PHYS 314 HOMEWORK #3
|
|
- Duane Gaines
- 5 years ago
- Views:
Transcription
1 PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des the scale measure at the mment the last link hits the scale? Slutin : This is a variable mass prblem, in that we are cmputin the frce exerted by the scale n the chain as the chain falls n the scale. As we discussed in class, part f the frce supprts the weiht f the chain n the scale, and part f the frce stps the mmentum f the fallin chain. We use the eneral frm f Newtn' s secnd law : F dp d (mv) m dv + v dm Since the chain is fallin under ravity with n air frictin (and n internal frictin between the links f the chain), we knw that dv/. Nw, we emply the chain rule and btain: v dm v dm dy dm/dy is just the mass density f the chain, λ, and dy/ is the speed f the fallin chain. Cmbinin all these, we et : dy F m + v λ where v is the speed f the last link as it hits the scale. We knw frm elementary physics that an bject fallin thruh a heiht L acquires a speed iven by: s we have: v L F m + L λ But L λ is just the mass f the entire chain, s we have finally:. Text, prblem, p. 9 F m + m 3 m. Slutin : We have a particle fallin in a ravitatinal field with quadratic air resistance. If we chse dwn as the neative directin (air frictin acts up) and ur frce equatin becmes :
2 phys34-07hw3s.nb F m dv - m + k m v (we' ll use the bk' s ntatin since we want t et their answer). Nw, the questin asks us t find the distance the bject falls in acceleratin frm initial t final velcity, this suests we shuld cnvert dv/ t dv/dx via : m dv m dv dx dx m dx We can separate variables (and divide ut a cmmn factr f m) t btain the differential equatin : Interatin bth sides between limits: v0 v k v - x (Since we chse up t be psitive, x > x. k v - dx x dx x - x -(x - x ) - v k ln k v - v 0 Evaluatin between limits and usin the prperties f ls ives the requested answer: s distance traveled k ln k - k v - Yu will btain the answer in the frm iven in the bk if yu set dwn as the psitive directin (and s wuld be psitive). 3. Text, prblem p. 9 Slutin : We break the prblem int tw parts, the upward prtin and the dwnward prtin. Fr the upward le, we write : F m dv -m - k m v Fllwin the pattern f the prblem abve, we cnvert dv/ t /dy and et: Interatin yields: + k v Apply the initial cnditin that v when y 0: - dy k ln + k v - y + C k ln + k C
3 phys34-07hw3s.nb 3 and cmbine results t et: y k ln + k v + k v We can use this equatin t find an expressin fr the maximum heiht f the prjectile. Since we knw the prjectile has zer speed at its hihest pint, we can write: y max k ln + kv Nw we cnsider the dwnward prtin. It is easiest t let dwn be the psitive directin, s that ur secnd law becmes: r This interates t: m dy m - k m v - k v dy - k ln - k v y + C Since we are chsin dwn as ur psitive directin, the trip starts at y 0 when v 0, s that we have: which yields : - k ln[] C y k ln - k v Nw, the hihest pint is cmmn t bth the upward and dwnward prtins. This means that their expressin fr the hihest pint must be the same, in ther wrds : r Slvin fr v : y max k ln + kv k ln - k v + k v - k v k k + k
4 4 phys34-07hw3s.nb We are asked t express this in terms f the terminal velcity. We can find the terminal velcity frm the statement f the secnd law fr the dwnward le. Terminal velcity ccurs when the velcity is cnstant, r when: dv 0 - k v 0 v t k Substitutin this int ur velcity expressin yields the desired result: v T v v T + v 4. Text, prblem 36, p. 95. Slutin : We start by writin the equatins f mtin : x (t) cs θ t y (t) h + sin θ t - t T find the rane, we slve fr the time f fliht by settin y0, and then use that time in the x(t) equatin t find rane. y (t) 0 t - sin θ t - h 0 We use the quadratic equatin t find: t sin θ + sin θ + h sin θ + sin θ + h Make sure yu can explain why we chse the plus branch f the slutin. If we substitute this fr time in the x(t) equatin, we et the rane: rane cs θ sin θ + sin θ + h Nte that if we set h 0, we recver the well knwn rane equatin fr a prjectile n level rund with n air frictin. Havin taken several semesters f calculus, yu knw that when yu are asked t maximize, yu set the first derivative f the apprpriate variable t zer. In this case, that means takin the first derivative f rane with respect t θ, which ives: d (rane) dθ
