# Physics 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn in the following problems from Chapter 4 Knight

Size: px
Start display at page:

Download "Physics 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn in the following problems from Chapter 4 Knight"

Transcription

1 Physcs 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn n the ollowng problems rom Chapter 4 Knght Conceptual Questons: 8, 0, ; 4.8. Anta s approachng ball and movng away rom where ball was thrown, so ball was thrown wth the greater speed. Ths can be determned numercally as well, treatng Anta as a movng reerence rame wth respect to the ground, so vanta vball 5 m/s. For ball, Anta measures 0 m/s v 5 m/s v 5 m/s. For ball, 0 m/s v 5 m/s v 5 m/s. So ball was thrown wth greater speed Zach should throw hs book outward and toward the back o the car. The book has the same ntal velocty as do Zach and the car, so throw or wll cause the book to land beyond the drveway n the same drecton as the car s travelng. 4.. Snce Zach and Yvette are travelng at the same speed they share the same reerence rame, so Zach should throw the book straght to her (throw.)

2 Problems: 0,, 3, 37, 47, 53, , Model: Use the partcle model or the puck. Solve: Snce the vx vs t and vy vs t graphs are straght lnes, the puck s undergong constant acceleraton along the x- and y- axes. The components o the puck s acceleraton are dvx vx 0 m/s ( m/s) ax.0 m/s dt t 0 s 0 s (0 m/s 0 m/s) ay m/s (0 s 0 s) x y The magntude o the acceleraton s a a a. m/s. Assess: The acceleraton s constant, so the computatons above apply to all tmes shown, not just at 5 s. The puck turns around at t 5 s n the x drecton, and constantly accelerates n the y drecton. Travelng 50 m rom the startng pont n 0 s s reasonable. 4.. Model: Assume the partcle model or the ball, and apply the constant-acceleraton knematc equatons o moton n a plane. Vsualze: Solve: (a) We know the velocty v ˆ ˆ (.0.0 j) m/s at t s The ball s at ts hghest pont at t s, so vy 0 m/s. The horzontal velocty s constant n projectle moton, so vx 0 m/s at all tmes. Thus v ˆ 0 m/s at t s We can see that the y-component o velocty changed by v y.0 m/s between t s and t s Because a y s constant, vy changes by.0 m/s n any -s nterval. At t 3 s, v y s.0 m/s less than ts value o 0 at value o.0 m/s at 0 t s Consequently, at t 0 s, t s At t 0 s, v y must have been.0 m/s more than ts v (.0ˆ 4.0 ˆj ) m/s, At t s, v() (.0ˆ.0 ˆj ) m/s At t s, v() (.0ˆ 0.0 ˆj ) m/s At t 3 s, v(3) (.0ˆ.0 ˆj ) m/s (b) Because v s changng at the rate.0 m/s per s, the y-component o acceleraton s y projectle moton, so the value o g on Exdor s g 0 m/s (c) From part (a) the components o v 0 are v0x.0 m/s and v0y 4.0 m/s. Ths means ay.0 m/s. But ay g or v0 y 4.0 m/s tan tan 63 above x v0x.0 m/s Assess: The y-component o the velocty vector decreases rom.0 m/s at m/s. All the other values obtaned above are also reasonable. t s to 0 m/s at t s Ths gves an acceleraton o

3 4.3. Model: The bullet s treated as a partcle and the eect o ar resstance on the moton o the bullet s neglected. Vsualze: Solve: (a) Usng 0 0y 0 y 0 y y v ( t t ) a ( t t ), we obtan t t (.0 0 m) 0 m 0 m ( 9.8 m/s )( 0 s) s s (b) Usng 0 0x 0 x 0 x x v ( t t ) a ( t t ), (50 m) 0 m v ( s 0 s) 0 m v 78 m/s 780 m/s 0x 0x Assess: The bullet alls cm durng a horzontal dsplacement o 50 m. Ths mples a large ntal velocty, and a value o 78 m/s s understandable Model: Assume the spaceshp s a partcle. The acceleraton s constant, so we can use the knematc equatons. Vsualze: We apply the knematc equaton s s v0t a ( t ) n each drecton. t 35 mn 00 s. Solve: 5 x km (9.5 km/s)(00 s) (0.040 km/s )(00 s) s km 5 y km (0 km/s)(00 s) (0 km/s )(00 s) s km 5 z.0 0 km (0 km/s)(00 s) (.00 km/s )(00 s) s km 3 Roundng to two sg gs gves r (70ˆ 400 ˆj 60 kˆ ) 0 km. Assess: The y-component ddn t change because there was no velocty or acceleraton n the y-drecton.

