Physics For The Life Sciences , 2nd UK Ed. Edition Class Notes

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1. PHYSICS AND THE LIFE SCIENCESIFNOTHINGELSE,MYSTUDENTSSHOULDLEARN…1.A physical model of a system is a description focusing on its most significant properties. Thedescription is built using observable phenomena, has a minimum number of assumptions,and should have predictive power.2.The accuracy of a measurement refers to how close it is to the accepted or correct value ofthe parameter being measured. The precision of a measurement refers to how repeatable themeasurement is, in other words how close different measurements of the same parameterconducted under identical conditions, are to each other. In general, the accuracy andprecision of a set of measurements are independent of each other.3.An order of magnitude refers to a rough numerical estimate of a physical quantity which isaccurate to within a factor of 10, or to within an order of magnitude.4.Dimensional analysis is a mathematical procedure in which information about relevantphysical variables in an equation can be obtained through manipulation, by equating thephysical dimensions of both sides of an equation.5.Scientific notation is a method of expressing very large or small numbers in a convenient andcompact fashion, also displaying all the relevant significant figures. It is very useful whenmaking order of magnitude estimates.6.Special mathematical functions such as the trigonometric functions, the exponential andlogarithmic functions, the square root function, and others, must always have dimensionlessarguments.LEARNINGOBJECTIVESStudents should be able to:Describe what a physical model is. (understand)Describe the characteristics that a good physical model must possess. (understand)Describe how significant figures are used in basic mathematical operations. (understand)

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Chapter 1Physics for the Life Sciences2Explain the concept of accuracy. (understand)Explain the concept of precision. (understand)Explainthedifferencebetweentheaccuracyandprecisionofasetofphysicalmeasurements. (understand)Be able to do order of magnitude estimates. (analyze)Be able to do basic mathematical operations using scientific notation. (analyze)Be able to explain how scientific notation is used in order of magnitude estimates.(understand)Have an understanding of - and be able to do mathematical operations in - the metricsystem. (understand)Be able to convert units in the metric system. (understand)Be able to do dimensional analysis to extract useful information from an equation relatingrelevant physical parameters. (understand)Be able to recognize when to use special mathematical functions such as trigonometric,exponential, and logarithmic functions. (evaluate)WHYISTHISCHAPTERIMPORTANTTOSCIENTISTS?In this chapter, the fundamental ideas of the scientific method are presented. In particular,the concept of a physical model is introduced. The advantages of physical models areexplained, as well as the conditions that all good physical models must satisfy.The concepts of accuracy and precision in physical measurement are introduced, as well astheir importance, and their very different natures.The power and efficiency of order of magnitude estimates are introduced and illustrated withrelevant examples. A close connection between this tool and the scientific notation isestablished.The metric, or SI system is introduced, and its power and elegance in the physical sciencesare explained with relevant examples.

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Physics for the Life SciencesChapter 13The deep implications and simplicity of the method of dimensional analysis are introduced.Emphasisisplacedontheideathatthemethodcanproducecrudemathematicalapproximations of relevant physical parameters with little if any understanding of the basicphysics of a given problem.The concepts of conversions between units in the metric system - and between systems - areintroduced. The sometimes catastrophic real consequences of improper unit conversions areanalyzed with relevant examples.A thorough introduction to the mechanics of significant figures is introduced, along with themotivation behind their use. Many practical examples are presented.WHYSHOULDSTUDENTSCARE?In this chapter, we introduce fundamental concepts needed for all of the sciences, such asthe metric system, dimensional analysis, significant figures, accuracy and precision, etc.These tools allow the student to get a feel for what the solution to a problem should looklike before, or without, solving the problem. For example, an order of magnitude estimatecan give one a numerical answer which is accurate to within a factor of 10, all with minimaleffort.Another important example of a labor saving tool is dimensional analysis. This technique cangive the student a rough idea of how the relevant physical parameters fit into an importantequation with very little if any knowledge of the underlying physics. The method does havelimitations, for example it cannot give information on constants of proportionality.Unit conversions within the metric system, as well as within different systems (i.e. metric vs.imperial)areintroducedinthischapter.Examplesofthesometimescatastrophicconsequencesofimproperunitconversionsarepresentedsostudentscanbegintoappreciate the potential implications of doing this incorrectly.