5 phys34-07hw3s.nb 5 -sin θ sin θ + sin θ + h + cs θ cs θ + sin θ + h sin θ cs θ 0 But this equatin is s nn-alebraic that is it nt pssible (r nt easily pssible) t slve fr the value f θ that maximizes rane fr a certain set f parameters. This is an example f a prblem that yu have t slve either by numerical r raphical means. Based n recent class wrk, yu miht think t expand the radical, but fr many values f and h, h v is nt smaller than, s that series expansin desn t help. Let s see hw raphical methds help. We already knw that if h 0 the anle that maximizes rane is 45. Let s cnsider: In[7]: Clear[rane, v0,, h, θ] 9.8;v030;h00; ranev0 Cs[θ] Sin[θ]+ Sin[θ]^ + h v0 ; Plt[rane,{θ,0,π/4}] Out[0] Remember that the hrizntal axis is in radians, s we can see that the maximum rane fr these parameters (launch speed 30 m/s, heiht 00m) is abut 9. We can be mre exact by usin the FindMaximum cmmand: In[]: FindMaximum[rane, θ] Out[] {63.7, {θ 0.55}} And we btain that the maximum rane is 63 meters and the launch anle is 0.5 radians (9.3 ). Or we culd try t differentiate the rane expressin, set it equal t zer, and slve fr θ by usin
6 6 phys34-07hw3s.nb FindRt: In[3]: FindRt[D[rane, θ], {θ, π / 4}] Out[3] {θ 0.55} Technly is yur friend. 5. Suppse the mn is stpped in its rbit at a distance r frm the Earth and beins t fall inward. Determine the time it will take fr the mn t crash int the Earth. Dependin n hw yu apprach this prblem, yu miht encunter an interal where the substitutin r r sin θ is useful. Lk up the values f the apprpriate astrnmical parameters (mass f Earth, averae distance f mn frm Earth, etc.) and calculate the time it will take fr the mn t hit the Earth. Slutin : We bein, as all thins d, with Newtn' a secnd law : F m dv - G m M r where r is the instantaneus distance f the mn frm the Earth. We can et an expressin fr v in terms f r by settin dv/ /dr and: separate variables, interate, and: we knw that v 0 when r r, s and : dr v 0 G M r - G M r G M r + C + C C -G M r v G M r - r T find time f infall, we nte that v dr/, s: dr v dr G M r - r Nw we make use f ur handy substitutin: and r r sin θ dr r sin θ cs θ dθ
7 phys34-07hw3s.nb 7 r - r r sin θ - r - sin θ r sin θ cs θ r sin θ substitutin this int ur interal: r sin θ cs θ dθ G M cs θ r sin θ r : r3/ t sin θ dθ G M we have left ut ur limits f interatin. In r space ur limits are r and 0; these translate int θ0 and θ π/, s ur cmplete interal is: G M r 3 0π/ sin θ dθ π 4 G M r3 Substitutin values (all in MKS (SI) units): G ; M k; r m we find that the time t infall is s r 4.84 days.
1 Course Notes in Introductory Physics Jeffrey Seguritan
Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationPhysics 141H Homework Set #4 Solutions
Phsics 4H Hmewrk Set #4 Slutins Chapter 4: Multiple-chice: 4) The maimum net frce will result when the tw frces are in the same directin. If s, the net frce will hae manitude F + F. The minimum net frce
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationAP Physics Kinematic Wrap Up
AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationPROJECTILES. Launched at an Angle
PROJECTILES Launched at an Anle PROJECTILE MOTION AT AN ANGLE An bject launched int space withut mtie pwer f its wn is called a prjectile. If we nelect air resistance, the nly frce actin n a prjectile
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationCHAPTER 6 -- ENERGY. Approach #2: Using the component of mg along the line of d:
Slutins--Ch. 6 (Energy) CHAPTER 6 -- ENERGY 6.) The f.b.d. shwn t the right has been prvided t identify all the frces acting n the bdy as it mves up the incline. a.) T determine the wrk dne by gravity
More informationMUMBAI / AKOLA / DELHI / KOLKATA / LUCKNOW / NASHIK / GOA / BOKARO / PUNE / NAGPUR IIT JEE: 2020 OLYMPIAD TEST DATE: 17/08/18 PHYSICS SOLUTION ...
