Physics 141H Homework Set #4 Solutions
|
|
- Austen Williamson
- 5 years ago
- Views:
Transcription
1 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 will ccur if the tw frces are in ppsite directins. In this case, the net frce will hae manitude F - F. Fr an ther relatie directin f the tw frces, the manitude f the net frce will be in between these alues. Thus, (C) is the crrect answer. 9) a) Here s what we knw: the rane is 40 miles, and the shell is launched with an initial anle f 45 (which ies the lnest rane fr a ien initial elcit). We als knw frm smmetr that the shell reaches its maimum heiht 0 miles frm the un (i.e., halfwa t the taret). The heiht at this pint is ien b t sinφ t. We als knw that at the maimum heiht, the cmpnent f elcit is 0. This lets us find t: sinφ t 0 sinφ t Pluin this back int ur equatin fr, we find that ( sinφ ). Nw we cmpare this heiht t the hrizntal distance traeled in the same time. This is csφ sinφ ien b t csφ. Fr the special case f φ 45, sinφ csφ, s we find that: sin φ In ther wrds, the maimum heiht is ½ f the hrizntal distance traeled t the maimum, r abut 0 miles in this case. (E)
2 ( ) sinφ b) Abe we fund that the maimum heiht is ien b. We knw φ ο is 45, s sin φ. Since we fund the maimum t be 0 miles, we hae: ( )( ) 4 3ft/s 0mi ( )( ) 3ft/s 5,800ft 600ft/s Chice (B) is the best apprimatin. 3) The parachute adds a dra frce in the ppsite directin f rait. Assumin this frce is reater in manitude than rait (which had better be true r else the parachutist will keep acceleratin dwnward!), the parachutist will under upward acceleratin immediatel after the chute pens. Nte thuh, that his elcit will still be dwnward. Eentuall the parachutist s dwnward elcit will decrease t er near the terminal elcit, as which pint the dra frce f the air n the parachute will eactl balance rait. Frm then n, the parachutist will drift t Earth at a cnstant (hpefull safe!) elcit. Chice (A) best represents this mtin. Questins: 7) a) N b) Let s assume the rpe were hrizntal. Then the free-bd diaram fr the weiht wuld be: T T m We see that rait acts in the directin, but bth tensins hae nl cmpnents. Therefre the weiht wuld accelerate dwnwards. T aid this, the tensin in the rpe needs t hae a cmpnent, which is nl pssible if the rpe is nt eactl hrizntal. ) Since the cmpnent f the elcit is cnstant, the ttal manitude f elcit is reatest when the cmpnent has the reatest abslute alue, and least when the cmpnent has the least abslute alue. The speed in is reatest just after the particle is launched (assumin it was launched upwards!) and just befre it hits the rund. It reaches its minimum at the maimum heiht.
3 5) a) This is a trick questin! Since all three prjectiles rise t the same heiht, the must all hae the same fliht time. (Remember that the mtin in is independent f that in.) b) A trick aain! All f them hae the same initial elcit in the directin. c) Since all three particles sta in the air fr an equal amunt f time, the elcit is cnstant thruhut the fliht, and particle c es the farthest in befre landin, particle c must hae the reatest hrizntal elcit cmpnent. d) B the same tken, particle a has the smallest hrizntal elcit. Since the ertical elcit cmpnent is the same fr all three particles, this als implies that particle a has the smallest speed. 8) Nt at all. Cnsider the mtin f the particle in and as a functin f time (assume 0 at t 0): t,, t t The secnd equatin tells us that the heiht s. time raph is a parabla. Slin the upper equatin fr t and pluin that int the lwer ne ies us as a functin f : t,,,, Nw we see that the heiht s. distance raph is als a parabla bth are cnsequences f the same phsics.