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Chapter 1Physics for the Life Sciences4WHATARECOMMONSTUDENTMISCONCEPTIONS/STUMBLINGBLOCKS?1.Students typically consider – incorrectly – that a physical model of a system under study is abetter model to the extent that it is more complicated and makes more, rather than fewerassumptions. In fact, the more complicated the model, the more parameters or factors tokeep track of. The difficulty here is that in an attempt to take into account these additionalparameters, the few really relevant ones can be relegated. Therefore it is important to stressthat good physical models are simple, they make few assumptions, and they focus only on afew relevant parameters while ignoring the rest.2.Students are notorious for confusing mathematical operations involving significant figures.The typical example goes something like this: the student is asked to find the area of a squarehaving ameasuredside of 7.23 m. They proceed to correctly square the side and merrilyreport the area of the square to be 52.279 m2, when of course the correct answer is 52.3 m2!In this example, the students made two errors, first their answer had more significant figuresthan the measured data, and second, they never rounded the last significant digit. It isimportant that students be made to understand how to manipulate significant figures.3.Perhaps the two most confusing concepts for students in this chapter are accuracy andprecision. Not only should students be made to understand that they are different concepts,they should also understand that they are independent of each other. The accuracy of ameasurement refers to how much it differs from the correct, or agreed upon value for agiven physical quantity. In essence, one only needs one measurement in order to talk aboutaccuracy. Precision on the other hand, refers to the repeatability of a series of measurements.It is an indication of how close measurements performed under identical conditions, are toeach other. It is a concept associated with an experimental uncertainty. In order to define aprecision, a set of measurements is necessary.4.Studentsinitiallytendtohaveenormousdifficultieswiththeconceptofordersofmagnitudes. It takes them great effort to understand that an increase or decrease of oneorder of magnitude actually means an increase or decrease of a factor of 10! Since theconcepts of logarithms and orders of magnitude are similar, students are often similarlyconfused by both. The typical confusion goes something like this: if the electrostatic forcebetween two masses is 10-9N and the gravitational force is 10-39N, how much larger is theelectrostatic force than the force of gravity? Student’s answer: it is about 30 times larger. Ofcourse the correct answer is that it is about 1030times larger, or 10 followed by 30 zeroes! Towrite this number out would take about two lines of text. It is a number so large, that wedon’t even have a name for it!

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Physics for the Life SciencesChapter 15WHATCANIDOINCLASS?Activity #1: Take a physical phenomenon such as the flight of a rocket or a tornado, and havestudents construct a physical model of the phenomenon. Remind students that their model shouldsatisfy four conditions: a) It should be based on observable phenomena, b) It should focus, or track,just a few of the most relevant physical properties of the phenomenon (in the case of the rocket,these could be position, velocity, and acceleration for example), c) It should contain a minimumnumber of assumptions, and most importantly, d) It must have predictive power, in other words ithas to be able to predict the future evolution of the phenomenon.Activity #2: Have student volunteers (those who are of the less shy type) come to the front of theclass and have them solve problems in addition, subtraction, multiplication, and/or divisioninvolving significant figures. When the volunteers make the inevitable mistakes, then let otherstudents in the class point out the errors and take this as a starting point for a discussion on the finerpoints of the mathematical rules of significant figure operations.Activity #3: Referring to example #4 above, ask students how much stronger the electrostatic forceis than the gravitational force for the example given. Once the usual incorrect answers are given,proceed to explain first, the magnitude of their errors, and then the correct way to solve thisproblem.Activity #4: As an example of the catastrophic consequences of not being able to properly convertunits, discuss the case of the “Gimli Glider”. This was a brand new state of the art Air CanadaBoeing 767 aircraft that was involved in a notable aviation incident. On July 23, 1983, the aircraftran out of fuel at 41,000 feet (12,500 m) of altitude, about halfway through its flight from Montrealto Edmonton. The crew was able to glide the aircraft safely to an emergency landing at a CanadianAir Force base in Gimli, Manitoba. The subsequent investigation revealed fuel loading wasmiscalculated through misunderstanding of the recently adopted metric system which replaced theimperial system. Luckily, not a single life was lost that day, and eventually the aircraft was repairedand returned to service.