4 4.47. Model: We wll use the partcle model and the constant-acceleraton knematc equatons n a plane. Vsualze: Solve: The x-and y-equatons o the ball are From the y-equaton, B 0B ( 0B) x( B 0B) ( B) x( B 0B) 65 m 0 m ( 0B cos30 ) B 0 m B 0B ( 0B) y( B 0B) ( B) y( B 0B) 0 m 0 m ( 0B sn30 ) B ( ) B x x v t t a t t v t y y v t t a t t v t g t Substtutng ths nto the x-equaton yelds v 0B gtb (sn30 ) gcos30t 65 m sn30 t.77 s For the runner: 0 m tr.50 s 8.0 m/s Thus, the throw s too late by 0.7 s. Assess: The tmes nvolved n runnng the bases are small, and a tme o.5 s s reasonable. B B Model: We dene the x-axs along the drecton o east and the y-axs along the drecton o north.

5 Solve: (a) The kayaker s speed o 3.0 m/s s relatve to the water. Snce he s beng swept toward the east, he needs to pont at angle west o north. Hs velocty wth respect to the water s v (3.0 m/s, west o north) ( 3.0sn m/s) ˆ (3.0cos m/s) ˆj KW We can nd hs velocty wth respect to the earth v KE v KW v WE, wth v ˆ WE (.0 m/s). Thus v (( 30sn 0) m/s) ˆ (3.0cos m/s) ˆj KE In order to go straght north n the earth rame, the kayaker needs ( v ) 0. Ths wll be true x KE.0.0 sn sn Thus he must paddle n a drecton 4 west o north. (b) Hs northward speed s vy 3.0 cos(4.8 ) m/s.36 m/s. The tme to cross s The kayaker takes 45 s to cross. 00 m t 44.7 s.36 m/s Model: Mke and Nancy concde at t 0 s Use subscrpts B, M, N or the ball, Mke, and Nancy respectvely. Solve: (a) Accordng to the Gallean transormaton o velocty v BN v BM v MN. Mke throws the ball wth velocty v ˆ ˆ BM ( m/s)cos63 ( m/s)sn63 j, and v ˆ NM (30 m/s). Thus wth respect to Nancy v v v (cos63 30) ˆ m/s (sn63 ) ˆj m/s ( 0.0 ˆ 9.6 ˆj ) m/s BN BM NM v y 9.6 m/s tan tan 44.4 v 0.0 m/s The drecton o the angle s 44.4 above the x axs (n the second quadrant). (b) Wth respect to Nancy and x x BN BN (0.0 m/s) t y 0 m (9.6 m/s) t (9.8 m/s ) t (9.6 m/s) t (4.9 m/s ) t

6 4.79. Model: Use the partcle model or the arrow and the constant-acceleraton knematc equatons. Vsualze: Solve: Usng v y v0 y ay ( t t0 ), we get Also usng 0 0x 0 x 0 x x v ( t t ) a ( t t ), v 0 m/s gt v gt y y 60 m 60 m 0 m v t 0 m v v Snce vy/ vx tan , usng the components o v 0 gves 0x 0x x t gt (0.054)(60 m) t s (60 m/ t ) (9.8 m/s ) Havng ound t, we can go back to the x-equaton to obtan v0 60 m/0.566 s 06 m/s 0 m/s x Assess: In vew o the act that the arrow took only s to cover a horzontal dstance o 60 m, a speed o 06 m/s or 37 mph or the arrow s understandable.

7 4.80. Model: Use the partcle model or the arrow and the constant-acceleraton knematc equatons. We wll assume that the archer shoots rom.75 m above the slope (about 5 9). Vsualze: Solve: For the y-moton: For the x-moton: Because y/ x tan5 0.68, 0 0y( 0) y( 0).75 m ( 0 sn0 ) y y v t t a t t y v t gt.75 m (50 m/s)sn 0 y t gt 0 0x( 0) ( x 0) 0 m ( 0 cos0 ) 0 m (50 m/s)(cos0 ) x x v t t a t t v t t.75 m (50 m/s)(sn 0 ) t (50 m/s)(cos0 ) t gt 0.68 t 6. s and s (unphyscal) Usng t 6 s n the x- and y-equatons above, we get y 77.0 m and x 87 m. Ths means the dstance down the slope s x y (87 m) ( 77.0 m) 97 m. Assess: Wth an ntal speed o mph (50 m/s) or the arrow, whch s shot rom a 5 slope at an angle o 0 above the horzontal, a horzontal dstance o 87 m and a vertcal dstance o 77.0 m are reasonable numbers.