MUMBAI / AKOLA / DELHI / KOLKATA / LUCKNOW / NASHIK / GOA / BOKARO / PUNE / NAGPUR IIT JEE: OLYMPIAD TEST DATE: 7/8/8 PHYSICS SOLUTION. (C) Averae acceleratin, vf vi tan tan a t. (B) ds Resistance kv Eqatins
More information. (7.1.1) This centripetal acceleration is provided by centripetal force. It is directed towards the center of the circle and has a magnitude
Lecture #7-1 Dynamics f Rtatin, Trque, Static Equilirium We have already studied kinematics f rtatinal mtin We discussed unifrm as well as nnunifrm rtatin Hwever, when we mved n dynamics f rtatin, the
More informationPhys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1
Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationLHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers
LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the
More informationFall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.
More informationWork, Energy, and Power
rk, Energy, and Pwer Physics 1 There are many different TYPES f Energy. Energy is expressed in JOULES (J 419J 4.19 1 calrie Energy can be expressed mre specifically by using the term ORK( rk The Scalar
More informationENGI 4430 Parametric Vector Functions Page 2-01
ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr
More informationLecture 7: Damped and Driven Oscillations
Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and
More informationAP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) =
P Physics Name Summer ssignment 0 Date I. The P curriculum is extensive!! This means we have t wrk at a fast pace. This summer hmewrk will allw us t start n new Physics subject matter immediately when
More informationChapter 5: Force and Motion I-a
Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse
More informationChapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion.
Chapter Kinematics in One Dimensin Kinematics deals with the cncepts that are needed t describe mtin. Dynamics deals with the effect that frces have n mtin. Tgether, kinematics and dynamics frm the branch
More informationCorrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec
U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.
More informationPhysics 101 Math Review. Solutions
Physics 0 Math eview Slutins . The fllwing are rdinary physics prblems. Place the answer in scientific ntatin when apprpriate and simplify the units (Scientific ntatin is used when it takes less time t
More information37 Maxwell s Equations
37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut
More informationPhysics 123 Lecture 2 1 Dimensional Motion
Reiew: Physics 13 Lecture 1 Dimensinal Mtin Displacement: Dx = x - x 1 (If Dx < 0, the displacement ectr pints t the left.) Aerage elcity: (Nt the same as aerage speed) a x t x t 1 1 Dx Dt slpe = a x 1
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationKinetics of Particles. Chapter 3
Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between
More information20 Faraday s Law and Maxwell s Extension to Ampere s Law
Chapter 20 Faraday s Law and Maxwell s Extensin t Ampere s Law 20 Faraday s Law and Maxwell s Extensin t Ampere s Law Cnsider the case f a charged particle that is ming in the icinity f a ming bar magnet
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,
More informationFunction notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property
Functin ntatin & cmpsite functins Factring Dividing plynmials Remainder therem & factr prperty Can d s by gruping r by: Always lk fr a cmmn factr first 2 numbers that ADD t give yu middle term and MULTIPLY
More informationRigid Body Dynamics (continued)
Last time: Rigid dy Dynamics (cntinued) Discussin f pint mass, rigid bdy as useful abstractins f reality Many-particle apprach t rigid bdy mdeling: Newtn s Secnd Law, Euler s Law Cntinuus bdy apprach t
More informationSolution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More informationLecture 2: Single-particle Motion
Lecture : Single-particle Mtin Befre we start, let s l at Newtn s 3 rd Law Iagine a situatin where frces are nt transitted instantly between tw bdies, but rather prpagate at se velcity c This is true fr
More informationCalculus Placement Review. x x. =. Find each of the following. 9 = 4 ( )
Calculus Placement Review I. Finding dmain, intercepts, and asympttes f ratinal functins 9 Eample Cnsider the functin f ( ). Find each f the fllwing. (a) What is the dmain f f ( )? Write yur answer in
More informationMath 105: Review for Exam I - Solutions
1. Let f(x) = 3 + x + 5. Math 105: Review fr Exam I - Slutins (a) What is the natural dmain f f? [ 5, ), which means all reals greater than r equal t 5 (b) What is the range f f? [3, ), which means all
More information1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?
1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is
More informationThis section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.
Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus
More informationPhysics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1
Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationEquilibrium of Stress
Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small
More informationYeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN
Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402
More information[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )
(Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well
More informationStudy Guide Physics Pre-Comp 2013
I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationKinematics. Describing Motion. Reference Frames. Measurements of position, distance or speed must be with respect to a frame of reference.