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2. KINEMATICSIFNOTHINGELSE,MYSTUDENTSSHOULDLEARN…1.Motion in the physical sense, can be analyzed through the parameters of position, time,velocity, and acceleration.2.These four parameters are related. For example, the velocity of an object is its change ofposition in a given time interval.3.Position, velocity, and acceleration, are vector quantities because they are specified by amagnitude and a direction. Speed on the other hand, is not a vector since it is just themagnitude of the velocity.4.Graphing motion as a function of time can give an intuitive feel for the motion of an object.The slopes of the position and velocity functions give the instantaneous velocity andacceleration of the object. These graphs are representations of the kinematic equations ofmotion.5.Motion in the universe, whether biological or not, depends on an object’s acceleration.Therefore we must pay special attention to developing a mathematical description ofacceleration.LEARNINGOBJECTIVESStudents should be able to:Understand that one dimensional motion takes place along a straight line. (understand)Understand that a vector is a mathematical representation of a physical quantity that hasboth a direction, and a magnitude. (understand)Understand that the position of an object is represented by a vector which begins at somedefined origin, and ends at the object’s location. It points away from the origin. (understand)Understand that the vector that begins at point A and ends at point B, is called thedisplacement vector from A to B. (understand)

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Physic for the Life SciencesChapter 27Understand that the distance between two points A and B is simply the magnitude of thedisplacement vector between them. (understand)Be able to compute the distance between two points A and B. (analyze)Understand that velocity is a vector which gives information on how fast an object moves,or its rate of motion, and the direction of the motion. (understand)Understand that the speed is the magnitude of the velocity vector. It is not a vector andtherefore gives no indication of the direction of the motion. (understand)Be able to compute speed, given the velocity. (evaluate)Understand that the average velocity is the quotient of the displacement vector and the timeinterval over which the displacement took place. It is a vector. (understand)Understand that the instantaneous velocity is the velocity at a given instant. By definition, itis given by the limit of the average velocity as the time interval goes to zero. It is a vector.(analyze)Understand that the average speed is simply the magnitude of the average velocity.(understand)If the average speed is zero, but there was overall motion, then the average speed is taken tobe the distance covered divided by time. (analyze)Be able to calculate the average speed given the average velocity. (evaluate)Understand that the instantaneous speed is simply the magnitude of the instantaneousvelocity. (understand)Be able to calculate the instantaneous speed given the instantaneous velocity. (evaluate)Understandthatthetangenttoacurveatagivenpointisthebeststraightlineapproximation to the curve, at the given point. (apply)Remember that acceleration is the change in velocity per unit time. It is a vector. (remember)Understand that the average acceleration is the quotient of the change in the velocity and thetime interval over which the change took place. It is a vector. (understand)Understand that the instantaneous acceleration is the acceleration at a given instant. Bydefinition, it is given by the limit of the average acceleration as the time interval goes to zero.It is a vector. (analyze)Remember that the acceleration of gravity is the acceleration that all freely falling bodies nearthe Earth’s surface experience. It is approximately equal to 9.8 m/sec2. (remember)

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Chapter2Physicsforthe Life Sciences8Remember that the resultant vector is obtained by adding all the vectors acting at a particularpoint. (remember)Remember that projectile motion refers to the motion of an object under the influence of asingle force, the gravitational force. The trajectory of such motion is generally a section of aparabola, however in the special case special case in which there is no horizontal component,it is just a straight line. (remember)Remember that uniform circular motion refers to motion in a circle with a constant speed.The velocity is changing constantly however. (remember)Remember that the centripetal acceleration is the radially inward acceleration which anyobject in circular motion is subjected to. (remember)WHYISTHISCHAPTERIMPORTANTTOSCIENTISTS?The central idea in this chapter is the mathematical analysis of motion, which is itself acentral unifying concept in all of physics. The basic mathematical structure of the study ofmotion - or kinematics - is introduced.Special cases of motion which will be of particular interest in the analysis of biologicalsystems are introduced. Examples of such special types of motion are rectilinear motion, freefall, projectile motion, and uniform circular motion.We begin in this chapter the task of applying physical analysis to biological systems, themajor thrust of this text. Two examples of this type of analysis are presented, a study of theacceleration sensors located in the human inner ear, and motion sensors located along theanatomy of certain species of fish.WHYSHOULDSTUDENTSCARE?In this chapter, the concept of motion of bodies is introduced. This is perhaps the singlemost important concept in all of physics. A minimum set of mathematical tools which allowsa rigorous definition and analysis of motion is presented.Special types of motion which will become useful in later analyses are presented in thischapter. Among these are rectilinear motion, free fall, projectile motion, and uniform circularmotion.