8 Turn n the ollowng. Show all your work clearly and neatly. Always draw a dagram, sketchng the stuaton and labelng varables dene drectons, etc Box nal answers. These are BRIEF INCOMPLET solutons. See solutons n glass case or complete solutons.. A partcle moves n the xy plane wth a constant acceleraton gven by a 4. 0j ˆ m/s. At t = 0, ts poston and velocty are 0 m and ( j) m/s, respectvely. What s the dstance rom the orgn to the partcle at t =.0 s? What s the velocty o the partcle? Sketch the dsplacement and velocty vector equatons as shown n the dagram 4.5 n the text. Answer: r (6ˆ 8 ˆj ) m, r 0m v ˆj m / s see keys n glass case or sketches.. A ball s thrown rom an upper story wndow o a buldng. The ball s gven an ntal velocty o 5.00 m/s at an angle o 0.0 above the horzontal. It strkes the ground 3.00 s later. a) Sketch the event, labelng EVERYTHING, ncludng the ntal and nal states. b) How ar horzontally rom the base o the buldng does the ball strke the ground? c) Fnd the heght rom whch the ball was thrown. d) Fnd the velocty that the balloon hts the ground wth (both magntude and drecton.) Answer: R 4. m, H 39.0 m, v (8. m / s, 80.0 ) 3. A quarterback throws a ootball straght toward a recever wth an ntal speed o 0.0m/s, at an angle o 35.0 above the horzontal. At that nstant, the recever s 0.0 m n ront (down eld) o the quarterback. Wth what constant speed should the recever run n order to catch the ootball at the level at whch t was thrown? Answer: v 7.86 / m s 5. A water balloon gun s held.40 m above the ground and ponted 5 degrees above the horzontal. It shoots a water balloon that lands on the ground 4.4 m away n the horzontal drecton. a) Sketch the event, labelng everythng, gvens, drectons, ncludng the ntal and nal states. b) Fnd the total tme the balloon travels n the ar. c) The ntal speed o the water balloon. d) Fnd the velocty that the balloon hts the ground wth. Answer: t 0.84 s, v 5.78 m / s, v (7.80 m / s, 47.8 )

9 4. A dve bomber has a velocty o 80 m/s at an angle below the horzontal. When the alttude o the arcrat s.5 km, t releases a bomb, whch subsequently hts a target on the ground. The magntude o the dsplacement rom the pont o release o the bomb to the target s 3.5 km. a) Fnd the dsplacement n the x drecton. b) Fnd the launch angle as shown. c) Fnd the tme t takes the bomb to strke the target. d) Fnd the velocty the bomb strkes the ground wth, both magntude and drecton and express t as an jk vector too! Answer: When the bomb has allen a vertcal dstance.5 km, t has traveled a horzontal dstance x gven by x 3.5 km.5 km.437 km gx y x tan v cos 50 m 437 m tan 9.8 m s 437 m 80 m s cos 50 m 437 m tan 37.9 m tan tan tan tan Select the negatve soluton, snce s below the horzontal. tan 0.66, Answers: x.437 km, 33.5, t 0.43 s, v (347 m / s, 47.8 ) 6. A tran travels due south at 30m/s (relatve to the ground) n a ran that s blown toward the south by the wnd blowng due south. The path o each randrop makes an angle o 70 degrees wth the vertcal, as measured by an observer statonary on the ground. An observer on the tran, however, sees the drops all perectly vertcally. Determne the speed o the randrops. Answer: v 3.9 m/ s RG 7. Tm n hs Corvette accelerates at the rate o (3.50ˆ.70 ˆj ) m / s, whle Jll n her Jaguar accelerates at ˆ ˆ ( j) m / s. They both start rom rest at the orgn o an xy coordnate system. Ater 5.0 s, Fnd Tm s and Jll s poston vectors, relatve to the orgn, expressed as jk vectors. What s the dstance between them? What s Jll s poston, relatve to Tm? Sketch all the vectors, labelng, etc. Answer: d 76.6 m, r ( 75.0ˆ 5.5 ˆj ) m, JT