Kinematics Describing Mtin Reference Frames Measurements f psitin, distance r speed must be with respect t a frame f reference. What is the speed f a persn with respect t the grund if she walks tward the
More informationCambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid
More informationEXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017
OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationSAFE HANDS & IIT-ian's PACE EDT-04 (JEE) Solutions
ED- (JEE) Slutins Answer : Optin () ass f the remved part will be / I Answer : Optin () r L m (u csθ) (H) Answer : Optin () P 5 rad/s ms - because f translatin ωr ms - because f rtatin Cnsider a thin shell
More informationi-clicker Question How many beans are in the 900 ml beaker? A. Fewer than 1000 B C D E.
i-clicker Questin Hw many beans are in the 900 ml beaker? A. Fewer than 1000 B. 1000-1500 C. 1500-000 D. 000-500 E. Mre than 500 Reiew: Physics 13 Lecture 1 Dimensinal Mtin Displacement: Dx = x - x 1 (If
More informationL a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.
ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake
More informationAP Physics Laboratory #4.1: Projectile Launcher
AP Physics Labratry #4.1: Prjectile Launcher Name: Date: Lab Partners: EQUIPMENT NEEDED PASCO Prjectile Launcher, Timer, Phtgates, Time f Flight Accessry PURPOSE The purpse f this Labratry is t use the
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationChapter II Newtonian Mechanics Single Particle
Chapter II Newtnian Mechanics Sinle Particle Recended prbles: -, -5, -6, -8, -9, -, -, -, -6, -, -, -, -5, -6, -7, -9, -30, -3, -3, -37, -38, -39, -, -, -3, -, -7, -5, -5, -53, -5.. . Newtn s Laws The
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationTrigonometry, 8th ed; Lial, Hornsby, Schneider
Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the
More informationInformation for Physics 1201 Midterm I Wednesday, February 20
My lecture slides are psted at http://www.physics.hi-state.edu/~humanic/ Infrmatin fr Physics 1201 Midterm I Wednesday, February 20 1) Frmat: 10 multiple chice questins (each wrth 5 pints) and tw shw-wrk
More informationPreparation work for A2 Mathematics [2017]
Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will
More informationES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER
ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24
More informationHess Law - Enthalpy of Formation of Solid NH 4 Cl
Hess Law - Enthalpy f Frmatin f Slid NH 4 l NAME: OURSE: PERIOD: Prelab 1. Write and balance net inic equatins fr Reactin 2 and Reactin 3. Reactin 2: Reactin 3: 2. Shw that the alebraic sum f the balanced
More informationEXAM #1 PHYSICAL SCIENCE 103 Spring, 2016
OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a
More informationQ x = cos 1 30 = 53.1 South
Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is
More informationPhysics 321 Solutions for Final Exam
Page f 8 Physics 3 Slutins fr inal Exa ) A sall blb f clay with ass is drpped fr a height h abve a thin rd f length L and ass M which can pivt frictinlessly abut its center. The initial situatin is shwn
More informationExample 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W
Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = 60 9. 81 =
More information= m. Suppose the speed of a wave on a string is given by v = Κ τμ
Phys101 First Majr-11 Zer Versin Sunday, Octber 07, 01 Page: 1 Q1. Find the mass f a slid cylinder f cpper with a radius f 5.00 cm and a height f 10.0 inches if the density f cpper is 8.90 g/cm 3 (1 inch
More informationf = µ mg = kg 9.8m/s = 15.7N. Since this is more than the applied
Phsics 141H lutins r Hmewrk et #5 Chapter 5: Multiple chice: 8) (a) he maimum rce eerted b static rictin is µ N. ince the blck is resting n a level surace, N = mg. the maimum rictinal rce is ( ) ( ) (
More informationPreparation work for A2 Mathematics [2018]
Preparatin wrk fr A Mathematics [018] The wrk studied in Y1 will frm the fundatins n which will build upn in Year 13. It will nly be reviewed during Year 13, it will nt be retaught. This is t allw time
More informationRevised 2/07. Projectile Motion
LPC Phsics Reised /07 Prjectile Mtin Prjectile Mtin Purpse: T measure the dependence f the range f a prjectile n initial elcit height and firing angle. Als, t erif predictins made the b equatins gerning
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationCop yri ht 2006, Barr Mabillard.
Trignmetry II Cpyright Trignmetry II Standards 006, Test Barry ANSWERS Mabillard. 0 www.math0s.cm . If csα, where sinα > 0, and 5 cs α + β value f sin β, where tan β > 0, determine the exact 9 First determine
More informationStudy Guide: PS. 10 Motion, Forces, Work & Simple Machines DESCRIBING MOTION SPEED
DESCRIBING MOTION Distance: hw far smething has mved; SI unit meters (m) Reference pint: nn-mving bject used as a cmparisn pint t detect an bject s mtin. Displacement: the distance between the starting
More informationPutting Scientific Notation to Work
10 Putting Scientific Ntatin t Wrk Physics deals with sme very large and very small numbers. T wrk with such numbers, yu use scientific ntatin. Scientific ntatin is expressed as a number multiplied by
More information14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?
Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes
More information14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?
Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which
More informationBeing able to connect displacement, speed, and acceleration is fundamental to working
Chapter The Big Three: Acceleratin, Distance, and Time In This Chapter Thinking abut displacement Checking ut speed Remembering acceleratin Being able t cnnect displacement, speed, and acceleratin is undamental
More informationCHAPTER 4 Dynamics: Newton s Laws of Motion /newtlaws/newtltoc.html
CHAPTER 4 Dynamics: Newtn s Laws f Mtin http://www.physicsclassrm.cm/class /newtlaws/newtltc.html Frce Newtn s First Law f Mtin Mass Newtn s Secnd Law f Mtin Newtn s Third Law f Mtin Weight the Frce f
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationConceptual Dynamics SDC. An Interactive Text and Workbook. Kirstie Plantenberg Richard Hill. Better Textbooks. Lower Prices.
Cnceptual Dynamics An Interactive Text and Wrkbk Kirstie Plantenberg Richard Hill SDC P U B L I C AT I O N S Better Textbks. Lwer Prices. www.sdcpublicatins.cm Pwered by TCPDF (www.tcpdf.rg) Visit the
More informationExaminer: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data
Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed
More informationUNIT 1 COPLANAR AND NON-COPLANAR FORCES
UNIT 1 COPLANA AND NON-COPLANA FOCES Cplanar and Nn-Cplanar Frces Structure 1.1 Intrductin Objectives 1. System f Frces 1.3 Cplanar Frce 1.3.1 Law f Parallelgram f Frces 1.3. Law f Plygn f Frces 1.3.3
More informationSolutions to the Extra Problems for Chapter 14
Slutins t the Extra Prblems r Chapter 1 1. The H -670. T use bnd energies, we have t igure ut what bnds are being brken and what bnds are being made, s we need t make Lewis structures r everything: + +
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationSection 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law
Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential
More informationFaculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm
Faculty f Engineering and Department f Physics Engineering Physics 131 Midterm Examinatin February 27, 2006; 7:00 pm 8:30 pm N ntes r textbks allwed. Frmula sheet is n the last page (may be remved). Calculatrs
More informationi-clicker i-clicker Newton s Laws of Motion First Exam Coming Up! Components of Equation of Motion
First Eam Cming Up! Sunda, 1 Octber 6:10 7:30 PM. Lcatins t be psted nline. Yes this is a Sunda! There will be 17 questins n eam. If u have a legitimate cnflict, u must ask Prf. Shapir b Oct. 8 fr permissin
More informationThree charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
More informationTrigonometric Ratios Unit 5 Tentative TEST date
1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin
More informationMaterials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion
Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential
More informationPHYSICS LAB Experiment 10 Fall 2004 ROTATIONAL DYNAMICS VARIABLE I, FIXED
ROTATIONAL DYNAMICS VARIABLE I, FIXED In this experiment we will test Newtn s Secnd Law r rtatinal mtin and examine hw the mment inertia depends n the prperties a rtating bject. THE THEORY There is a crrespndence
More informationPlan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations
STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.
More informationProjectile Motion. What is projectile? Projectile -Any object which projected by some means and continues to move due to its own inertia (mass).
Prjectile Mtin AP Phyic B What i prjectile? Prjectile -Any bject which prjected by me mean and cntinue t me due t it wn inertia (ma). 1 Prjectile me in TWO dimenin Since a prjectile me in - dimenin, it
More informationENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lecture 11: 2D and 3D Particle Equilibrium Shawn Kenny, Ph.D., P.Eng. Assistant Prfessr aculty f Engineering and Applied Science Memrial University f Newfundland spkenny@engr.mun.ca
More informationLifting a Lion: Using Proportions
Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They
More information1/2 and e0 e s ' 1+ imm w 4 M s 3 πρ0 r 3 m. n 0 ktr. .Also,since n 0 ktr 1,wehave. 4 3 M sπρ 0 r 3. ktr. 3 M sπρ 0
Chapter 6 6.1 Shw that fr a very weak slutin drplet (m 4 3 πr3 ρ 0 M s ), (6.8) can be written as e 0 ' 1+ a r b r 3 where a σ 0 /n 0 kt and b imm w / 4 3 M sπρ 0. What is yur interpretatin f thecnd and
More informationLead/Lag Compensator Frequency Domain Properties and Design Methods
Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin
More information