Physics 111: Mechanics Lecture Week 1
Physics 111: MechanicsLecture Week 1Bin ChenNJIT Physics Department
IntroductionqqqPhysics 111 – Course InformationBrief Introduction to PhysicsChapter 1 – Measurements (sect. 1-6)nnnnqMeasuring thingsSI unitsUnit conversionDimensionChapter 2 – 1D motion (sect. 1-5)nnnnnDisplacement, Time and AverageVelocityInstantaneous VelocityAverage and Instantaneous AccelerationMotion with Constant AccelerationFree Falling Bodies
Course Information: InstructorqInstructor: Prof. Bin ChenqOffice: Tiernan Hall, Room 101qOffice hour: Fridays 11:00 am-12:00 pm.Other time by appointment.qEmail: bin.chen@njit.eduqWebsite: http://web.njit.edu/ binchen/phys111nThis is where I post my lecture slides!
Course Information: MaterialsqClass:nnqq04:00 pm – 05:20 pm, Tuesdays and Thursdays in TiernanHall 107Lecture notes available at http://web.njit.edu/ binchen/phys111(which will be uploaded after every lecture)Primary Textbook: “Sears and Zumansky’s UniversityPhysics with Modern Physics” by Young and Freedman(13th edition), available via NJIT BookstoreLab (required): Must register separately for Phys111A
Course Information: GradingqCommon Exams (16% each, 48% total)nCommon Exam 1: TBD 4:15 - 5:45 pmnCommon Exam 2: TBD 4:15 - 5:45 pmnCommon Exam 3: TBD 4:15 - 5:45 pmqFinal Exam (32%)qHomework (10%)qIn-class Quizzes (10%)qFinal Letter GradeA 85B 80-85B 70-80C 65-70C 55-65D 50-55F 50
Course Information: HomeworkqHomework problem assignments will be posted on-line usingthe Mastering Physics Homework System (“access codecard” purchase with textbook)qHomework Registration, Login, Physics Course ID: MPCHENFALL18qHomeworks are usually due on Sundays at 23:59 PM EasternTime.
Doing homework is important!q Learningphysics needs a lot of practiceq Gives you a chance to review the textbookq Helps you understand the course materialq The best way to get a good grade!nRoughly half of all the exam questions (whichare worth 80% of your total grade) are basedon the homework questions!
In-Class Quiz: iClickerqqiClicker is required as part of the coursenSimilar to requiring a textbook for the coursenCan be purchased/rented at the NJIT bookstorenCan’t share with your classmateiClicker use will be integrated into the coursenTo be used during most or all lectures/discussionsniClicker questions will be worked into subject matterqWatch out for slides with an iClicker symbolq10% of the final gradeqWe will start to use it from the second week
complete the registration. Use the loan a clicker to a student option to permanently conna student to a device.Register your iClicker online3. Web registrationFollow these instructions to complete the web registration.3.1 Instruct your students to complete the online registration rUse your 8-digit student IDMost importantly, enteryour iClicker remote ID onthe backDo this before the secondweekHave students go to www.iclicker.com, locate the registration form, and register theirclicker. As a suggestion, require that your students complete the online registration forma specified date.i clicker 7.8Instructor User Guide
How will we use the clicker?qI post questions on the slide duringlecture.qYou answer using your i-clicker remote.qClass results are tallied.qI can display a graph with the classresults on the screen.qWe discuss the questions and answers.qYou can get points (for participatingand/or answering correctly)! These willbe recorded (e.g., for quizzes andattendance).
Course Information: RemarksThis is one of the difficult 100-level courses –many students fail!q To succeed, spending time/effort is crucialq Taught at a much much faster pace than yourhigh schoolq Do not hesitate to get help!qoooCome to my office hourGo to Phys Dept. tutoring sessions (time TBD)Your fellow classmates
Physics and MechanicsqqPhysics deals with the nature and properties of matterand energy. Common language is math (Co-Reqs: Math111 or Math 132). Physics is based on experimentalobservations and quantitative measurements.The study of physics can be divided into six main areas:nnnnnnqClassical mechanics – Physics I (Phys. 111)Electromagnetism – Physics II (Phys. 121)Optics – Physics III (Phys. 234, 418)Relativity – Phys. 420Thermodynamics – Phys. 430Quantum mechanics – Phys. 442Classical mechanics deals with the motion andequilibrium of material bodies and the action of forces.