4 Eercises: 7) a) The free-bd diaram fr the blck is: N P θ m Takin the cmpnents f each ectr, we can find the net frce in the and directins: F P csθ F N + Psinθ m We assume that the flr is strn enuh that the blck can t fall thruh. Therefre F can nt be less than 0, and the flr will pride a nrmal frce lare enuh t uarantee this. In ther wrds, if m is reater than the nrmal frce will make up the difference; if m is less than Psinθ there will be n nrmal frce and the blck will eperience a net frce with a psitie cmpnent. In this prblem, Psinθ N sin5 5.N, while m 5.k 9.8m/s 50N. Since m is reater than Psinθ, a nrmal frce f 46.9N will be applied b the flr, and F will equal 0. S, the net frce n the blck is F P cs θi, and the acceleratin is: F m P csθ m a i.m/s i b) The blck will lift ff the flr when the nrmal frce is 0. As discussed abe, this will happen when Psinθ m, s ( 5.k)( 9.8m/s ) m P 8N sinθ sin 5 c) Just befre the blck lifts ff the flr the net frce will still be nl in the directin, and the acceleratin will be:
5 P csθ 8N cs 5 m 5.k a i i.0m/s i 9) Let s start with the free-bd diaram fr the car: T 7 N m 8 With the aes chsen as shwn, the car mes nl in the directin. The net frce is thus: F T cs 7 m sin8 Since we want the maimum distance the car can in 7.5s, we need t appl the maimum pssible frce. S set T t the breakin strenth f the rpe, 4.6kN. With this we find: F 4.6kN cs 7 00k 9.8m/s sin8 4.kN 3.6kN 500N This means that the car s acceleratin is it traels in the first 7.5s is: F 500N 0.4m/s a, s that the distance m 00k at.5m 7) The heiht is ien b t t,. Takin the ais hrizntal, this becmes t t time and set it equal t 0 (phsicall, this just means that the elcit is 0 at the maimum heiht): sinφ. T find the maimum alue, we take the deriatie with respect t
6 d sinφ t 0 dt sinφ t Usin this time in ur equatin fr, we find that: sinφ sinφ ma sinφ ( sinφ ) ) Fr simplicit, we take 0 at the mment the ball is released. The basket is three feet abe the release pint and 3 ft awa hrizntall, s we want 3ft when 3ft: t cs55 3ft t t sin 55 We can sle the first equatin fr t and plu int the secnd: 3ft 3ft t cs55 sin 55 3ft 3ft 3ft 3ft 3ft 9ft 3ft 3ft 6ft 3ft 3ft 59ft /s ( 3ft ) 3ft/s ( 3ft ) 3ft/s Prblems: 3) a) Start with the free-bd diaram fr the rcket:
7 T 58 m The net frce n the rcket while the enine is firin is: F cs58 6.kN cs58 3.4kN T F T m sin kN 3030k 9.8m/s.kN Therefre, a a 3.4kN 0.7m/s 3030k.kN 7.3m/s 3030k Since the rcket was launched at rest frm 0, its heiht when the rcket burns ut is ien b: a 7.3m/s ( 48s ) t 8.4km b) After the enine burns ut, the rcket is a prjectile. At the mment the rcket burns ut: 8.4km a 0.7m/s ( 48s ) t.3km a t 7.3m/s 48s 350m/s a t 0.7m/s 48s 53m/s We can nw find the time between the enine burnut and the rcket returnin t 0:
8 Applin the quadratic frmula, we find: t t +, 0 ± 4 t,, ( ) 350m/s ± 350m/s m/s 8.4km t 9.8m/s 90.4s r -9.0s We nl care abut the psitie-time slutin (e.. the time after the enine burns ut). We can nw find the hrizntal distance: +, t.3km + 53m/s 90.4s 58.7km 6) a) We hae alread shwn (Eercise 7) that a prjectile reaches a maimum heiht f: ma ( sinφ ) It reaches this pint halfwa thruh its trip; hence the alue fr which ma is reached is half the rane, r (usin Equatin 4-4 frm the tet): ma R sin φ sinφ csφ Therefre, tanθ ( sinφ ) ma ma tan φ sinφ sinφ csφ csφ
9 b) If φ 45, tanφ, s: θ tan 7 9) Fr the ftball t clear the crssbar, must be reater than 3.44m when 50m. This time is ien b: The psitin at that time is:, t t csφ 50m 50m t csφ, t t t sinφ t 3.44m 50m 50m sinφ 3.44m csφ csφ sinφ 50m 50m 3.44m csφ csφ sinφ 50m csφ 5m/s csφ sinφ 0m 50m 3.44m csφ cs φ 50m 9.8m/s 3.44m -3.44m cs φ+50m sinφ csφ 0m 0 cs φ The abe equatin will be true wheneer the numeratr n the left-hand side is 0: -3.44m cs φ+50m sinφcsφ 0m 0 50m cs φ csφ 3.44m cs φ + 0m Squarin bth sides ies: ( ) 500m cs φ cs φ.8m cs φ + 38m cs φ + 400m 4 4 5cs φ 36cs φ