10 8. A shp s launched rom shore s crossng a lake, headng 30.0 degrees west o north at 30.0 m/s relatve to the water. The velocty o the shp relatve to the shore s 0.0 m/s due north. Fnd the velocty (jk vector and magntude and drecton) o the water relatve to the shore both by graphcal methods and the method o components. Wrte the vector equaton or the relatve moton Express the drecton o the water relatve to due east (the + x-axs.) Calculate the percent derence or the velocty rom each method, whch should be wthn a ew percent o each other. Answer: v (6. m / s,0 ) WS 9. A coast guard shp s travelng at a constant velocty o 4.0 m/s, due east, relatve to the water. On hs radar screen the navgator detects an object that s movng at a constant velocty. The object s located at a dstance o 30 m wth respect to the shp, n a drecton 3.0 degrees south o east. Sx mnutes later, he notes that the object s poston relatve to the shp has changed to 0 m, 57.0 degrees south o west. What are the magntude and drecton o the velocty o the object relatve to the water? Express the drecton as an angle wth respect to due west. Try solvng both by methods o component and by law o snes and cosnes. Whch s easer? Answer: v (3.04 m / s,5. ) OW

### Physics 2A Chapter 3 HW Solutions

Phscs A Chapter 3 HW Solutons Chapter 3 Conceptual Queston: 4, 6, 8, Problems: 5,, 8, 7, 3, 44, 46, 69, 70, 73 Q3.4. Reason: (a) C = A+ B onl A and B are n the same drecton. Sze does not matter. (b) C

### Chapter 3. r r. Position, Velocity, and Acceleration Revisited

Chapter 3 Poston, Velocty, and Acceleraton Revsted The poston vector of a partcle s a vector drawn from the orgn to the locaton of the partcle. In two dmensons: r = x ˆ+ yj ˆ (1) The dsplacement vector

### Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

### GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME PHYSICAL SCIENCES GRADE 12 SESSION 1 (LEARNER NOTES)

PHYSICAL SCIENCES GRADE 1 SESSION 1 (LEARNER NOTES) TOPIC 1: MECHANICS PROJECTILE MOTION Learner Note: Always draw a dagram of the stuaton and enter all the numercal alues onto your dagram. Remember to

### Name: PHYS 110 Dr. McGovern Spring 2018 Exam 1. Multiple Choice: Circle the answer that best evaluates the statement or completes the statement.

Name: PHYS 110 Dr. McGoern Sprng 018 Exam 1 Multple Choce: Crcle the answer that best ealuates the statement or completes the statement. #1 - I the acceleraton o an object s negate, the object must be

### PHYSICS 203-NYA-05 MECHANICS

PHYSICS 03-NYA-05 MECHANICS PROF. S.D. MANOLI PHYSICS & CHEMISTRY CHAMPLAIN - ST. LAWRENCE 790 NÉRÉE-TREMBLAY QUÉBEC, QC GV 4K TELEPHONE: 48.656.69 EXT. 449 EMAIL: smanol@slc.qc.ca WEBPAGE: http:/web.slc.qc.ca/smanol/

### Section 8.1 Exercises

Secton 8.1 Non-rght Trangles: Law of Snes and Cosnes 519 Secton 8.1 Exercses Solve for the unknown sdes and angles of the trangles shown. 10 70 50 1.. 18 40 110 45 5 6 3. 10 4. 75 15 5 6 90 70 65 5. 6.

### Supplemental Instruction sessions next week

Homework #4 Wrtten homework due now Onlne homework due on Tue Mar 3 by 8 am Exam 1 Answer keys and scores wll be posted by end of the week Supplemental Instructon sessons next week Wednesday 8:45 10:00

### Spring Force and Power

Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems

### = 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

Secton 1.3: Acceleraton Tutoral 1 Practce, page 24 1. Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement:

### 11. Dynamics in Rotating Frames of Reference

Unversty of Rhode Island DgtalCommons@URI Classcal Dynamcs Physcs Course Materals 2015 11. Dynamcs n Rotatng Frames of Reference Gerhard Müller Unversty of Rhode Island, gmuller@ur.edu Creatve Commons

