Physics 111. Exam #1. January 24, 2014

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Physics 111. Exam #1. January 24, 2014"

Transcription

1 Phyic 111 Exam #1 January 24, 2014 Name Pleae read and follow thee intruction carefully: Read all problem carefully before attempting to olve them. Your work mut be legible, and the organization clear. You mut how all work, including correct vector notation. You will not receive full credit for correct anwer without adequate explanation. You will not receive full credit if incorrect work or explanation are mixed in with correct work. So erae or cro out anything you don t want graded. Make explanation complete but brief. Do not write a lot of proe. Include diagram. Show what goe into a calculation, not jut the final number. For example p m v = ( 5kg) ( 2 m ) =10 kg m Give tandard SI unit with your reult unle pecifically aked for a certain unit. Unle pecifically aked to derive a reult, you may tart with the formula given on the formula heet including equation correponding to the fundamental concept. Go for partial credit. If you cannot do ome portion of a problem, invent a ymbol and/or value for the quantity you can t calculate (explain that you are doing thi), and ue it to do the ret of the problem. All multiple choice quetion are worth 3 point and each free-repone part i worth 9 point Problem #1 /24 Problem #2 /27 Problem #3 /21 Total /72 I affirm that I have carried out my academic endeavor with full academic honety.

2 1. Suppoe that you are given the ytem of point charge, where q 1 = +2µ i located at the point (x,y) = (0,0.5m), while q 2 = 6µ i located at the point (x,y) = (0, 0.2m). a. What i the electric field at a point P with coordinate (x,y) = (0.7m, 0.4m)? The component of the net electric field vector are given a E net,x = E 1,x E 2,x = kq 1 r coθ kq coθ 2 2 1,P r 2,P E net,y = E 1,y + E 2,y = kq 1 r inθ + kq inθ 2 2 1,P r 2,P From the geometry of the ytem we can determine the ditance between each charge and point P along with the value of each of the trig function. coθ 1 = = 0.61 coθ = = 0.97 inθ 1 = = 0.79 inθ 2 = = 0.28 r 1,P = ( 0.7m) 2 + ( 0.9m) 2 =1.14m r 2,P = ( 0.7m) 2 + ( 0.2m) 2 = 0.72m Inerting the quantitie into the expreion for the net horizontal and vertical component of the electric field we find E net,x = Nm ( 0.61) ( 0.97) 2 ( 1.14m) 2 ( 0.72m) 2 = N E net,y = Nm m ( 0.79) ( 0.28) ( ) 2 ( 0.72m) 2 = N Therefore the net electric field at point P i given a 2 2 E net,p = E net,x + E = tan E 1 net,y E net,p = N E = 78.8o above the negative x-axi.

3 b. How much work i required to bring in a third charge q 3 = 5µ and place it at point P? kq W = q 3 ΔV P,2 q 3 ΔV P,1 = q kq 1 0 r P,2 r P,1 = kq q q 1 r P,2 r P,1 W = Nm ( ) m = 0.3J 1.14m c. If q 3 were releaed from ret at point P, it would 1. accelerate in the direction of the net electric field at point P. 2. accelerate in the direction oppoite to the net electric field at point P. 3. feel no net force and thu remain at ret at point P. 4. feel no net force and continue moving at a contant velocity along the charge original direction of motion. d. Suppoe that q 3 were placed again at point P. If all three charge had identical mae and if the charge were releaed from ret imultaneouly, when all three charge are very far away from each other their peed would be given by 1. v = kq 1Q 2 Q 3 3rm. 2. v = 3kQ Q Q rm 6 Q 3. v = 1 Q 2 + Q 2Q 3 + Q 1Q 3. m r 1,2 r 2,3 r 1,3 2 Q 4. v = 1 Q 2 + Q 2Q 3 + Q 1Q 3. 3m r 1,2 r 2,3 r 1,3 There wa no correct anwer given to thi quetion o everyone got credit for the quetion. The correct anwer hould be v = 2k Q 1 Q 2 + Q 2Q 3 + Q 1Q 3 3m r 1,2 r 2,3 r 1,3.