10 Nte that ur units (m ) hae cancelled and can be drpped. This makes sense, since the anle needed desn t depend n hw we measure distance! We can appl the quadratic equatin t sle fr cs φ : cs ( )( ) 36 ± φ 0. r csφ 0.47 r 0.85 φ 6 r 3 ) The manitude f the displacement ectr is ien b: r ( t) r( t) ( t) + ( t) T determine if r is increasin r decreasin, we cmpute: d d + dr dt dt dt S the cnditin fr r alwas increasin is + 0. Thus we want t find the anle f launch such that the abe quantit equals 0 at ne pint durin the fliht. Pluin in what we knw abut,,, and fr prjectile mtin, this becmes: cs cs + sin sin t cs φ tsin φ t sinφ + t t ( sin φ cs φ ) + t sinφ t ( t φ )( φ ) t φ t ( φ t) We can cancel ne t eerwhere (and use a tri identit) t btain: t sinφ t
11 This is a quadratic equatin in t. In eneral, an equatin f the frm a + b + c 0 will hae a slutin when b 4ac 0 (as can be seen frm the quadratic frmula). Applin that t ur prblem, we want the case when we just barel hae a slutin, b 4ac 0, r: 9 sin φ Nw we see that all the s and s cancel ut, which is d news ur answer wn t depend n what planet we re n, nr n hw fast the bject is launched. After the cancellatins, we hae: Chapter 5: 9 sin φ sin φ 9 sinφ 0.94 φ 70 Multiple chice: ) The tensin in each rpe must be 0N t supprt the weiht n each side, and the sprin scale measures the frce applied b the sprin. T see what this is, make a freebd diaram f the scale s hk: T F S Since we knw that the scale is nt acceleratin, the sprin frce F S must be just lare enuh t cancel the tensin, r 0N (C). 5) Let s make a free-bd diaram fr a little piece f the rpe: T m The weiht bein supprted is that f the little bit f rpe, plus all the rpe belw it. At the bttm f the rpe, this weiht is er small (0 in the limit that the little bit f rpe
12 we cnsider is infinitel small), s the tensin is 0. At the tp, the full weiht f the rpe must be supprted, s the tensin is 0.98N. (D) Eercises: 3) a) The free-bd diaram fr the lamp is: T m If the eleatr is deceleratin, the lamp must eperience a net upwards frce: net ( ) F T m j maj T m ma m( a + ) T T 89N m 7.3k a +.4m/s + 9.8m/s b) Trick questin aain! The net acceleratin was.4m/s upwards in part (a), and we alread knw that the tensin is 89 N. 5) a) We start with the free-bd diarams fr the sandba and man: Sandba: Man: T T m S m M
13 Nte that T is the same in bth diarams (the rpe can nl eert ne tensin). Als, all the mtin is in the directin, which is cnenient. We can find the acceleratin f bth bjects: a a F net,s S ms F net,m M mm T ms j m S T mm j m M Since the strin can t be stretched, bth the man and the sandba hae the same manitude f acceleratin but in different directins. S we knw that: T ms mm T m m S m T m m m m m T ( ) T m + m m m M M S M S M S M S S M ( )( )( ) m 74k 0k 9.8m/s SmM T 870N m + m 74k + 0k With this, we can find the man s acceleratin: T mm am j m This is dwnward, as we suspected. M S M 870N 0k 9.8m/s j.9m/s j 0k We can nw find ut hw ln it takes the man t fall m (startin frm rest): His elcit upn landin is: at (.9m/s ) m 4m t 3.6s.9m/s t m
14 at.9m/s 3.6s 6.8m/s b) If the man attempts t climb up the rpe, he will pull it er the pulle faster. This means that the acceleratin f the sandba must increase, which in turn implies that the tensin in the rpe must increase. Since the tensin acts aainst rait, increasin it will reduce the man s acceleratin.