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Physic for the Life SciencesChapter 29In this chapter, we also introduce the graphical method of motion analysis, which helps givethe student a feel for the type of motion being studied, without the added mathematicalcomplications.Most importantly, in this chapter we begin to make the connection between the biologicalsciences and physics, by introducing biological motion sensors such as the accelerometerslocated in the inner ear in humans, and motion sensors in fish. This connection is a motif wewill continue to focus on throughout the remainder of the text.WHATARECOMMONSTUDENTMISCONCEPTIONS/STUMBLINGBLOCKS?1.Students typically confuse - at least initially - the concepts of average velocity withinstantaneous velocity. They typically have a good understanding of the concept of averagevelocity, but take longer to assimilate and have more trouble with, instantaneous velocity.Three facts need to be stressed to students in an attempt to get them to understand theconcept instantaneous velocity: 1) the instantaneous velocity is the velocity vector at anygiven time, 2) as such, it is not an average of any sort, and 3) as such, it is constantlychanging. This same sort of confusion can exist for students between the average andinstantaneous accelerations, and the same remedies should be attempted.2.Students will typically have early difficulties differentiating the concepts of displacement anddistance. We start by pointing out that displacement is a vector, but distance is a scalar. Thatdifference alone sets them apart. But there’s more; a simple way to illustrate furtherdifferences is this: take the example of a newspaper delivery boy who does his rounds andeventually ends up where he started. In this case the distance covered might be a fewkilometres and real energy was expended, the boy sweats, he gets tired, his legs hurt, heconsumed glucose in the process etc. However, because he ended up exactly at the point oforigin, the displacement vector is zero! In this case, the average velocity over the entiredelivery route is zero, but the average speed is the total distance divided by time whichclearly is non zero since there was motion. So in this sense, displacement is related toaverage velocity in the same way as distance is to average speed.3.Studentscanhavedifficultieswiththeconceptsofthecentripetalacceleration,andcentripetal force. They will assume that when moving in a circular path such as when a car istaking a turn, there is a force that “pushes” objects outward, “the passengers are thrownoutwards by the centrifugal force” they are heard to say often! This of course is incorrect.The “centrifugal” force as such does not exist, it is fictitious. In reality, it is the absence of acentripetal (i.e. radially inward) force which causes the passengers to travel in a tangentialpath with respect to the circle, thus giving the illusion that they are “thrown” out. If there isan adequate centripetal force such as from a tightly fitting seat belt, or bucket type seats thatfirmly contour the bodies of passengers, then the passengers will follow a circular path andnot be “thrown” out!

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Chapter2Physicsforthe Life Sciences10WHATCANIDOINCLASS?Activity #1: Since the concepts of instantaneous velocity and acceleration are defined as limits as theintervalΔtgoes to zero, this would be a good opportunity to either introduce, or review, the conceptof a limit. This can be done with relative ease by picking out limit exercises from either a calculus oralgebra textbook, and going over them in class with students. When doing these exercises, it shouldbe emphasized that these instantaneous quantities are vectors, and they ARE NOT quotients, butrather limits! Even though they might look like quotients, they are not! Emphasize also that whentaking limits, first you simplify the expression algebraically as far as possible, and only then is thelimit to be taken. This means that to the extent possible, theΔt’s should be cancelled out beforetaking the limit.Activity #2: Discuss and analyze methods by which the brain when presented with accelerationinformation from the accelerometers in the inner ear, can quantify both velocity and distancetravelled. In the discussion, make the argument that the human brain (and that of other species aswell) basically has the ability to integrate (in the calculus sense) acceleration once to produce velocityestimates, and twice to produce displacement estimates.