4 2. A proton i accelerated from ret through a potential difference of ΔV acc = 2.3MV a hown below. a. How much work (in ev and J) wa done on the proton and what i it peed when it leave the accelerating region? ( )[ 0 V acc ] = ev acc = 2.3MeV. Thi The work done i given by W = qδv = e energy convert to W = qδv = ( e) [ 0 V acc ] = ev acc = 2.3MeV. The work done i equal to the change in kinetic energy of the proton. Thu the final peed of the proton i given by W = ΔKE = 1 m v 2 2 p p v p = 2W = J m p kg = m ΔV acc The proton that leave the accelerator above and i directed vertically upward and approache a econd et of capacitor plate angled at θ = 37 o with repect to the horizontal a hown below. The proton enter thi econd et of capacitor plate through the left-mot hole in the bottom plate. The capacitor plate are ued to teer the proton by 90 o and make it leave through the right-mot hole in the bottom plate. +Q -Q θ = 37 o ΔV acc

5 b. What electric field i needed to make the proton enter through the left hole and exit though the right hole if the ditance between the center of the hole i L = 0.5mand the plate are eparated by d = 0.1m? (Hint: Since, the proton i o mall, you can aume that it enter at the center of the left hole and exit at the center of the right hole.) The econd capacitor i inclined at θ = 37 o, the proton enter the left-mot hole and it velocity vector make a φ = 90 o 37 o = 53 o angle with repect to the lower capacitor plate. Thu the horizontal and vertical component of the initial velocity are v ix = v i coφ = m co53 = m v iy = v i inφ = m in53 = m Auming that the x-axi run along the lower capacitor plate and the y-axi i perpendicular to the lower capacitor plate, we find the time that i needed for the charge to cover the ditance L along the lower capacitor plate between the hole. The time i given from the horizontal trajectory equation where the horizontal acceleration i zero. Thu, x f = x i + v ix t t = L 0.5m = = v ix m Then to calculate the electric field that i needed we ue the vertical trajectory equation. Thu we have y f = y i + v iy t + 1 a t 2 2 a 0 = v iy + 1 a t t = 0 ( 2 y )t ( v iy + 1 a t. The acceleration i 2 y ) = 0 given by a y = F y = ee. ombining thee two reult we can olve for the m p m p electric field. We have 0 = v iy + 1 a t ( 2 y ) = v iy ee 2m t v ee iy p 2m L p v ix E = 2m v v p iy ix = kg m m = N el m and the direction of the field i from the upper plate to the lower plate. c. What i the charge Q on either plate, if the plate each have an area A = 0.1m 2 and the pace between the plate i filled with air with dielectric contant κ =1? The charge i given by Q = V = ( Ed) = κε oaed = κε o AE d Q = m N = = 7.9µ Nm 2

6 3. The Earth atmophere can act a a capacitor, with the ground acting a one plate, the cloud acting a the econd plate and the pace between the cloud and ground filled with air. Air i normally an inulating material, but under certain condition can be made to conduct electricity, o that electric charge can flow from the cloud to the ground, in what we call a lightning trike. Aume that the cloud are uniformly ditributed around the entire Earth at a fixed ditance of 5000m (~ 3mi)above the 2 ground of area 4πR Earth, where R Earth = 6400km. Further, aume that the air between the cloud and the ground ha a reitance taken to be R = 350Ω. a. Taking the upper negative plate to be the cloud and the lower poitive plate to be the ground, what i the magnitude of the difference in potential that exit between the cloud and the ground if in a typical day a maximum of of charge i pread over the urface of the Earth? The capacitance i given a: = κε 0 A d ( ) 2 = π m Nm m = 0.91F. The magnitude of the difference in potential that exit between the cloud and the ground i Q = V V = Q = F = V b. Approximately how long would it take the Earth-cloud capacitor to dicharge of 99%it total initial charge, Q max? Further, auming that the charge i immediately replenihed a oon a the dicharge proce end, how many lightning trike are produced in a ingle day if each trike contain 25 of charge? The time to dicharge 99%it total initial charge, Q max i given a t R Q t t = Rln 0.01 ( ) = 0.01Q max = Q max e ( ) = 300Ω 0.91F ln( 0.01) =1467 In thi time we dicharge of charge by lightning trike that contain of charge each. Thu we have trike trike ~ 14. onverting thi to 25 lightning trike per day we have 14 trike hr 1hr 1day =1.2 trike 106 day.

7 c. Of coure if you ve ever driven in the rain (and epecially during a thundertorm) you probably have had the occaion to et your car windhield wiper to wipe the window at interval that match the amount of rainfall hitting the window. Your car ha intermittent windhield wiper that control when the wiper actually move acro the window and you can elect how quick or low thi occur by uing a R circuit. A charging R circuit control the intermittent windhield wiper in your car by uing the car battery, which i rated at V B. Suppoe that for a particular etting, the wiper are triggered when the voltage acro a capacitor reache V, where V V B. At thi point the capacitor i quickly dicharged (through a much maller reitor) and the cycle repeat. What variable reitance R hould be ued in a charging circuit if the wiper are to operate once every t econd, where t i the amount of time between each wipe cycle of the wiper? t R = ln 1 V V B t R = ln 1 V B V t R = ln 1 V B V t R = ln 1 V V B Jut for reference, the charging/dicharging circuit i given below. When charging the capacitor, the witch S i connected to the battery (in the left mot poition), capacitor and variable reitor R (the one with the arrow through it). When the potential reache a pecified value, the witch S move to the right mot poition and dicharge the capacitor through the wiper and the wiper motor move the actual wiper. After the dicharge the witch move back to the left and the circuit charge the capacitor again. The witch move back and forth at the time t above. Thi circuit hould look reaonably familiar and not all of the control circuitry i hown. R S V B Wiper