MeasurementqqqBeing quantitative in Physics requires measurementsHow tall is LeBron James? How abouthis weight?n Height: 2.03 m (6 ft 8 in)n Weight: 113.4 kg (250 lb)Numbernn Unit“thickness is 10.” has no physical meaningBoth numbers and units necessary forany meaningful physical quantities
SI Unit for 3 Basic QuantitiesMany possible choices for units of Length,Mass, Time (e.g. LeBron is 2.03 m or 6 ft 8 in)q In 1960, standards bodies control and defineSystème Internationale (SI) unit as,qnnnLENGTH: MeterMASS: KilogramTIME: Second
Prefixes for SI Unitsqqqqqq3,000 m 3 x 1,000 m 3 x 103 m 3 km1,000,000,000 109 1G1,000,000 106 1M1,000 103 1k141 kg ? g1 GB ? Byte ? MBIf you are rusty with scientific notation,see appendix B.1 of the text10xx 18151296321Prefix SymbolexapetateragigamegakilohectodecaEPTGMkhda
Prefixes for SI Units10xPrefix Symbolx 15-18dcmµnpfaqqqqqqqq0.003 s 3 x 0.001 s 3 x 10-3 s 3 ms0.01 10-2 centi0.001 10-3 milli0.000 001 10-6 micro0.000 000 001 10-9 nano0.000 000 000 001 10-12 pico p1 nm ? m ? cm3 cm ? m ? mm
Derived Quantities and UnitsMultiply and divide units just like numbersq Derived quantities: area, speed, volume, density qnnnnArea Length x LengthVolume Length x Length x LengthSpeed Length / timeDensity Mass / VolumeSI unit m2SI unit m3SI unit m/sSI unit kg/m3
Other Unit SystemqqqU.S. customary system (or imperial units): foot, slug,secondCGS system: cm, gram, second (another variant of themetric system, heavily used in astrophysics)We will use SI units in this course, but it is useful toknow conversions between systems.nnnn1 mile 1609 m 1.609 km1 m 39.37 in. 3.281 ft1 lb 0.465 kg 1 oz 28.35 gMore can be found in Appendices1 ft 0.3048 m 30.48 cm1 in. 0.0254 m 2.54 cm1 slug 14.59 kgA & D in your textbook.
Why metric is better?“In metric, one milliliter of water occupiesone cubic centimeter, weighs one gram,and requires one calorie of energy to heatup by one degree centigrade—which is 1percent of the difference between itsfreezing point and its boiling point. Anamount of hydrogen weighing the sameamount has exactly one mole of atoms init. Whereas in the American system, theanswer to ‘How much energy does it taketo boil a room-temperature gallon ofwater?’ is ‘Go f**k yourself,’ because youcan’t directly relate any of thosequantities.” – Wild Thing by Josh Bazell
Why should we care about units?Loss of NASA’s Mass Climate Orbiter:https://www.youtube.com/watch?v urcQAKKAAl0q Official erq
Unit Conversionq38.0m / s 2.36 10 2 mile / s 3600s / hr 85.0mile / hr 85.0mph
Summary – Part IqThe three fundamental physical quantities of mechanicsare length, mass and time, which in the SI system havethe units meter (m), kilogram (kg), and second (s),respectively.qUnits in physics equations must always be consistent.Converting units is a matter of multiplying the givenquantity by a fraction, with one unit in the numeratorand its equivalent in the other units in the denominator,arrange so the unwanted units in the given quantity arecancelled out in favor of the desired units.
Chapt. 2: 1D MotionqqqqEverything moves! Motion isone of the main topics inPhysics IMotion can be studied withKinematics and DynamicsSimplification: Consider amoving object as a particle,i.e. it moves like a particle—a “point object”In the spirit of taking thingsapart for study, then puttingthem back together, we willfirst consider only motionalong a straight line: onedimensional motionLAXNewark
Straight LineWhich case is a motion along a straightline?A)B)C)D) All of the aboveq This is the simplest type of motion.q Straight line can be oriented along any direction: Horizontal,vertical, or at some angle.q It lays the groundwork for more complex motion.
