter 1Interactions and MotionThis course deals with the nature of matter and its interactions. The varietyof phenomena that we will be able to explain and understand is very wide,including the orbit of stars around a black hole, nuclear fusion, and thespeed of sound in a solid. The main goal of this course is to have you engage in a process cen-tral to science: the attempt to explain in detail a broad range of phe-nomena using a small set of powerful fundamental principles.The specific focus is on learning how to model the nature of matterand its interactions in terms of a small set of physical laws that gov-ern all mechanical interactions, and in terms of the atomic struc-ture of matter.This first chapter introduces the notion of interactions and the changesthey produce. The major topics are:• The kinds of matter we will deal with• How to detect interactions • Precise description of position and motion in 3D space• Momentum1.1 Kinds of matterIn this course we will deal with material objects of many sizes, from subatom-ic particles to galaxies. All of these objects have certain things in common.Atoms and nucleiOrdinary matter is made up of tiny atoms. An atom isn’t the smallest type ofmatter, for it is composed of even smaller objects (electrons, protons, andneutrons), but many of the ordinary everyday properties of ordinary mattercan be understood in terms of atomic properties and interactions. As youprobably know from studying chemistry, atoms have a very small, very densecore, called the nucleus, around which is found a cloud of electrons. Thenucleus contains protons and neutrons, collectively called nucleons. Elec-trons are kept close to the nucleus by electric attraction to the protons (theneutrons don’t interact with the electrons).? Recall your previous studies of chemistry. How many protons andelectrons are there in a hydrogen atom? In helium or carbon atoms? If you don’t remember the properties of these atoms, see the periodic tableon the inside front cover of this textbook. Hydrogen is the simplest atom,with just one proton and one electron. A helium atom has two protons andtwo electrons. A carbon atom has six protons and six electrons. Near theother end of the chemical periodic table, a uranium atom has 92 protonsand 92 electrons. Figure 1.1 shows the approximate cloud of electrons forHydrogen1 electronCarbon6 electronsIron26 electronsUranium92 electrons1×10-10 mFigure 1.1 Atoms of hydrogen, carbon,iron, and uranium. The white dot showsthe location of the nucleus. On this scale,however, the nucleus would be much toosmall to see.Throughout this text you will encounter questions like the preceding one,which ask you to stop and think before reading further. An important partof reading and understanding a scientific text is to ask yourself questionsand to try to answer them. You will learn more from reading this text if youtry to answer these questions before looking at the discussion in the sub-sequent paragraph.1.1: Kinds of matter 3several elements but cannot show the nucleus to the same scale; the tiny dotmarking the nucleus in the figure is much larger than the actual nucleus. The radius of the electron cloud for a typical atom is about meter. The reason for this size can be understood using the principles ofquantum mechanics, a major development in physics in the early 20th cen-tury. The radius of a proton is about meter, very much smaller thanthe radius of the electron cloud. Nuclei contain neutrons as well as protons (Figure 1.2). The most com-mon form or “isotope” of hydrogen has no neutrons in the nucleus. How-ever, there exist isotopes of hydrogen with one or two neutrons in thenucleus (in addition to the proton). Hydrogen atoms containing one or twoneutrons are called deuterium or tritium. The most common isotope of he-lium has two neutrons (and two protons) in its nucleus, but a rare isotopehas only one neutron; this is called helium-3. The most common isotope of carbon has six neutrons together with thesix protons in the nucleus (carbon-12), while carbon-14 with eight neutronsis an isotope that plays an important role in dating archeological objects. Near the other end of the periodic table, uranium-235, which can under-go a fission chain reaction, has 92 protons and 143 neutrons, while urani-um-238, which does not undergo a fission chain reaction, has 92 protonsand 146 neutrons.Molecules and solidsWhen atoms come in contact with each other, they may stick to each other(“bond” to each other). Several atoms bonded together can form a mole-cule—a substance whose physical and chemical properties differ from thoseof the constituent atoms. For example, water molecules (H2O) have prop-erties quite different from the