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3. FORCESIFNOTHINGELSE,MYSTUDENTSSHOULDLEARN…1.Force is defined by the interaction between separate objects. The term force is used todescribe and measure the interaction. Force has several properties but is mainly characterizedby its two quantitative properties: magnitude and direction.2.There are four fundamental forces in nature: (1) gravity, (2) the electromagnetic force, (3) thestrong nuclear force, and (4) the weak nuclear force. These forces are contact-free forces thatdo not require contact between objects; they are calledfieldforces. All other forces areconsidered to be non-fundamental.3.Muscle tissue serves the specific purpose of exerting forces; locomotion in turn is achievedwhen several muscles and other tissues, such as bone, cooperate.LEARNINGOBJECTIVESStudents should be able to:Remember that muscles are divided according to form and function into three types:skeletal, smooth, and cardiac. (remember)Understand that a force is an interaction betweenobjects, such asa push or pull.(understand)Understand that forces can act through direct contact between objects, and these are calledcontact forces. Examples are the normal force, tension on a string, and friction. (understand)Understand that forces can act between objects over great distances without the need forcontact.Thesearecalledfieldforces.Examplesaregravityandtheelectricforce.(understand)Understand that force is a vector, thus it always has adirection and a magnitude.(understand)

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Chapter 3Physics for the Life Sciences12Evaluate the additive nature of forces. The effect of two simultaneous forces on the sameobject is the same as that of a single force equal to the addition of the forces. The addition isvector addition and the resultant force is called the net force. (evaluate)Analyze forces acting on an object, i.e. changes in the velocity of the object. (analyze)Understand that a restoring force in one which tends to bring an object back to its initialposition, or to a position of equilibrium. An example of such a force is the elastic force of aspring, which always tends to return to its uncompressed or unstretched length whenreleased. (understand)Analyze how forces always act in pairs. (analyze)Remember that the unit of force is the newton (N). The newton is a derived (SI) unit. Interms of fundamental units, 1 N = 1 kg·s2/m. (remember)Remember that the gravitational force of the Earth on any object, is commonly called theobject’s weight. (remember)Solve mathematically the force of gravity between two masses, given by the expression:where m1and m2are the masses of the objects, r is the distance between the two objects,and G is the universal gravitational constant 6.674 ×10−11N · m2/kg2. (apply)Understand that “g” is the acceleration of gravity. At the surface of the Earth, it isapproximately equal to 9.8 m/s2.It is the quotient of an object’s weight and its mass.(understand)Determine mathematically the electric or Coulombic force between two charges, given bythe expression:where q1and q2are the magnitudes of the charges of each object (in coulombs, “C”), r isthe distance between the two objects, and the constant k is the electric force (or Coulomb)constant and is equal to k = 8.99 × 109Nm2/C2. (analyze)Remember that the electric force is attractive if the charges are of opposite sign, and it isrepulsive otherwise. (remember)

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Physics for the Life SciencesChapter 313Remember that the strong force holds protons and neutrons together in the nucleus. Since itovercomes the repulsive electric force, it is the strongest of the fundamental forces, but ithas no significant effect outside the atomic nucleus. So the nuclear force is very strong andshort-ranged. (remember)Remember that the weak force - the last of the four fundamental forces - plays a role in thedecay of certain nuclei, and it extremely short-ranged. (remember)Classify examples of everyday non-fundamental forces such as the normal force, tension ona cable, the force of a spring, friction, air drag, and others. These forces are all macroscopicmanifestations of microscopic electrical forces. (analyze)Analyze a free body diagram which is a sketch of all forces acting on an object. It includesthe object and vectors representing the applied forces on it. It shows all types of forces, bothfundamental and convenience, exerted on the object. (analyze)Understand that if the net force that acts on an object is zero, the object is in equilibrium,and the object stays at rest or continues to move without changing its velocity. (understand)The mathematical condition for equilibrium is expressed as:where Fi is the ith force acting on the object.Remember that the vestibular apparatus in our inner ears are capable of detecting thedirection of gravity - and thus - of establishing up and down, independent of visual cues.(remember)Remember that our skins are equipped with mechano-receptors capable of indicating themagnitude of forces acting on them. They work by correlating the magnitude of a force withthe compression of the skin. (remember)WHYISTHISCHAPTERIMPORTANTTOSCIENTISTS?The concept of a force as an interaction between two objects is introduced. A classificationof forces intofundamentaland non-fundamental or ofconvenienceis introduced. Adescription of each type of force is presented.The properties of forces are introduced, and their vector nature is established. The muscularsystem as the origin of mechanical forces in the body is presented.