8 Electric Force, Field and Potential Electric ircuit Light a a Wave F = k Q Q 1 2 r ˆ E = F q r 2 E Q = k Q r r ˆ 2 PE = k Q 1Q 2 r V ( r) = k Q r E x = ΔV Δx W = qδv Phyic 111 Equation Sheet Magnetic Force and Field Light a a Particle & Relativity Nuclear Phyic ontant g = 9.8 m 2 1e = k = 1 = Nm 2 4πε 2 o ε o = eV = J µ o = 4π 10 7 Tm A c = m h = J Nm 2 m e = kg = 0.511MeV c 2 m p = kg = 937.1MeV c 2 m n = kg = 948.3MeV c 2 1amu = kg = 931.5MeV c 2 N A = Ax 2 + Bx + = 0 x = B ± B2 4A 2A Geometry ircle : = 2πr = πd A = πr 2 Triangle : A = 1 bh 2 Sphere : A = 4πr 2 V = 4 3 πr3 Mic. Phyic 110 Formulae F = Δ p Δt = Δ( mv) = ma Δt F = ky F = m v 2 R r ˆ W = ΔKE = 1 m v f v i PE gravity = mgy PE pring = 1 2 ky 2 x f = x i + v ix t a xt 2 v fx = v ix + a x t v 2 fx = v 2 ix + 2a x Δx ( ) = ΔPE

MECH 2110 - Statics & Dynamics

MECH 2110 - Statics & Dynamics Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11 - Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic - Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight

More information

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement

More information

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction. Newton Law Newton firt law: An object will tay at ret or in a tate of uniform motion with contant velocity, in a traight line, unle acted upon by an external force. In other word, the bodie reit any change

More information

Discussion Session 4 Projectile Motion Week 05. The Plan

Discussion Session 4 Projectile Motion Week 05. The Plan PHYS Dicuion Seion 4 Projectile Motion Week 5 The Plan Thi week your group will practice analyzing projectile otion ituation. Why do we pend a whole eion on thi topic? The anwer i that projectile otion

More information

Ch. 22 Electromagnetic Induction

Ch. 22 Electromagnetic Induction Ch. 22 Electromagnetic Induction 22.1 Induced emf So electric current (moving charge) create agnetic Field. I the revere true? Can magnetic field create current??? D Ye!!! ut it take a changing magnetic

More information

Description: Conceptual questions about projectile motion and some easy calculations. (uses applets)

Description: Conceptual questions about projectile motion and some easy calculations. (uses applets) Week 3: Chapter 3 [ Edit ] Overview Suary View Diagnotic View Print View with Anwer Week 3: Chapter 3 Due: 11:59p on Sunday, February 8, 2015 To undertand how point are awarded, read the Grading Policy

More information

Linear Momentum and Collisions

Linear Momentum and Collisions Chapter 7 Linear Momentum and Colliion 7.1 The Important Stuff 7.1.1 Linear Momentum The linear momentum of a particle with ma m moving with velocity v i defined a p = mv (7.1) Linear momentum i a vector.

More information

CHAPTER 23: ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES

CHAPTER 23: ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES College Phyic Student Manual Chapter CHAPTE : EECTOMAGNETC NDUCTON, AC CCUTS, AND EECTCA TECHNOOGES. NDUCED EMF AND MAGNETC FUX. What i the value of the magnetic flux at coil in Figure.5 due to coil? Uing

More information

Chapter H - Problems

Chapter H - Problems Chapter H - Problem Blinn College - Phyic 45 - Terry Honan Problem H.1 A wheel rotate from ret to 1 ê in 3. Aume the angular acceleration i contant. (a) What i the magnitude of the wheel' angular acceleration?