Basic Quantities in Kinematics
One Dimensional Position xqqqMotion can be defined as the change of position overtime.How can we represent position along a straight line?Position definition:nnnqDefines a starting point: origin (x 0), x relative to originDirection: positive (usually right or up), negative (usually left ordown)It depends on time: t 0 (start clock), x(t 0) does not have to bezero.Position has SI units of meters.x 2.5 mx -3m
Vector and ScalarqA vector quantity is characterized by having both amagnitude and a direction.nnqA scalar quantity has magnitude, but no direction.nqDistance, Mass, Temperature, Time For motion along a straight line, the direction isrepresented simply by and – signs.nnqDisplacement, Velocity, Acceleration, Force Denotedin boldface type v, a, F . or with an arrow over the! ! !top v , a , F . . sign: Right or Up.- sign: Left or Down.1-D motion can be thought of as acomponent of 2-D and 3-D motions.
Displacement Displacement is a change of position in timeDisplacement: x x f (t f ) xi (ti )f stands for final and i stands for initial It is a vector quantityIt has both magnitude and direction ( or – sign)SI unit: meterx1 (t1) 2.5 mx2 (t2) - 2.0 mΔx -2.0 m - 2.5 m -4.5 mx1 (t1) - 3.0 mx2 (t2) 1.0 mΔx 1.0 m 3.0 m 4.0 m
Distance and Position-time graphqDisplacement in spacennqDistance is the length of a path followed by an objectnnqIn 10 s: Δx xB – xA 52 m – 30 m 22 mIn 20 s: Δx xC – xA 38 m – 30 m 8 mIn 10 s: d xB – xA 52 m – 30 m 22 mIn 20 s: d xB – xA xC – xB 22 m 38 m – 52 m 36 mDisplacement is not Distance
Position-time graphqA person who walks for exercise produces theposition-time graph as below. Which segmentrepresents that the person remains at rest?q In 0.6 hr, what’s the person’sdisplacement?q In 0.6 hr, what’s the distance the personhas travelled?
Recap Problems 1:Who is faster?q Kangaroovs. Usain BoltKangaroos can hop at a speed of 40 mphn Bolt set the 100-m world record of 9.58 s in2009v Break it down n1 mile ? m, given there are 5280 feet/mile and3.28 feet/mn 1 hr ? sn 1 mph ? m/sn
VelocityqqqqqVelocity is the rate of change of position.Velocity is a vector quantity.displacementVelocity has both magnitude and direction.Velocity has a SI unit of meter/second.distanceWe will be concerned with three quantities, defined as:n Average velocityΔx x f xivavg nnAverage speedInstantaneousvelocitysavg Δt Δttotal distanceΔtΔx dx Δt 0 Δtdtv limdisplacement
Average VelocityqAverage velocityvavgqqΔx x f xi ΔtΔtis the slope of the line segmentbetween end points on a graph.SI unit: m/s.It is a vector (i.e. is signed), anddisplacement direction sets itssign.
Average SpeedqAverage speedsavg qqqtotal distanceΔtDimension: length/time, [m/s].Scalar: No direction involved.Not necessarily close to Vavg:nnSavg (6m 6m)/(3s 3s) 2 m/sVavg (0 m)/(3s 3s) 0 m/s
Instantaneous VelocityqqInstantaneous means “at some given instant”. Theinstantaneous velocity indicates what is happening atevery point of time.Limiting process:nnqqqqqChords approach the tangent as Δt 0Slope measure rate of change of positionInstantaneous velocity:Δx dxv lim It is a vector quantity.Δt 0 ΔtdtSI unit: m/s.It is the slope of the tangent line x(t).Instantaneous velocity v(t) is a function of time.
Instantaneous Velocityq Atwhich time(s) the instantaneousvelocity v(t) is zero?
Uniform VelocityqqqUniform velocity is the special case of constant velocityIn this case, instantaneous velocities are always thesame, all the instantaneous velocities will also equalthe average velocityBegin with v Δx x f xi then x f xi v x ΔtxxΔtΔtNote: we are plottingvelocity vs. timevx(t)vxxfxi0v(t)t0titft
Position-time grapht
Video Time!q Lightingseen in slow-motion (1 s in 6-minvideo footage):https://www.youtube.com/watch?v W9xzU0xjlhEq Average velocity of a lighting leader (orderof magnitude estimation)nnn 𝑣 𝑎𝑣𝑔 𝑥/ 𝑡 𝑥? 𝑡?