PHYS 314 HOMEWORK #3
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
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 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 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 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 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 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 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 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 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 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 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 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 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 information1 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 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 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 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 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 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 informationPhysics 1200 Mechanics, Kinematics, Fluids, Waves
Physics 100 Mechanics, Kinematics, Fluids, Waes Lecturer: Tm Humanic Cntact inf: Office: Physics Research Building, Rm. 144 Email: humanic@mps.hi-state.edu Phne: 614 47 8950 Office hurs: Tuesday 3:00 pm,
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 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 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 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 informationAs we have already discussed, all the objects have the same absolute value of
Lecture 3 Prjectile Mtin Lst time we were tlkin but tw-dimensinl mtin nd intrduced ll imprtnt chrcteristics f this mtin, such s psitin, displcement, elcit nd ccelertin Nw let us see hw ll these thins re
More informationi-clicker!! x 2 lim Lecture 3 Motion in 2- and 3-Dimensions lim REVIEW OF 1-D MOTION
Lecture 3 Mtin in - and 3-Dimensins REVIEW OF -D MOTION TODY: LSTCHNCETOMKEUPTHEPHYSICS PRETEST(u get pints fr cmpleting the pre and pst tests) Where: SERC 6 (SEC 6) When: Yucanarrieantime3:0pm 6:30 pm
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 informationPhy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1
Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.
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 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 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 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 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 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 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 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 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 informationChapter 4 Motion in Two and Three Dimensions
Chapte 4 Mtin in Tw and Thee Dimensins In this chapte we will cntinue t stud the mtin f bjects withut the estictin we put in chapte t me aln a staiht line. Instead we will cnside mtin in a plane (tw dimensinal
More informationPre-Calculus Individual Test 2017 February Regional
The abbreviatin NOTA means Nne f the Abve answers and shuld be chsen if chices A, B, C and D are nt crrect. N calculatr is allwed n this test. Arcfunctins (such as y = Arcsin( ) ) have traditinal restricted
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 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 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 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 informationWYSE Academic Challenge Regional Mathematics 2007 Solution Set
WYSE Academic Challenge Reginal Mathematics 007 Slutin Set 1. Crrect answer: C. ( ) ( ) 1 + y y = ( + ) + ( y y + 1 ) = + 1 1 ( ) ( 1 + y ) = s *1/ = 1. Crrect answer: A. The determinant is ( 1 ( 1) )
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 informationPRE-CALCULUS B FINAL REVIEW NAME Work out problems in your notebook or on a separate piece of paper.
PRE-CALCULUS B FINAL REVIEW NAME Wrk ut prblems in yur ntebk r n a separate piece f paper. CHAPTER 5 Simplify each t ne trig wrd r a number: tan (1) sec sec () sin ct + 1 + cs + ( sin cs ) () sin - cs
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 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 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 informationName: Date: AP Physics 1 Per. Vector Addition Practice. 1. F1 and F2 are vectors shown below (N is a unit of force, it stands for Newton, not north)
ame: Date: AP Phsics 1 Per. Vectr Additin Practice 1. F1 and F are ectrs shwn belw ( is a unit f frce, it stands fr ewtn, nt nrth) F1 = 500 F = 300 40 50 a) Add the ectrs F1 and F: F1+F = 1. Add graphicall
More informationCLASS XI SET A PHYSICS
PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the
More informationIntroduction to Spacetime Geometry
Intrductin t Spacetime Gemetry Let s start with a review f a basic feature f Euclidean gemetry, the Pythagrean therem. In a twdimensinal crdinate system we can relate the length f a line segment t the
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 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 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 information2015 Regional Physics Exam Solution Set
05 Reginal hysics Exa Slutin Set. Crrect answer: D Nte: [quantity] dentes: units f quantity WYSE Acadeic Challenge 05 Reginal hysics Exa SOLUTION SET r F r a lengthass length / tie ass length / tie. Crrect
More informationPhys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively.
More informationPHYSICS 151 Notes for Online Lecture #23
PHYSICS 5 Ntes fr Online Lecture #3 Peridicity Peridic eans that sething repeats itself. r exaple, eery twenty-fur hurs, the Earth aes a cplete rtatin. Heartbeats are an exaple f peridic behair. If yu
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 information39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution
39th Internatinal Physics Olympiad - Hani - Vietnam - 8 Theretical Prblem N. /Slutin Slutin. The structure f the mrtar.. Calculating the distance TG The vlume f water in the bucket is V = = 3 3 3 cm m.