More information

Harmonic Oscillations / Complex Numbers

Harmonic Oscillations / Complex Numbers Harmonic Ocillation / Complex Number Overview and Motivation: Probably the ingle mot important problem in all of phyic i the imple harmonic ocillator. It can be tudied claically or uantum mechanically,

More information

A) When two objects slide against one another, the magnitude of the frictional force is always equal to μ

A) When two objects slide against one another, the magnitude of the frictional force is always equal to μ Phyic 100 Homewor 5 Chapter 6 Contact Force Introduced ) When two object lide againt one another, the magnitude of the frictional force i alway equal to μ B) When two object are in contact with no relative

More information

322 CHAPTER 11 Motion and Momentum Telegraph Colour Library/FPG/Getty Images

322 CHAPTER 11 Motion and Momentum Telegraph Colour Library/FPG/Getty Images Standard 7.7.4: Ue ymbolic equation to how how the quantity of omething change over time or in repone to change in other quantitie. Alo cover: 7.2.6, 7.2.7 (Detailed tandard begin on page IN8.) What i

More information

Simple Harmonic Motion. AP Physics B

Simple Harmonic Motion. AP Physics B Simple Harmonic Motion AP Phyic B Simple Harmonic Motion Back and forth motion that i caued by a force that i directly proportional to the diplacement. The diplacement center around an equilibrium poition.

More information

Projectile Motion. Vectors and Projectiles

Projectile Motion. Vectors and Projectiles Nae: Projectile Motion Read fro Leon 2 of the Vector and Motion in Two-Dienion chapter at The Phyic Claroo: http://www.phyicclaroo.co/cla/vector/u3l2a.htl http://www.phyicclaroo.co/cla/vector/u3l2b.htl

More information

Incline and Friction Examples

Incline and Friction Examples Incline and riction Eample Phic 6A Prepared b Vince Zaccone riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC

More information

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 7: Synchronous Machines and Drives (Textbook Chapter 5)

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 7: Synchronous Machines and Drives (Textbook Chapter 5) ECE 30 Energy Converion and Power Electronic Dr. Tim Hogan Chapter 7: ynchronou Machine and Drive (Textbook Chapter 5) Chapter Objective For induction machine, a the rotor approache ynchronou peed, the

More information

Example (1): Motion of a block on a frictionless incline plane

Example (1): Motion of a block on a frictionless incline plane Firm knowledge of vector analysis and kinematics is essential to describe the dynamics of physical systems chosen for analysis through ewton s second law. Following problem solving strategy will allow

More information

6. Friction, Experiment and Theory

6. Friction, Experiment and Theory 6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal

More information

PH202-5D Final Comprehensive Exam (August 10, 2007)

PH202-5D Final Comprehensive Exam (August 10, 2007) NAME SCORE PH202-5D Final Comprehensive Exam (August 0, 2007) You may not open the textbook nor notebook. A letter size information may be used. A calculator may be used. However, mathematics or physics

More information

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,

More information

State-space analysis of control systems: Part I

State-space analysis of control systems: Part I Why a different approach? State-pace analyi of control ytem: Part I Uing a tate-variable approach give u a traightforward way to analyze MIM multiple-input, multiple output ytem. A tate variable model

More information

CHAPTER 21: CIRCUITS, BIOELECTRICITY, AND DC INSTRUMENTS

CHAPTER 21: CIRCUITS, BIOELECTRICITY, AND DC INSTRUMENTS College Phyic Student Manual Chater CHAPT : CCUTS, BOLCTCTY, AND DC NSTUMNTS. SSTOS N SS AND PAALLL. (a) What i the reitance of ten 75 -Ω reitor connected in erie? (b) n arallel? (a) From the equation

More information

Name: SID: Instructions

Name: SID: Instructions CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction - Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/

More information

Chapter 32. OPTICAL IMAGES 32.1 Mirrors

Chapter 32. OPTICAL IMAGES 32.1 Mirrors Chapter 32 OPTICAL IMAGES 32.1 Mirror The point P i called the image or the virtual image of P (light doe not emanate from it) The left-right reveral in the mirror i alo called the depth inverion (the

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #4 March 15, 2007 Time: 90 minutes NAME: (Last) Please Print (Given) STUDENT NO.: LECTURE SECTION (please

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 802 Spring 2013 Conflict Exam Two Solutions Problem 1 (25 points): answers without work shown will not be given any credit A uniformly charged

More information

Recall the commutative and associative properties of multiplication. The Commutative Property of Multiplication. If a and b are any integers,

Recall the commutative and associative properties of multiplication. The Commutative Property of Multiplication. If a and b are any integers, 6 MODULE 2. FUNDAMENTALS OF ALGEBRA 2b Order of Operation Simplifying Algebraic Expreion Recall the commutative and aociative propertie of multiplication. The Commutative Property of Multiplication. If

More information

Vectors. Graphical Representation of a Vector

Vectors. Graphical Representation of a Vector Vector There i a great teptation to put ector tail-to-tail when ou go to add the. Ma all the battle that ou wage in our war againt that teptation end with our gloriou triuph. Vector add head-to-tail. We