### Chapter 8 Potential Energy and Conservation of Energy Important Terms (For chapters 7 and 8)

Pro. Dr. I. Nasser Chapter8_I November 3, 07 Chapter 8 Potental Energy and Conservaton o Energy Important Terms (For chapters 7 and 8) conservatve orce: a orce whch does wor on an object whch s ndependent

### Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak Lnear Momentum Lnear momentum o an object o mass m movng wth a velocty v s dened to be p mv Momentum and lnear momentum

### Motion in One Dimension

Moton n One Dmenson Speed ds tan ce traeled Aerage Speed tme of trael Mr. Wolf dres hs car on a long trp to a physcs store. Gen the dstance and tme data for hs trp, plot a graph of hs dstance ersus tme.

### Please initial the statement below to show that you have read it

EN40: Dynamcs and Vbratons Mdterm Examnaton Thursday March 5 009 Dvson of Engneerng rown Unversty NME: Isaac Newton General Instructons No collaboraton of any knd s permtted on ths examnaton. You may brng

### Work is the change in energy of a system (neglecting heat transfer). To examine what could

Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes

### Displacement at any time. Velocity at any displacement in the x-direction u 2 = v ] + 2 a x ( )

The Language of Physcs Knematcs The branch of mechancs that descrbes the moton of a body wthout regard to the cause of that moton (p. 39). Average velocty The average rate at whch the dsplacement vector

### Chapter 3 and Chapter 4

Chapter 3 and Chapter 4 Chapter 3 Energy 3. Introducton:Work Work W s energy transerred to or rom an object by means o a orce actng on the object. Energy transerred to the object s postve work, and energy

### AP Physics 1 & 2 Summer Assignment

AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers

### Conservation of Energy

Lecture 3 Chapter 8 Physcs I 0.3.03 Conservaton o Energy Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcsall.html 95.4, Fall 03,

### Prof. Dr. I. Nasser T /16/2017

Pro. Dr. I. Nasser T-171 10/16/017 Chapter Part 1 Moton n one dmenson Sectons -,, 3, 4, 5 - Moton n 1 dmenson We le n a 3-dmensonal world, so why bother analyzng 1-dmensonal stuatons? Bascally, because

### Physics 2A Chapter 9 HW Solutions

Phscs A Chapter 9 HW Solutons Chapter 9 Conceptual Queston:, 4, 8, 13 Problems: 3, 8, 1, 15, 3, 40, 51, 6 Q9.. Reason: We can nd the change n momentum o the objects b computng the mpulse on them and usng

### Slide. King Saud University College of Science Physics & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART 2) LECTURE NO.

Slde Kng Saud Unersty College of Scence Physcs & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART ) LECTURE NO. 6 THIS PRESENTATION HAS BEEN PREPARED BY: DR. NASSR S. ALZAYED Lecture

### Linear Momentum. Center of Mass.

Lecture 6 Chapter 9 Physcs I 03.3.04 Lnear omentum. Center of ass. Course webste: http://faculty.uml.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcssprng.html

### Mathematics Intersection of Lines

a place of mnd F A C U L T Y O F E D U C A T I O N Department of Currculum and Pedagog Mathematcs Intersecton of Lnes Scence and Mathematcs Educaton Research Group Supported b UBC Teachng and Learnng Enhancement

### ONE-DIMENSIONAL COLLISIONS

Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal

### A Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph

A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular

### PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014

PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 Work-Knetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o

### PHYS 1441 Section 002 Lecture #16

PHYS 1441 Secton 00 Lecture #16 Monday, Mar. 4, 008 Potental Energy Conservatve and Non-conservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!

### ˆ (0.10 m) E ( N m /C ) 36 ˆj ( j C m)

7.. = = 3 = 4 = 5. The electrc feld s constant everywhere between the plates. Ths s ndcated by the electrc feld vectors, whch are all the same length and n the same drecton. 7.5. Model: The dstances to

### Page 1. Clicker Question 9: Physics 131: Lecture 15. Today s Agenda. Clicker Question 9: Energy. Energy is Conserved.