Average AccelerationqqqqqqChanging velocity (non-uniform) means anacceleration is present.Acceleration is the rate of change of velocity.Acceleration is a vector quantity.Acceleration has both magnitude and direction.Acceleration has a dimensions of length/time2: [m/s2].Definition:nAverage accelerationnInstantaneous accelerationaavg Δv v f vi Δt t f tiΔv dv d dx d 2va lim 2dt dt dt dtΔt 0 Δt
Average AccelerationqAverage accelerationaavg qNote: we are plottingvelocity vs. timeΔv v f vi Δt t f tiVelocity as a function of timev f (t ) vi aavg ΔtqIt is tempting to call a negative acceleration a “deceleration,” butnote:nnqWhen the sign of the velocity and the acceleration are the same (eitherpositive or negative), then the speed is increasingWhen the sign of the velocity and the acceleration are in the oppositedirections, the speed is decreasingAverage acceleration is the slope of the line connecting the initialand final velocities on a velocity-time graph
Acceleration of the Tesla Model SP100DqElon Musk claims that his Tesla Model S P100 Dcan accelerate from 0–60 mph in 2.5 s, becomingthe third-fastest-acceleration production car inthe world. If so, what is the acceleration in m/s2?aavg Δv / Δt (v f vi ) / (t f ti ) 60mph / 2.5s 60 0.45m / s / 2.5s 10.8m / s 2
Speed up and Slow downqVelocity as a function of time v (t ) v a ΔtfiavgqWhen the sign of the velocity and the acceleration are thesame (either positive or negative), then the speed isincreasingWhen the sign of the velocity and the acceleration are inthe opposite directions, the speed is decreasingqJanuary 28, 2015
Instantaneous and Uniform AccelerationqThe limit of the average acceleration as the timeinterval goes to zeroΔv dv d dx d 2va limΔt 0qqΔt dt dt dt dt 2When the instantaneous accelerations are always thesame, the acceleration will be uniform. Theinstantaneous acceleration will be equal to the averageaccelerationInstantaneous acceleration is theslope of the tangent to the curveof the velocity-time graph
AccelerationqAn object travels 3 m in the 1st second of travel,3 m again during the 2nd second of travel, and 3m again during the 3rd second. What is theapproximate average acceleration of the objectduring this time interval?A) 3 m/s2B) 6 m/s2C) 9 m/s2D) 0 m/s2E) unable to determine
Relationship betweenAcceleration and VelocityqqqqVelocity and acceleration are in thesame directionAcceleration is uniform (blue arrowsmaintain the same length)Velocity is increasing (red arrows aregetting longer) v f (t ) vi atPositive velocity and positiveacceleration
Relationship betweenAcceleration and VelocityqqUniform velocity (shown by redarrows maintaining the same size)Acceleration equals zerov f (t ) vi at
Relationship betweenAcceleration and VelocityqqqqAcceleration and velocity are inopposite directionsAcceleration is uniform (blue arrowsmaintain the same length)Velocity is decreasing (red arrows aregetting shorter) v f (t ) vi atVelocity is positive and acceleration isnegative
Kinematic Variables: x(t), v(t), aqqqPosition is a function of time: x x (t )Velocity is the rate of change of position.Acceleration is the rate of change ofvelocity.Δv dvΔx dxv limΔt 0ddtqqΔt dta limΔt 0Δt dtddtPositionVelocityAccelerationGraphical relationship between x, v, and aAn elevator is initially stationary, then moves upward,and then stops. Plot v and a as a function of time.