More information

Physics 201 Homework 5

Physics 201 Homework 5 Physics 201 Homework 5 Feb 6, 2013 1. The (non-conservative) force propelling a 1500-kilogram car up a mountain -1.21 10 6 joules road does 4.70 10 6 joules of work on the car. The car starts from rest

More information

Lab 4: Motor Control

Lab 4: Motor Control 2.017 Deign of Electromechanical Robotic Sytem, Fall 2009 Lab 4: Motor Control Aigned: 10/5/09 1 Overview So far we have learnt how to ue the Arduino to acquire variou type of ignal from enor uch a the

More information

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test Report 4668-1b Meaurement report Sylomer - field tet Report 4668-1b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of

More information

Laboratory 3 Diode Characteristics

Laboratory 3 Diode Characteristics Laboratory 3 Diode Characteritic BACKGROUND A diode i a non-linear, two terminal emiconductor device. he two terminal are the anode and the cathode. he circuit ymbol of a diode i depicted in Fig. 3-1.

More information

You may use a scientific calculator (non-graphing, non-programmable) during testing.

You may use a scientific calculator (non-graphing, non-programmable) during testing. TECEP Tet Decription College Algebra MAT--TE Thi TECEP tet algebraic concept, procee, and practical application. Topic include: linear equation and inequalitie; quadratic equation; ytem of equation and

More information

Chapter 10 Velocity, Acceleration, and Calculus

Chapter 10 Velocity, Acceleration, and Calculus Chapter 10 Velocity, Acceleration, and Calculu The firt derivative of poition i velocity, and the econd derivative i acceleration. Thee derivative can be viewed in four way: phyically, numerically, ymbolically,

More information

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

More information

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE 1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object

More information

Exam 2 Solutions. PHY2054 Spring Prof. P. Kumar Prof. P. Avery March 5, 2008

Exam 2 Solutions. PHY2054 Spring Prof. P. Kumar Prof. P. Avery March 5, 2008 Prof. P. Kumar Prof. P. Avery March 5, 008 Exam Solutions 1. Two cylindrical resistors are made of the same material and have the same resistance. The resistors, R 1 and R, have different radii, r 1 and

More information

Concept Review. Physics 1

Concept Review. Physics 1 Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or

More information

A Review of Vector Addition

A Review of Vector Addition Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine

More information

Section 2.2 Arc Length and Sector Area. Arc Length. Definition. Note:

Section 2.2 Arc Length and Sector Area. Arc Length. Definition. Note: Section. Arc Length and Sector Area Arc Length Definition If a central angle, in a circle of a radiu r, cut off an arc of length, then the meaure of, in radian i: r r r r ( in radian) Note: When applying

More information

4.1 Radian and Degree Measure

4.1 Radian and Degree Measure 4. Radian and Degree Meaure An angle AOB (notation: AOB ) conit of two ray R and R with a common vertex O (ee Figure below). We often interpret an angle a a rotation of the ray R onto R. In thi cae, R

More information

2After completing this chapter you should be able to

2After completing this chapter you should be able to After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

More information

Chapter 19 Magnetic Forces and Fields

Chapter 19 Magnetic Forces and Fields Chapter 19 Magnetic Forces and Fields Student: 3. The magnetism of the Earth acts approximately as if it originates from a huge bar magnet within the Earth. Which of the following statements are true?

More information

Rotation of an Object About a Fixed Axis

Rotation of an Object About a Fixed Axis Chapter 1 Rotation of an Object About a Fixed Axi 1.1 The Important Stuff 1.1.1 Rigid Bodie; Rotation So far in our tudy of phyic we have (with few exception) dealt with particle, object whoe patial dimenion

More information

Projectile motion simulator. http://www.walter-fendt.de/ph11e/projectile.htm

Projectile motion simulator. http://www.walter-fendt.de/ph11e/projectile.htm More Chapter 3 Projectile motion simulator http://www.walter-fendt.de/ph11e/projectile.htm The equations of motion for constant acceleration from chapter 2 are valid separately for both motion in the x

More information

PHYSICS 151 Notes for Online Lecture 1.7

PHYSICS 151 Notes for Online Lecture 1.7 PHYSICS 151 Note for Online Lecture 1.7 In the real world, we don t eit in jut one dienion We need to decribe how thin ove in two and three dienion! We will ue ubcript for the velocitie and acceleration

More information

Exam No. 1 Solutions

Exam No. 1 Solutions Exam No. 1 Solutions I. (20 pts) Three positive charges q 1 = +2 μc, q 2 = +1 μc, and q 3 = +1 μc are arranged at the corners of an equilateral triangle of side 2 m as shown in the diagram. Calculate:

More information

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N) Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in

