ESCAPE VELOCITY EXAMPLES

Size: px
Start display at page:

Download "ESCAPE VELOCITY EXAMPLES"

Transcription

1 ESCAPE VELOCITY EXAMPLES 1. Escape velocity is the speed that an object needs to be taveling to beak fee of planet o moon's gavity and ente obit. Fo example, a spacecaft leaving the suface of Eath needs to be going 7 miles pe second, o nealy 5,000 miles pe hou, to ente obit. A Delta II ocket blasting off. A lage amount of enegy is needed to achieve escape velocity. Photo fom Jet Populsion Laboatoy's Planetay Missions & Instuments image galley Escape Velocity 00 Rev

2 . The ability to use and compute squae oots is often a necessay tool in physics. Fo example, squae oots ae used to compute the minimum velocity a spacecaft must have to escape the gavitational foce of a planet. The escape velocity, v, can be calculated using the following fomula: Escape Velocity In this fomula, G is a gavitational constant, M is the mass of the planet, and is the adius of the planet.. Since escape velocity depends on the mass of the planet o moon fom which a spacecaft is blasting, a spacecaft leaving the moon's suface could go slowe than one blasting off fom the Eath, because the moon has less gavity than the Eath. On the othe hand, the escape velocity fo Jupite would be many times that of Eath's because Jupite is so huge and has so much gavity. 4. Example: Compute the escape velocity fo Eath if its mass is 5.98 x 10 4 kg, its adius is.7 x 10 m, and G =.7 x N-m /Kg. The abbeviation N epesents Newton, a unit of foce in the metic 1kg m 1 N = system. Using these constaints, the answes will be in m/s. s (.7x10 (5.98x10.7x x x10 The escape velocity fo Eath is appoximately 1.1 x 10 4 m/s Point out that the gavitational constant is given in N-m /kg. The abbeviation N stands fo Newton. One Newton of foce acting on a mass of one kilogam causes acceleation of one mete pe second pe second (the thought pocess in this application is challenging. Exceptional students will have no poblem but it may be easie fo aveage students to accept this unit instead of deiving it. Escape Velocity 00 Rev

3 . You may want to show students why the answe is labeled in m/s. Nm kg( m G is in with N in. (kg m Thus G is in. kg( s M is in kg. R is in m. Theefoe, And is in s m kg kg( s m m o o. m s s m m o. s s 7. Thought Povoke: Is it bette to launch a ship into obit fom nea o away fom the equato? (AWAY. The adius is geate at the equato than at the poles. This lowes the escape velocity. 8. Though Povoke: Why is mass impotant? (Mass is impotant because of two majo factos affecting how things move in space: inetia and gavity. The moe mass something has, the moe inetia and gavity affect it. That is why heavy things (things with a lot of mass ae had to move. When an object is sitting still, it esists moving, and the moe mass it has, the moe it esists. The amount of thust needed to move something and how fast it ends up moving ae both diectly tied to its mass. On the othe hand, once something massive stats moving, it is vey had to stop. This is also due to the elationship between mass and inetia. Gavity is also popotional to how much mass each thing has. The bigge an object is, the lage the gavitational pull it exets. Because of gavity and inetia, the moe massive something is, the hade it is to get into space, the hade it is to keep it thee, and the hade it is to move it whee you want it to go when it is thee. 9. Thought Povoke: Why is it difficult to plan inta-planet missions? (One eason that manned missions to othe planets ae difficult to plan is that a ship would have to take enough fuel into space to blast off of the othe planet when the astonauts wanted to go home. The weight of the fuel would make the spaceship so heavy it would be had to blast it off Eath. Escape Velocity 00 Rev

4 Name: Date: Class: ESCAPE VELOCITY WORKSHEET Compute the escape velocity fo the indicated planet using the fomula below. Use G =.7 x N m. kg 1. Mas: mass.4 x 10 kg; adius.9 x 10 m. Mecuy: mass.5 x 10 kg; adius.44 x 10 m. Venus: mass 4.90 x 10 4 kg; adius.0 x 10 m Escape Velocity 00 Rev