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Chapter 3Physics for the Life Sciences14Thefree body diagramis introduced as a useful analytical tool for solving mechanicalproblems.Theconceptofmechanicalequilibriumisintroduced.Theconditionsrequiredtoestablished equilibrium are defined.WHYSHOULDSTUDENTSCARE?In this chapter, we introduce qualitatively, the mechanical concept of aforceas aninteraction between objects.We distinguish the four known fundamental forces from other everyday forces which aremacroscopic manifestations of the electromagnetic force.We introduce within the human body, the muscular system as the origin of most mechanicalforces. A detailed physiological model for muscle action is presented.The basic properties of a force are discussed, along with the vector nature of all forces.An introductory description of everyday – or convenience – forces such as tension, friction,normal, and drag forces, is presented.The concept of afree body diagramis introduced, and its usefulness as an analytical tool isdiscussed.The concept ofmechanical equilibrium, and its consequences, is analyzed.Physiological mechanisms which allow us to keep our balance, and judge the magnitude ofexternal forces acting on our bodies, are discussed.WHATARECOMMONSTUDENTMISCONCEPTIONS/STUMBLINGBLOCKS?1.Students can have a difficult time understanding the concept that forces ALWAYS act inpairs. There is no such thing as an isolated, single force acting on an object. When object Aexerts a force on object B - whether through contact or through the action of a field(gravitational, electric, or magnetic) - object B exerts an identical force on object A, exceptfor one characteristic: the force is antiparallel. Many examples can be given to substantiatethis claim.

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Physics for the Life SciencesChapter 3152.The concept of equilibrium may cause students some difficulty. If a body is in equilibrium,this does NOT mean there are no forces acting on it! Equilibrium is defined as a mechanicalcondition in which the NET force acting on an object is vectorially equal to zero, in otherwords they cancel out. The mechanical effect of this condition is equivalent to having NOforce acting on the object, but the two conditions are different. Of course, a condition ofequilibrium implies that the velocity of the object remains constant.3.Friction is a concept that often creates trouble for students. For example, they can havesome difficulty comprehending, or accepting, that the force of friction between two bodies isindependent of the contact area between them, depending only on the normal forcespressing them together. There may also be some difficulty understanding that static frictionis typically larger than sliding friction.WHATCANIDOINCLASS?Activity #1: In simple illustrations of the limitations of the human vestibular apparatus, have astudent spin around on his axis a few times, until he/she is clearly dizzy, but not overly so. Then askthe student to attempt to walk in a straight line, and observe the deviations or zig-zag - like path thywill describe. In a similar vein, have a student lie down on the floor for about 10 or 15 minutes(without going to sleep!) and ask him/her to quickly stand up and walk straight. Again there will besome zig-zag – like motion. Explain that what is happening here is that the fluid in the vestibularapparatus is being shaken to the point of becoming turbulent. This has the effect of causing ratherlarge and sudden oscillations in the hair-like structures of the apparatus, which sends confusingelectrical signals to the brain such that it compromises the ability to maintain proper balance. Theeffect of alcohol in the brain is somewhat similar to this.Activity #2: In an exercise designed to improve the students’ understanding of how friction works(and how it doesn’t) the following simple exercise may be useful. Take a book with a known massand place it on a table. Tie a string around it such that the string does not make contact with thetable, and tie the other end of the string to a spring balance. Begin slowly dragging the book acrossthe table, measuring the force necessary to do so by reading it off the scale. As one knows fromtheory, if the normal force on the book is doubled, the sliding friction should more or less double aswell. So next put an identical book on top of the original one (to double the normal force), andrepeat the experiment. The force required to pull the two books across the table should roughlyhave doubled. This illustrates two key points discussed in the chapter: the first one being thatfriction is directly proportional to normal force; the second one being that it is independent ofcontact area (in other words, no change in contact area results in a doubling of friction).

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