More information

Force on Moving Charges in a Magnetic Field

Force on Moving Charges in a Magnetic Field [ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

More information

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

More information

MA 408 Homework m. f(p ) = f ((x p, mx p + b)) = s, and. f(q) = f (x q, mx q + b) = x q 1 + m2. By our assumption that f(p ) = f(q), we have

MA 408 Homework m. f(p ) = f ((x p, mx p + b)) = s, and. f(q) = f (x q, mx q + b) = x q 1 + m2. By our assumption that f(p ) = f(q), we have MA 408 Homework 4 Remark 0.1. When dealing with coordinate function, I continually ue the expreion ditance preerving throughout. Thi mean that you can calculate the ditance in the geometry P Q or you can

More information

On Reference RIAA Networks by Jim Hagerman

On Reference RIAA Networks by Jim Hagerman On eference IAA Network by Jim Hagerman You d think there would be nothing left to ay. Everything you need to know about IAA network ha already been publihed. However, a few year back I came acro an intereting

More information

Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

More information

Physics Midterm Review Packet January 2010

Physics Midterm Review Packet January 2010 Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:15-10:15 Room:

More information

Solution. Section 2.8 Related Rates. Exercise. Exercise. Exercise. dx when y 2. and. 3, then what is when x 1. Solution dy dy.

Solution. Section 2.8 Related Rates. Exercise. Exercise. Exercise. dx when y 2. and. 3, then what is when x 1. Solution dy dy. Section.8 Related Rate Eercie If y and d, then what i when 1 d d 6 6 1 1 6 Eercie If y y and 5, then what i d when y d d y 1 5 5 y 1 d 5 1 55 y Eercie A cube urface area increae at the rate of 7 when the

More information

Chapter 22 Homework Solutions

Chapter 22 Homework Solutions Chater Homework Solution 3. REASOIG AD SOLUTIO The motional emf generated by a conductor moving erendicular to a magnetic field i given by Equation. a = vbl, where v and L are the eed and length, reectively,

More information

MSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents

MSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................

More information

SPH4U UNIVERSITY PHYSICS

SPH4U UNIVERSITY PHYSICS SPH4U UNIVERSITY PHYSICS GRAVITATIONAL, ELECTRIC, &... FIELDS L Magnetic Force on Moving Charges (P.386-391) Particle Accelerators As was stated earlier, the ability to accelerate charged particles with

More information

Physics 107 Problem 2.5 O. A. Pringle. Physics 107 Problem 2.6 O. A. Pringle

Physics 107 Problem 2.5 O. A. Pringle. Physics 107 Problem 2.6 O. A. Pringle Phyi 07 Problem 2.5 O. A. Pringle := 3 0 8 h := 6.63 0 34 := 700 0 9 := h = 2.84 0 9 Joule Note I had to et the zero tolerane here. e :=.6 0 9 ev joule onverion ator ev := e ev =.776 ev Phyi 07 Problem

More information

AP2 Electrostatics. Three point charges are located at the corners of a right triangle as shown, where q 1. are each 1 cm from q 3.

AP2 Electrostatics. Three point charges are located at the corners of a right triangle as shown, where q 1. are each 1 cm from q 3. Three point charges are located at the corners of a right triangle as shown, where q 1 = q 2 = 3 µc and q 3 = -4 µc. If q 1 and q 2 are each 1 cm from q 3, what is the magnitude of the net force on q 3?

More information

Magnetism Conceptual Questions. Name: Class: Date:

Magnetism Conceptual Questions. Name: Class: Date: Name: Class: Date: Magnetism 22.1 Conceptual Questions 1) A proton, moving north, enters a magnetic field. Because of this field, the proton curves downward. We may conclude that the magnetic field must

More information

A technical guide to 2014 key stage 2 to key stage 4 value added measures

A technical guide to 2014 key stage 2 to key stage 4 value added measures A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool

More information

Original Article: TOWARDS FLUID DYNAMICS EQUATIONS

Original Article: TOWARDS FLUID DYNAMICS EQUATIONS Peer Reviewed, Open Acce, Free Online Journal Publihed monthly : ISSN: 8-8X Iue 4(5); April 15 Original Article: TOWARDS FLUID DYNAMICS EQUATIONS Citation Zaytev M.L., Akkerman V.B., Toward Fluid Dynamic

More information

Test - A2 Physics. Primary focus Magnetic Fields - Secondary focus electric fields (including circular motion and SHM elements)

Test - A2 Physics. Primary focus Magnetic Fields - Secondary focus electric fields (including circular motion and SHM elements) Test - A2 Physics Primary focus Magnetic Fields - Secondary focus electric fields (including circular motion and SHM elements) Time allocation 40 minutes These questions were ALL taken from the June 2010