Physcs 3: Lecture 5 Today s Agenda Intro to Conseraton o Energy Intro to some derent knds o energy Knetc Potental Denton o Mechancal Energy Conseraton o Mechancal Energy Conserate orces Examples Pendulum

### v c motion is neither created nor destroyed, but transferred via interactions. Fri. Wed (.18,.19) Introducing Potential Energy RE 6.

r. 6.5-.7 (.) Rest Mass,ork by Changng orces Columba Rep 3pm, here RE 6.b (last day to drop) ed. 6.8-.9(.8,.9) Introducng Potental Energy RE 6.c Tues. H6: Ch 6 Pr s 58,59, 99(a-c), 05(a-c) moton s nether

### So far: simple (planar) geometries

Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector

### Gravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)

Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng

### Kinematics in 2-Dimensions. Projectile Motion

Knematcs n -Dmensons Projectle Moton A medeval trebuchet b Kolderer, c1507 http://members.net.net.au/~rmne/ht/ht0.html#5 Readng Assgnment: Chapter 4, Sectons -6 Introducton: In medeval das, people had

### χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body

Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown

### where v means the change in velocity, and t is the

1 PHYS:100 LECTURE 4 MECHANICS (3) Ths lecture covers the eneral case of moton wth constant acceleraton and free fall (whch s one of the more mportant examples of moton wth constant acceleraton) n a more

### Recitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk.

Rectaton: Energy, Phys 207. Energy. Energes. An acorn fallng from an oak tree onto the sdewalk. The acorn ntal has gravtatonal potental energy. As t falls, t converts ths energy to knetc. When t hts the

### PHYS 1441 Section 002 Lecture #15

PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton Announcements Mdterm comprehensve exam

### TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS, Exam Secton Verson October 8, 03 Total Weght: 00 ponts. Check your examnaton or completeness pror to startng. There are a total o nne

### EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

### Conservation of Angular Momentum = "Spin"

Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts

### Chapter 5. Answers to Even Numbered Problems m kj. 6. (a) 900 J (b) (a) 31.9 J (b) 0 (c) 0 (d) 31.9 J. 10.

Answers to Even Numbered Problems Chapter 5. 3.6 m 4..6 J 6. (a) 9 J (b).383 8. (a) 3.9 J (b) (c) (d) 3.9 J. 6 m s. (a) 68 J (b) 84 J (c) 5 J (d) 48 J (e) 5.64 m s 4. 9. J 6. (a). J (b) 5. m s (c) 6.3

### Chapter Seven - Potential Energy and Conservation of Energy

Chapter Seven - Potental Energy and Conservaton o Energy 7 1 Potental Energy Potental energy. e wll nd that the potental energy o a system can only be assocated wth specc types o orces actng between members

### Chapter 7: Conservation of Energy

Lecture 7: Conservaton o nergy Chapter 7: Conservaton o nergy Introucton I the quantty o a subject oes not change wth tme, t means that the quantty s conserve. The quantty o that subject remans constant

### Chapter 2. Pythagorean Theorem. Right Hand Rule. Position. Distance Formula

Chapter Moton n One Dmenson Cartesan Coordnate System The most common coordnate system or representng postons n space s one based on three perpendcular spatal axes generally desgnated x, y, and z. Any

### Section 8.3 Polar Form of Complex Numbers

80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the

### Physics 106 Lecture 6 Conservation of Angular Momentum SJ 7 th Ed.: Chap 11.4

Physcs 6 ecture 6 Conservaton o Angular Momentum SJ 7 th Ed.: Chap.4 Comparson: dentons o sngle partcle torque and angular momentum Angular momentum o a system o partcles o a rgd body rotatng about a xed

### Conservation Laws (Collisions) Phys101 Lab - 04

Conservaton Laws (Collsons) Phys101 Lab - 04 1.Objectves The objectves o ths experment are to expermentally test the valdty o the laws o conservaton o momentum and knetc energy n elastc collsons. 2. Theory

### An Algorithm to Solve the Inverse Kinematics Problem of a Robotic Manipulator Based on Rotation Vectors

An Algorthm to Solve the Inverse Knematcs Problem of a Robotc Manpulator Based on Rotaton Vectors Mohamad Z. Al-az*, Mazn Z. Othman**, and Baker B. Al-Bahr* *AL-Nahran Unversty, Computer Eng. Dep., Baghdad,

### Physics 114 Exam 3 Spring Name:

Physcs 114 Exam 3 Sprng 015 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem 4. Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse

### ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

### Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

### Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds

The speed o a nere mpulse n the human body s about 100 m/s. I you accdentally stub your toe n the dark, estmatethe tme t takes the nere mpulse to trael to your bran. Tps: pcture, poste drecton, and lst

### Physics 207 Lecture 6

Physcs 207 Lecture 6 Agenda: Physcs 207, Lecture 6, Sept. 25 Chapter 4 Frames of reference Chapter 5 ewton s Law Mass Inerta s (contact and non-contact) Frcton (a external force that opposes moton) Free

### Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

### Module 14: THE INTEGRAL Exploring Calculus

Module 14: THE INTEGRAL Explorng Calculus Part I Approxmatons and the Defnte Integral It was known n the 1600s before the calculus was developed that the area of an rregularly shaped regon could be approxmated

### Unit 5: Quadratic Equations & Functions

Date Perod Unt 5: Quadratc Equatons & Functons DAY TOPIC 1 Modelng Data wth Quadratc Functons Factorng Quadratc Epressons 3 Solvng Quadratc Equatons 4 Comple Numbers Smplfcaton, Addton/Subtracton & Multplcaton

### EMU Physics Department

Physcs 0 Lecture 8 Potental Energy and Conservaton Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aovgun.com Denton o Work W q The work, W, done by a constant orce on an object s dened as the product

### Physics 101 Lecture 9 Linear Momentum and Collisions

Physcs 0 Lecture 9 Lnear Momentum and Collsons Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum and Collsons q q q q q q q Conseraton o Energy Momentum Impulse Conseraton o Momentum -D Collsons

### Energy and Energy Transfer

Energy and Energy Transer Chapter 7 Scalar Product (Dot) Work Done by a Constant Force F s constant over the dsplacement r 1 Denton o the scalar (dot) product o vectors Scalar product o unt vectors = 1

### Week 6, Chapter 7 Sect 1-5

Week 6, Chapter 7 Sect 1-5 Work and Knetc Energy Lecture Quz The frctonal force of the floor on a large sutcase s least when the sutcase s A.pushed by a force parallel to the floor. B.dragged by a force

### Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics

Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn

### Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis

Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta

### 1. The number of significant figures in the number is a. 4 b. 5 c. 6 d. 7

Name: ID: Anwer Key There a heet o ueul ormulae and ome converon actor at the end. Crcle your anwer clearly. All problem are pont ecept a ew marked wth ther own core. Mamum core 100. There are a total

### Chapter 8. Potential Energy and Conservation of Energy

Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and non-conservatve forces Mechancal Energy Conservaton of Mechancal

### You will analyze the motion of the block at different moments using the law of conservation of energy.

Physcs 00A Homework 7 Chapter 8 Where s the Energy? In ths problem, we wll consder the ollowng stuaton as depcted n the dagram: A block o mass m sldes at a speed v along a horzontal smooth table. It next

### Math1110 (Spring 2009) Prelim 3 - Solutions

Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.

### Physics 2A Chapters 6 - Work & Energy Fall 2017

Physcs A Chapters 6 - Work & Energy Fall 017 These notes are eght pages. A quck summary: The work-energy theorem s a combnaton o Chap and Chap 4 equatons. Work s dened as the product o the orce actng on

### PHYS 1443 Section 002

PHYS 443 Secton 00 Lecture #6 Wednesday, Nov. 5, 008 Dr. Jae Yu Collsons Elastc and Inelastc Collsons Two Dmensonal Collsons Center o ass Fundamentals o Rotatonal otons Wednesday, Nov. 5, 008 PHYS PHYS

### Page 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces

Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Non-constant forces Imulse-momentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs

### Translational Equations of Motion for A Body Translational equations of motion (centroidal) for a body are m r = f.

Lesson 12: Equatons o Moton Newton s Laws Frst Law: A artcle remans at rest or contnues to move n a straght lne wth constant seed there s no orce actng on t Second Law: The acceleraton o a artcle s roortonal

### a) No books or notes are permitted. b) You may use a calculator.

PHYS 050 Sprng 06 Name: Test 3 Aprl 7, 06 INSTRUCTIONS: a) No books or notes are permtted. b) You may use a calculator. c) You must solve all problems begnnng wth the equatons on the Inormaton Sheet provded

### EMU Physics Department.

Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons

### Dynamics 4600:203 Homework 08 Due: March 28, Solution: We identify the displacements of the blocks A and B with the coordinates x and y,

Dynamcs 46:23 Homework 8 Due: March 28, 28 Name: Please denote your answers clearly,.e., box n, star, etc., and wrte neatly. There are no ponts for small, messy, unreadable work... please use lots of paper.