Special Case: Motion with UniformAcceleration (our typical case)qqAcceleration is a constantKinematic Equations (whichwe will derive in a moment)v v0 at1Δx v t (v0 v)t2Δx v0t 12 at 22v v0 2aΔx2
Derivation of the Equation (1)qGiven initial conditions:n a(t) constant a, v(t 0) v0, x(t 0) x0qStart with definition of average acceleration:Δv v v0 v v0 v v0aavg aΔt t t0t 0tqWe immediately get the first equationv v0 atqqShows velocity as a function of acceleration and timeUse when you don’t know and aren’t asked to findthe displacement
Derivation of the Equation (2)qqqqqGiven initial conditions:n a(t) constant a, v(t 0) v0, x(t 0) x0Start with definition of average velocity:x x0 Δxvavg ttSince velocity changes at a constant rate, we have1Δx vavg t (v0 v)t2Gives displacement as a function of velocity and timeUse when you don’t know and aren’t asked for theacceleration
Derivation of the Equation (3)qGiven initial conditions:n a(t) constant a, v(t 0) v0, x(t 0) x0qStart with the two just-derived equations:v v0 atqqq1Δx vavg t (v0 v)t2111We have Δx (v0 v)t (v0 v0 at )t Δx x x0 v0t at 2222Gives displacement as a function of all three quantities: time,initial velocity and accelerationUse when you don’t know and aren’t asked to find the finalvelocity
Derivation of the Equation (4)qqqGiven initial conditions:n a(t) constant a, v(t 0) v0, x(t 0) x0Rearrange the definition of average accelerationΔv v v0 , to find the timev v0aavg at ΔttaUse it to eliminate t in the second equation:2v 2 v0 , rearrange to get11Δx (v v)t (v v )(v v ) 202a002a22v 2 v0 2aΔx v0 2a( x x0 )qqGives velocity as a function of acceleration anddisplacementUse when you don’t know and aren’t asked for the tim
Problem-Solving HintsqqRead the problemDraw a diagramnqLabel all quantities, be sure all the units are consistentnqqConvert if necessaryChoose the appropriate kinematic equationSolve for the unknownsnqChoose a coordinate system, label initial and final points,indicate a positive direction for velocities and accelerationsYou may have to solve two equations for two unknownsCheck your results
ExampleqAn airplane has a lift-off speed of 30 m/safter a take-off run of 300 m, whatminimum constant acceleration?v v0 atqΔx v0t 12 at 22v 2 v0 2aΔxWhat is the corresponding take-off time?v v0 atΔx v0t 12 at 22v 2 v0 2aΔx
Free Fall AccelerationyqqqqqEarth gravity provides a constantacceleration. Most important case ofconstant acceleration.Free-fall acceleration is independent ofmass.Magnitude: a g 9.8 m/s2Direction: always downward, so ag isnegative if we define “up” as positive,a -g -9.8 m/s2Try to pick origin so that yi 0v v0 gt1 2y y0 v0t gt2
Free Fall AccelerationIn 1600, Italian physicist Galileo performed ax famous experiment on the top of theq0Leaning tower of Pisa. He dropped two ballswith different weights simultaneously. If airresistance is negligible, which ball hit theground first?1x x0 v0t gt 22A) heavy ball hit the ground firsB) light ball hit the ground firstC) they hit the ground at the same timeD) unable to determineBegin with t0 0, v0 0, x0 0So, t2 2 x /g same for two balls!Assuming the leaning tower of Pisa is 150 fthigh, t (2x150x0.305/9.8)1/2 3.05 s
Free Fall for RookieqqqqqqA stone is thrown from the top of a building with aninitial velocity of 20.0 m/s straight upward, at aninitial height of 50.0 m above the ground. The stonejust misses the edge of the roof on the its way down.Determine(a) the time needed for the stone to reach itsmaximum height.(b) the maximum height.(c) the time needed for the stone to return to theheight from which it was thrown and the velocity ofthe stone at that instant.(d) the time needed for the stone to reach theground(e) the velocity and position of the stone at t 5.00s
SummaryqqqThis is the simplest type of motionIt lays the groundwork for more complex motionKinematic variables in one ationa(t)m/s2All depend on timeAll are vectors: magnitude and direction vector:Equations for motion with constant acceleration:nv v0 atnx x0 v0t 12 at 2nv v0 2a( x x0 )nx x0 12 (v v0 )tn22x x0 vt 12 at 2LL/TL/T2missing quantitiesx – x0vtav0
Physics and Mechanics q Physics deals with the nature and properties of matter and energy. Common language is math (Co-Reqs: Math 111 or Math 132). Physics is based on experimental observations and quantitative measurements. q The study of physics can be divided into six main areas: n Classical mechanics – Physics I (Phys. 111)
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