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 informationTrigonometry Semester Review a pam productions review packet. 9. In the diagram, circle P is a unit circle. If point B is located at 2 π, what are the
Trignmetr Semester Review a pam prductins review packet. Find the degree measure f an angle that measures 7 6 radians.. What is the radian measure f an angle that has degree measure 675?. What is the radian
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 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 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 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 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 informationDINGWALL ACADEMY NATIONAL QUALIFICATIONS. Mathematics Higher Prelim Examination 2010/2011 Paper 1 Assessing Units 1 & 2.
INGWLL EMY Mathematics Higher Prelim Eaminatin 00/0 Paper ssessing Units & NTIONL QULIFITIONS Time allwed - hur 0 minutes Read carefull alculatrs ma NOT be used in this paper. Sectin - Questins - 0 (0
More informationCHAPTER 1 -- MATH REVIEW
Slutins--Ch. 1 (Math Review) CHAPTER 1 -- MATH REVIEW 1.1) Bth Parts a and b are straight vectr additin, graphical stle. Yu need a centimeter stick and prtractr t d them. a.) In this case, the velcit cmpnent
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 informationHere is instructions on how to use the simulation program.(the first simulation is used in question 5)
Larmr Precessin Tutrial Here is instructins n hw t use the simulatin prgram.(the first simulatin is used in questin 5). Duble click the file sp_spins. On the tp f the new windw, click File Open Internal
More informationFundamental Concepts in Structural Plasticity
Lecture Fundamental Cncepts in Structural Plasticit Prblem -: Stress ield cnditin Cnsider the plane stress ield cnditin in the principal crdinate sstem, a) Calculate the maximum difference between the
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 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 information205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3
ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at
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 informationChapter 9 Vector Differential Calculus, Grad, Div, Curl
Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields
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 informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationWYSE Academic Challenge Regional Physics 2008 SOLUTION SET
WYSE cdemic Chllenge eginl 008 SOLUTION SET. Crrect nswer: E. Since the blck is mving lng circulr rc when it is t pint Y, it hs centripetl ccelertin which is in the directin lbeled c. Hwever, the blck
More informationProblem Set: Fall #1 - Solutions
Problem Set: Fall #1 - Solutions 1. (a) The car stops speedin up in the neative direction and beins deceleratin, probably brakin. (b) Calculate the averae velocity over each time interval. v av0 v 0 +
More informationChapter 2. Coulomb s Law and Electric Field Intensity
Chapter. Culmb s Law and lectric Field Intensit Hat; 9/9/009; -1.1 The perimental Law f Culmb Frm the eperiment the frce between tw charged bjects is QQ F k : Frce in Newtn (N) where Q1 and Q : Charges
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 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 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 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 informationLim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?
THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,
More informationHigher Mathematics Booklet CONTENTS
Higher Mathematics Bklet CONTENTS Frmula List Item Pages The Straight Line Hmewrk The Straight Line Hmewrk Functins Hmewrk 3 Functins Hmewrk 4 Recurrence Relatins Hmewrk 5 Differentiatin Hmewrk 6 Differentiatin
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 informationChapter 5: Diffusion (2)
Chapter 5: Diffusin () ISSUES TO ADDRESS... Nn-steady state diffusin and Fick s nd Law Hw des diffusin depend n structure? Chapter 5-1 Class Eercise (1) Put a sugar cube inside a cup f pure water, rughly
More informationPHYSICS Unit 3 Trial Examination
STAV Publishing Pty Ltd 005 PHYSICS Unit 3 Trial Examinatin SOLUTIONS BOOK Published by STAV Publishing Pty Ltd. STAV Huse, 5 Munr Street, Cburg VIC 3058 Australia. Phne: 6 + 3 9385 3999 Fax: 6 + 3 9386
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 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 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 informationPhysics 12 Assignment KEY Equilibrium & 2-D Dynamics
Physics Assignment KEY Equilibrium & -D Dynamics. Deine the llwing terms: Newtn s laws mtin - three undamental laws mtin which are the basis Newtnian mechanics are: ) an bject will remain at rest r in
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 informationChapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
More information