### CHAPTER 8 Potential Energy and Conservation of Energy

CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated

### Solutions to Selected Exercises

6 Solutons to Selected Eercses Chapter Secton.. a. f ( 0) b. Tons of garbage per week s produced by a cty wth a populaton of,000.. a. In 99 there are 0 ducks n the lake b. In 000 there are 0 ducks n the

### Chapter 07: Kinetic Energy and Work

Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy.

### Momentum. Momentum. Impulse. Momentum and Collisions

Momentum Momentum and Collsons From Newton s laws: orce must be present to change an object s elocty (speed and/or drecton) Wsh to consder eects o collsons and correspondng change n elocty Gol ball ntally

### EN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics

N40: ynamcs and Vbratons Homewor 7: Rgd Body Knematcs School of ngneerng Brown Unversty 1. In the fgure below, bar AB rotates counterclocwse at 4 rad/s. What are the angular veloctes of bars BC and C?.

### Chapter 11 Angular Momentum

Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle

### CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton

### Physics 207, Lecture 13, Oct. 15. Energy

Physcs 07 Lecture 3 Physcs 07, Lecture 3, Oct. 5 Goals: Chapter 0 Understand the relatonshp between moton and energy Dene Potental Energy n a Hooke s Law sprng Deelop and explot conseraton o energy prncple

### Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

### Physics 5153 Classical Mechanics. Principle of Virtual Work-1

P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal

### PHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76

PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s

### Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004

Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a

### Physics 207 Lecture 13. Lecture 13

Physcs 07 Lecture 3 Goals: Lecture 3 Chapter 0 Understand the relatonshp between moton and energy Defne Potental Energy n a Hooke s Law sprng Develop and explot conservaton of energy prncple n problem

### Old Dominion University Physics 420 Spring 2010

Projects Structure o Project Reports: 1 Introducton. Brely summarze the nature o the physcal system. Theory. Descrbe equatons selected or the project. Dscuss relevance and lmtatons o the equatons. 3 Method.

### Linear Momentum and Collisions

Lnear Momentum and Collsons Chater 9 Lnear Momentum [kg m/s] x y mv x mv y Newton s nd Law n terms o momentum: Imulse I - [kg m/s] I t t Fdt I = area under curve bounded by t axs Imulse-Momentum Theorem

### First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

### Chapter 8: Further Applications of Trigonometry

Secton 8. Polar Form of Complex Numbers 1 Chapter 8: Further Applcatons of Trgonometry In ths chapter, we wll explore addtonal applcatons of trgonometry. We wll begn wth an extenson of the rght trangle

### Four Bar Linkages in Two Dimensions. A link has fixed length and is joined to other links and also possibly to a fixed point.

Four bar lnkages 1 Four Bar Lnkages n Two Dmensons lnk has fed length and s oned to other lnks and also possbly to a fed pont. The relatve velocty of end B wth regard to s gven by V B = ω r y v B B = +y

### Chapter 7. Potential Energy and Conservation of Energy

Chapter 7 Potental Energy and Conservaton o Energy 1 Forms o Energy There are many orms o energy, but they can all be put nto two categores Knetc Knetc energy s energy o moton Potental Potental energy

### What happens when objects fall?!? g - The Magic Number

NAME: DATE: PERIOD: AP1 PHYSICS Freeall Notes Teacher Key - Physcsts DO NOT KNOW WHY objects all! But, we can escrbe HOW they all As they all, THEY GO FASTER Ths means that they ACCELERATE! What happens

### How Differential Equations Arise. Newton s Second Law of Motion

page 1 CHAPTER 1 Frst-Order Dfferental Equatons Among all of the mathematcal dscplnes the theory of dfferental equatons s the most mportant. It furnshes the explanaton of all those elementary manfestatons

### Physics 111 Final Exam, Fall 2013, Version A

Physcs 111 Fnal Exam, Fall 013, Verson A Name (Prnt): 4 Dgt ID: Secton: Honors Code Pledge: For ethcal and farness reasons all students are pledged to comply wth the provsons of the NJIT Academc Honor

### Spin-rotation coupling of the angularly accelerated rigid body

Spn-rotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 E-mal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s