5 ESCAPE VELOCITY WORKSHEET KEY Compute the escape velocity fo the indicated planet using the fomula below. Use G =.7 x N m. kg 1. Mas: mass.4 x 10 kg; adius.9 x 10 m (.7x10 (.4x10.9x x10 The escape velocity fo Eath is appoximately 5.04 x 10 m/s.. Mecuy: mass.5 x 10 kg; adius.44 x 10 m (.7x10 (.5x10.44x x10 The escape velocity fo Eath is appoximately 4.8 x 10 m/s.. Venus: mass 4.90 x 10 4 kg; adius.0 x 10 m (.7x10 (4.90x10.0x x10 The escape velocity fo Eath is appoximately 1.04 x 10 4 m/s. Escape Velocity 00 Rev

6 Student Name: Date: ESCAPE VELOCITY CHECKLIST 1. On question 1, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points. On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points. On question, did the student compute the escape velocity fo the indicated planet? a. Yes (5 points b. No, but only made mino mathematical eos (0 points c. No, used escape velocity fomula incoectly (15 points d. No, student could only set poblem up but could not solve (10 points Total Numbe of Points A B C D F 7 points and above 0 points and above 5 points and above 45 points and above 44 points and below Any scoe below C needs emediation! Escape Velocity 00 Rev

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

A) 2 B) 2 C) 2 2 D) 4 E) 8

A) 2 B) 2 C) 2 2 D) 4 E) 8 Page 1 of 8 CTGavity-1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Gravitation. AP Physics C

Gravitation. AP Physics C Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013 PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

More information

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

14. Gravitation Universal Law of Gravitation (Newton):

14. Gravitation Universal Law of Gravitation (Newton): 14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1) Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number.

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number. Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 1-5 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE

More information

6.2 Orbits and Kepler s Laws

6.2 Orbits and Kepler s Laws Eath satellite in unstable obit 6. Obits and Keple s Laws satellite in stable obit Figue 1 Compaing stable and unstable obits of an atificial satellite. If a satellite is fa enough fom Eath s suface that

More information

Lesson 32: Measuring Circular Motion

Lesson 32: Measuring Circular Motion Lesson 32: Measuing Cicula Motion Velocity hee should be a way to come up with a basic fomula that elates velocity in icle to some of the basic popeties of icle. Let s ty stating off with a fomula that

More information

Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.

Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C. Physics: Mechanics 1 Gavity D. Bill Pezzaglia A. The Law of Gavity Gavity B. Gavitational Field C. Tides Updated: 01Jul09 A. Law of Gavity 3 1a. Invese Squae Law 4 1. Invese Squae Law. Newton s 4 th law

More information

F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.

F G r. Don't confuse G with g: Big G and little g are totally different things. G-1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P

More information

2. An asteroid revolves around the Sun with a mean orbital radius twice that of Earth s. Predict the period of the asteroid in Earth years.

2. An asteroid revolves around the Sun with a mean orbital radius twice that of Earth s. Predict the period of the asteroid in Earth years. CHAPTR 7 Gavitation Pactice Poblems 7.1 Planetay Motion and Gavitation pages 171 178 page 174 1. If Ganymede, one of Jupite s moons, has a peiod of days, how many units ae thee in its obital adius? Use

More information

Introduction to Fluid Mechanics

Introduction to Fluid Mechanics Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapte 5. Foce and Motion In this chapte we study causes of motion: Why does the windsufe blast acoss the wate in the way he does? The combined foces of the wind, wate, and gavity acceleate him accoding

More information

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics 3/4/0 Resouces Cicula Motion: Fom Moto Racing to Satellites D Jeff McCallum School of Physics http://www.gap-system.og/~histoy/mathematicians/ Newton.html http://www.fg-a.com http://www.clke.com/clipat

More information

Gravity and the figure of the Earth

Gravity and the figure of the Earth Gavity and the figue of the Eath Eic Calais Pudue Univesity Depatment of Eath and Atmospheic Sciences West Lafayette, IN 47907-1397 ecalais@pudue.edu http://www.eas.pudue.edu/~calais/ Objectives What is

More information

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary 7 Cicula Motion 7-1 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o

More information

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the

More information

On the Relativistic Forms of Newton's Second Law and Gravitation

On the Relativistic Forms of Newton's Second Law and Gravitation On the Relativistic Foms of Newton's Second Law and avitation Mohammad Bahami,*, Mehdi Zaeie 3 and Davood Hashemian Depatment of physics, College of Science, Univesity of Tehan,Tehan, Islamic Republic

More information

Phys 2101 Gabriela González. cos. sin. sin

Phys 2101 Gabriela González. cos. sin. sin 1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe

More information

Solutions to Homework Set #5 Phys2414 Fall 2005

Solutions to Homework Set #5 Phys2414 Fall 2005 Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is

More information

PY1052 Problem Set 3 Autumn 2004 Solutions

PY1052 Problem Set 3 Autumn 2004 Solutions PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the

More information

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum Final Exam Duing class (1-3:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday

More information

Section 5-3 Angles and Their Measure

Section 5-3 Angles and Their Measure 5 5 TRIGONOMETRIC FUNCTIONS Section 5- Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,

More information

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2 F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,

More information

PHYSICS 218 Honors EXAM 2 Retest. Choose 5 of the following 6 problems. Indicate which problem is not to be graded.