More information

Physics 2101, First Exam, Fall 2007

Physics 2101, First Exam, Fall 2007 Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the

More information

Simple Modular Half-Bridge

Simple Modular Half-Bridge Simple Modular HalfBridge Shane Colton Email: colton@mit.edu Maachuett Intitute of Technology Rev.1.1 13 March, 2009 Simple Modular HalfBridge Module Overview V i V i Iolated DCDC Supply: Supplied by 12V

More information

PHYSICS 151 Notes for Online Lecture #11

PHYSICS 151 Notes for Online Lecture #11 PHYSICS 151 ote for Online Lecture #11 A free-bod diagra i a wa to repreent all of the force that act on a bod. A free-bod diagra ake olving ewton econd law for a given ituation eaier, becaue ou re odeling

More information

Modern Physics Laboratory e/m with Teltron Deflection Tube

Modern Physics Laboratory e/m with Teltron Deflection Tube Modern Physics Laboratory e/m with Teltron Deflection Tube Josh Diamond & John Cummings Fall 2010 Abstract The deflection of an electron beam by electric and magnetic fields is observed, and the charge

More information

PSI AP Physics B Kinematics Multiple-Choice Questions

PSI AP Physics B Kinematics Multiple-Choice Questions PSI AP Physics B Kinematics Multiple-Choice Questions 1. An object moves around a circular path of radius R. The object starts from point A, goes to point B and describes an arc of half of the circle.

More information

PHYS-2020: General Physics II Course Lecture Notes Section II

PHYS-2020: General Physics II Course Lecture Notes Section II PHYS-2020: General Physics II Course Lecture Notes Section II Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and

More information

2. METHOD DATA COLLECTION

2. METHOD DATA COLLECTION Key to learning in pecific ubject area of engineering education an example from electrical engineering Anna-Karin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S- Jönköping,

More information

Chapter 20. Magnetic Forces and Magnetic Fields

Chapter 20. Magnetic Forces and Magnetic Fields Chapter 20 Magnetic Forces and Magnetic Fields Magnetic Fields The most familiar example of magnetism for most people is a magnet. Every magnet has two poles, North and South --> called this since if the

More information

HMWK 3. Ch 23: P 17, 23, 26, 34, 52, 58, 59, 62, 64, 73 Ch 24: Q 17, 34; P 5, 17, 34, 42, 51, 52, 53, 57. Chapter 23

HMWK 3. Ch 23: P 17, 23, 26, 34, 52, 58, 59, 62, 64, 73 Ch 24: Q 17, 34; P 5, 17, 34, 42, 51, 52, 53, 57. Chapter 23 HMWK 3 Ch 23: P 7, 23, 26, 34, 52, 58, 59, 62, 64, 73 Ch 24: Q 7, 34; P 5, 7, 34, 42, 5, 52, 53, 57 Chapter 23 P23.7. Prepare: The connecting wires are ideal with zero resistance. We have to reduce the

More information

( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011

( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011 Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q = - 4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force

More information

VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

More information

Position: The location of an object; in physics, typically specified with graph coordinates Introduction Position

Position: The location of an object; in physics, typically specified with graph coordinates Introduction Position .0 - Introduction Object move: Ball bounce, car peed, and pacehip accelerate. We are o familiar with the concept of motion that we ue ophiticated phyic term in everyday language. For example, we might

More information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014 Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

More information

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh. 1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach

More information

Lesson 12: Magnetic Forces and Circular Motion!

Lesson 12: Magnetic Forces and Circular Motion! Lesson 12: Magnetic Forces and Circular Motion If a magnet is placed in a magnetic field, it will experience a force. Types of magnets: Direction of the force on a permanent magnet: Direction of the force

More information

Midterm Exam 1 October 2, 2012

Midterm Exam 1 October 2, 2012 Midterm Exam 1 October 2, 2012 Name: Instructions 1. This examination is closed book and closed notes. All your belongings except a pen or pencil and a calculator should be put away and your bookbag should

More information

f max s = µ s N (5.1)

f max s = µ s N (5.1) Chapter 5 Forces and Motion II 5.1 The Important Stuff 5.1.1 Friction Forces Forces which are known collectively as friction forces are all around us in daily life. In elementary physics we discuss the

More information

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD

More information

NAME. and 2I o. (1) Two long wires carry magnetic fields I o. , where I o

NAME. and 2I o. (1) Two long wires carry magnetic fields I o. , where I o (1) Two long wires carry magnetic fields I o and 2I o, where I o is a constant. The two wires cross at the origin (but without making any electrical connection), and lie in the x-y plane. (a) Find the