PHYSICS 218 Honors EXAM 2 Retest. Choose 5 of the following 6 problems. Indicate which problem is not to be graded. PHYSICS 18 Honos EXAM Retest Choose 5 of the following 6 pobles. Indicate which poble is not to be gaded. 1. A ope is affixed at one end to the i of a pulley, and wapped five tuns aound the pulley. The

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Orbital Motion & Gravity

Orbital Motion & Gravity Astonomy: Planetay Motion 1 Obital Motion D. Bill Pezzaglia A. Galileo & Fee Fall Obital Motion & Gavity B. Obits C. Newton s Laws Updated: 013Ma05 D. Einstein A. Galileo & Fee Fall 3 1. Pojectile Motion

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013 PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80-kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,

More information

2. Orbital dynamics and tides

2. Orbital dynamics and tides 2. Obital dynamics and tides 2.1 The two-body poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra and Trig. I. A point is a location or position that has no size or dimension. Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite

More information

Theory and measurement

Theory and measurement Gavity: Theoy and measuement Reading: Today: p11 - Theoy of gavity Use two of Newton s laws: 1) Univesal law of gavitation: ) Second law of motion: Gm1m F = F = mg We can combine them to obtain the gavitational

More information

L19 Geomagnetic Field Part I

L19 Geomagnetic Field Part I Intoduction to Geophysics L19-1 L19 Geomagnetic Field Pat I 1. Intoduction We now stat the last majo topic o this class which is magnetic ields and measuing the magnetic popeties o mateials. As a way o

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

Displacement, Velocity And Acceleration

Displacement, Velocity And Acceleration Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,

More information

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003 Geostophic balance John Mashall, Alan Plumb and Lodovica Illai Mach 4, 2003 Abstact We descibe the theoy of Geostophic Balance, deive key equations and discuss associated physical balances. 1 1 Geostophic

More information

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a .1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q -q a +q a -q F = kq 1q F 1 = k(q)(q) a F 13

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions Name St.No. - Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100-minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,

More information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2 Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the

More information

Solutions for Physics 1301 Course Review (Problems 10 through 18)

Solutions for Physics 1301 Course Review (Problems 10 through 18) Solutions fo Physics 1301 Couse Review (Poblems 10 though 18) 10) a) When the bicycle wheel comes into contact with the step, thee ae fou foces acting on it at that moment: its own weight, Mg ; the nomal

More information

Multiple choice questions [70 points]

Multiple choice questions [70 points] Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions

More information

Multiple choice questions [60 points]

Multiple choice questions [60 points] 1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions

More information

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions Physics 111 Fall 007 Electostatic Foces an the Electic Fiel - Solutions 1. Two point chages, 5 µc an -8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the

More information

The Gravity Field of the Earth - Part 1 (Copyright 2002, David T. Sandwell)

The Gravity Field of the Earth - Part 1 (Copyright 2002, David T. Sandwell) 1 The Gavity Field of the Eath - Pat 1 (Copyight 00, David T. Sandwell) This chapte coves physical geodesy - the shape of the Eath and its gavity field. This is just electostatic theoy applied to the Eath.

More information

Chapter 13. Vector-Valued Functions and Motion in Space 13.6. Velocity and Acceleration in Polar Coordinates

Chapter 13. Vector-Valued Functions and Motion in Space 13.6. Velocity and Acceleration in Polar Coordinates 13.6 Velocity and Acceleation in Pola Coodinates 1 Chapte 13. Vecto-Valued Functions and Motion in Space 13.6. Velocity and Acceleation in Pola Coodinates Definition. When a paticle P(, θ) moves along

More information

9.5 Volume of Pyramids

9.5 Volume of Pyramids Page of 7 9.5 Volume of Pyamids and Cones Goal Find the volumes of pyamids and cones. Key Wods pyamid p. 49 cone p. 49 volume p. 500 In the puzzle below, you can see that the squae pism can be made using