More information

Exam 1 Solutions. PHY2054 Fall 2014. Prof. Paul Avery Prof. Andrey Korytov Sep. 26, 2014

Exam 1 Solutions. PHY2054 Fall 2014. Prof. Paul Avery Prof. Andrey Korytov Sep. 26, 2014 Exam 1 Solutions Prof. Paul Avery Prof. Andrey Korytov Sep. 26, 2014 1. Charges are arranged on an equilateral triangle of side 5 cm as shown in the diagram. Given that q 1 = 5 µc and q 2 = q 3 = 2 µc

More information

Independent Samples T- test

Independent Samples T- test Independent Sample T- tet With previou tet, we were intereted in comparing a ingle ample with a population With mot reearch, you do not have knowledge about the population -- you don t know the population

More information

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES FLUID MECHANICS TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES In thi tutorial you will continue the work on laminar flow and develop Poieuille' equation to the form known a the Carman - Kozeny equation. Thi

More information

EXAM I Phys 172H Fall 2009 Modern Mechanics - Honors Instructor: Prof. E. W. Carlson

EXAM I Phys 172H Fall 2009 Modern Mechanics - Honors Instructor: Prof. E. W. Carlson EXAM I Phys 172H Fall 2009 Modern Mechanics - Honors Instructor: Prof. E. W. Carlson TEST FORM A There are two parts to Exam I: The machine-graded part of this test, and the last page that you turn in

More information

University of Calgary. Labatorial 4: Motion of electric charges in electric fields

University of Calgary. Labatorial 4: Motion of electric charges in electric fields University of Calgary Department of Physics and Astronomy PHYS 259, Winter 2016 Labatorial 4: Motion of electric charges in electric fields A charged particle in an electric field experiences a force,

More information

Figure 1.1 Vector A and Vector F

Figure 1.1 Vector A and Vector F CHAPTER I VECTOR QUANTITIES Quantities are anything which can be measured, and stated with number. Quantities in physics are divided into two types; scalar and vector quantities. Scalar quantities have

More information

Physics 9 Fall 2009 Homework 2 - Solutions

Physics 9 Fall 2009 Homework 2 - Solutions Physics 9 Fall 009 Homework - s 1. Chapter 7 - Exercise 5. An electric dipole is formed from ±1.0 nc charges spread.0 mm apart. The dipole is at the origin, oriented along the y axis. What is the electric

More information

Physics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion)

Physics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion) Physics 101 Prof. Ekey Chapter 5 Force and motion (Newton, vectors and causing commotion) Goal of chapter 5 is to establish a connection between force and motion This should feel like chapter 1 Questions

More information

AP PHYSICS C Mechanics - SUMMER ASSIGNMENT FOR 2016-2017

AP PHYSICS C Mechanics - SUMMER ASSIGNMENT FOR 2016-2017 AP PHYSICS C Mechanics - SUMMER ASSIGNMENT FOR 2016-2017 Dear Student: The AP physics course you have signed up for is designed to prepare you for a superior performance on the AP test. To complete material

More information

University Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples

University Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples University Physics 226N/231N Old Dominion University Newton s Laws and Forces Examples Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012-odu Wednesday, September

More information

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

More information

Lecture Presentation Chapter 2 Motion in One Dimension

Lecture Presentation Chapter 2 Motion in One Dimension Lecture Presentation Chapter 2 Motion in One Dimension Suggested Videos for Chapter 2 Prelecture Videos Motion Along a Line Acceleration Free Fall Video Tutor Solutions Motion in One Dimension Class Videos

More information

CHARGE TO MASS RATIO OF THE ELECTRON

CHARGE TO MASS RATIO OF THE ELECTRON CHARGE TO MASS RATIO OF THE ELECTRON In solving many physics problems, it is necessary to use the value of one or more physical constants. Examples are the velocity of light, c, and mass of the electron,

More information

Gravitational Potential Energy

Gravitational Potential Energy Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the

More information

Pearson Physics Level 30 Unit VII Electromagnetic Radiation: Chapter 14 Solutions

Pearson Physics Level 30 Unit VII Electromagnetic Radiation: Chapter 14 Solutions Pearon Pyic Level 30 Unit VII Electromagnetic Radiation: Capter 14 Solution Student Book page 704 Concept Ceck Te colour of te tar are a firt indication of te temperature of teir urface. Te brigt red tar,

More information

Chapter 2 - Representing Motion w./ QuickCheck Questions

Chapter 2 - Representing Motion w./ QuickCheck Questions Chapter 2 - Representing Motion w./ QuickCheck Questions 2015 Pearson Education, Inc. Anastasia Ierides Department of Physics and Astronomy University of New Mexico August 27, 2015 Review of Last Time

More information