More information

Analytical Proof of Newton's Force Laws

Analytical Proof of Newton's Force Laws Analytical Poof of Newton s Foce Laws Page 1 1 Intouction Analytical Poof of Newton's Foce Laws Many stuents intuitively assume that Newton's inetial an gavitational foce laws, F = ma an Mm F = G, ae tue

More information

Classical Lifetime of a Bohr Atom

Classical Lifetime of a Bohr Atom 1 Poblem Classical Lifetime of a Boh Atom James D. Olsen and Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 85 (Mach 7, 5) In the Boh model of the hydogen atom s gound state,

More information

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

More information

Chapter 8, Rotational Kinematics. Angular Displacement

Chapter 8, Rotational Kinematics. Angular Displacement Chapte 8, Rotational Kinematics Sections 1 3 only Rotational motion and angula displacement Angula velocity and angula acceleation Equations of otational kinematics 1 Angula Displacement! B l A The length

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

Newton s Shell Theorem

Newton s Shell Theorem Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheically-ymmetic maive bodie (like planet,

More information

CHAPTER 17 MAGNETIC DIPOLE MOMENT

CHAPTER 17 MAGNETIC DIPOLE MOMENT 1 CHAPTER 17 MAGNETIC DIPOLE MOMENT 17.1 Intoduction A numbe of diffeent units fo expessing magnetic dipole moment (heeafte simply magnetic moment ) ae commonly seen in the liteatue, including, fo example,

More information

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION MOTION IN FIELDS MOTION IN FIELDS 9 9. Pojectile motion 9. Gavitational field, potential and enegy 9.3 Electic field, potential and enegy 9. PROJECTILE MOTION 9.. State the independence of the vetical

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Circular Motion and Other Applications of Newton s Laws

Circular Motion and Other Applications of Newton s Laws P U Z Z L E R This sky dive is falling at moe than 50 m/s (120 mi/h), but once he paachute opens, he downwad velocity will be geatly educed. Why does she slow down apidly when he chute opens, enabling

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Circumference and Arc Length

Circumference and Arc Length 11.4 icumfeence and c Length efoe Now You found the cicumfeence of a cicle. You will find ac lengths and othe measues. Why? So you can find a unning distance, as in Example 5. Key Vocabulay cicumfeence

More information

SCHWARZSCHILD SOLUTION IN GENERAL RELATIVITY. Marko Vojinović

SCHWARZSCHILD SOLUTION IN GENERAL RELATIVITY. Marko Vojinović SCHWARZSCHILD SOLUTION IN GENERAL RELATIVITY Mako Vojinović Mach 200 Contents The meaning of the metic tenso 2 2 Einstein equations and Schwazschild solution 5 3 Physical intepetation and consequences

More information

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6 Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe

More information

Nuclear models: Fermi-Gas Model Shell Model

Nuclear models: Fermi-Gas Model Shell Model Lectue Nuclea mode: Femi-Gas Model Shell Model WS/: Intoduction to Nuclea and Paticle Physics The basic concept of the Femi-gas model The theoetical concept of a Femi-gas may be applied fo systems of weakly

More information

Economics 326: Input Demands. Ethan Kaplan

Economics 326: Input Demands. Ethan Kaplan Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly

More information

Chapter 3: Vectors and Coordinate Systems

Chapter 3: Vectors and Coordinate Systems Coodinate Systems Chapte 3: Vectos and Coodinate Systems Used to descibe the position of a point in space Coodinate system consists of a fied efeence point called the oigin specific aes with scales and

More information

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w 1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a

More information

K.S.E.E.B., Malleshwaram, Bangalore SSLC Mathematics-Model Question Paper-1 (2015) Regular Private Candidates (New Syllabus)

K.S.E.E.B., Malleshwaram, Bangalore SSLC Mathematics-Model Question Paper-1 (2015) Regular Private Candidates (New Syllabus) K.S.E.E.B., Malleshwaam, Bangaloe SSLC Mathematics-Model Question Pape-1 (015) Regula Pivate Candidates (New Syllabus) Max Maks: 100 No. of Questions: 50 Time: 3 Hous Code No. : Fou altenatives ae given

More information

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

More information

Road tunnel. Road tunnel information sheet. Think about. Using the information

Road tunnel. Road tunnel information sheet. Think about. Using the information Road tunnel This activity is about using a gaphical o algebaic method to solve poblems in eal contets that can be modelled using quadatic epessions. The fist poblem is about a oad tunnel. The infomation

More information