DO PHYSICS ONLINE. WEB activity: Use the web to find out more about: Aristotle, Copernicus, Kepler, Galileo and Newton.
|
|
- Audra Long
- 6 years ago
- Views:
Transcription
1 DO PHYSICS ONLINE DISPLACEMENT VELOCITY ACCELERATION The objects that make up space are in motion, we moe, soccer balls moe, the Earth moes, electrons moe, Motion implies change. The study of the motion of objects is called kinematics. We will construct simple models starting with the motion of a single object. The object will be modelled as a point particle in space and who dimensions are ignored. A particle is represented in a diagram as a dot. Since the beginning of human time the study of the motions of the heaens has been important. People who had knowledge of the motion of the heaens had power and control oer others because they knew about the seasons, eclipses and could make predictions. In ancient cultures, people were ery frighted during solar and moon eclipses. Deeloping theories about the motion of the Sun and planets was ery frustrating. Many religions had the Earth at the centre of the Unierse. For presenting iews opposing the Earth centred Unierse one could be burnt alie at the stake. Deeloping a consistent theory of motion was difficult. Physical theories are not just discoered, they are creations of the human mind and must be inented and not discoered. It is claimed that the study of physics is man s greatest intellectual achieement. Physics is a creatie process and physicists build on the best of the past to create new isions of the future. A significant time for science was when Nicholas Copernicus ( ) concluded from experimental data on the motion of the planets, that the Earth reoled around the Sun. Johannes Kepler ( ) was able to decipher accurately and precisely the paths of the planets and produced mathematical laws accounting for the motion of the planets around the Sun. The work of Galileo Galilei ( ) produced a dramatic change in the way science was to be done. Galileo s ideas oerturned the Aristotelian iew of the world that had persisted for more than 2000 years. Galileo s genius was that he realized that the world can be described through mathematics and that that experimentation and measurement were crucial elements in deeloping scientific theories where approximation were necessary to limit complexity. Following on from Galileo was Isaac Newton ( ), who deeloped the underlying theory of the causes of motion (dynamics). He published one of the most famous books of science in 1686, Principia. WEB actiity: Use the web to find out more about: Aristotle, Copernicus, Kepler, Galileo and Newton. Group discussion: Why did people such as priests who had scientific knowledge of the seasons and astronomy hae control oer the bulk of the population in their societies? Group discussion: In the period from the 15 th century to the 19 th century in western Europe there was a dramatic change in social, cultural and technological aspects for people but this did not occur in China, which at the beginning of the 15 th century could be consider to be more adanced socially, culturally and technologically than Europe. Explain why the no change in China compared with the scientific and technological deelopments that occurred in Western Europe in this 400 year period.
2 DISTANCE AND DISPLACEMENT In our study of kinematics will we only consider the motion of objects in one-dimension. This is called rectilinear motion. It is a relatie straight forward task to extend the knowledge one gains in studying one-dimensional motion to two- and three-dimensions. One adantage of studying one-dimensional motion is that we don t hae to use ector notation although displacement, elocity and acceleration are ectors. The sign of the physical quantity in this instance gies the direction of the ector. Consider the displacement ectors shown in figure (1). You can t associate a positie or negatie sign with a ector quantity unless it has a direction parallel to one of the coordinate axes. For example, a component of a ector which is parallel to x-axis in a direction pointing towards +x is assigned a positie number and a component pointing towards the x is assigned a negatie number. +y +x s 2 s 1 s 1y s y2 s 1x For the components only: Since the components of the ectors are directed along the coordinate axes we can assign a positie or negatie alue to the components of a ector. The sign then gies the direction. Can not gie the ectors s1 s2 a + or - sign s 2x s s s 1x 1x 1x s s s 1y 1y 1y s s s 2x 2x 2x s s s 2 y 2 y 2 y Fig. 1. axis. A ector can t be a positie or negatie number unless it is parallel to a coordinate Before reading further, iew the animation of the rectilinear motion of a tram that traels to the right then back to the left. Think about the scientific language that you will need to describe the motion of the tram View the animation of a tram To describe the motion of a moing object you must first define a frame of reference (origin and x-axis) and the object becomes a particle. Consider the tram moing backward and forwards along a straight 2.00 km track. The x-axis is taken along the track with the origin at x = 0. The left end of the track is at x =.00 km and the right end of the track is at x = km. The tram start at time t 1 at the left end of the track moes to the right where it stops at the right end and returns to the left end of the track arriing at a later time t 2. At any time t, the position of the tram is gien by its x-coordinate as shown in figure (2).
3 an object becomes a particle represented by a dot -x 0 position x (km) +1 +x Fig. 2. A frame of reference for the rectilinear motion of the tram with the origin at x = 0. The trams traels from the left to the right end and traels back to the left end of the track. At time t1 0 the tram starts its journey at position x km. At time t hours the train completes one cycle to the right end of the track and back again where the final position of the train is x2 1.00km. The time interal t for the journey is t t2t h = 900 s is the Greek letter Delta meaning change in or increment. Note: Time and time interal are different physical quantities. The distance traelled d = 4.00 km. d is The magnitude of the displacement the final position x 2 s x2 x1=.00 (.00) km = 0 km s is the straight line distance between the initial position x 1 and Distance traelled (scalar) is not the same physical quantity as displacement (ector)
4 SPEED AND VELOCITY Speed and elocity refer to how fast something is traelling but are different physical quantities. Also, we need to distinguish between aerage and instantaneous quantities. The aerage speed defined by equation (1) (1) ag ag of a particle during a time interal t in which the distance traelled is d t definition of aerage speed The aerage speed is a positie scalar quantity and not a ector. d is The aerage elocity particle in the time interal (2) ag ag of a particle is defined as the ratio of the change in position ector s of the s t t during which the change occurred as gien by equation (2) definition of aerage elocity For one-dimensional motion directed along the x-axis we do not need the use the ector notation shown by the arrow aboe the symbol. In the example of our tram: aerage speed t t2t h 900 s d = 4.00 km = m. s x2 x1=.00 (.00) km = 0 km = 0 m ag ag aerage elocity ag d 4 km.h t d 410 t 900 m.s s 0 km.h 0 m.s t 16.0 km.h 4.44 m.s S.I. units Note: ery different alues for the aerage speed and aerage elocity. Often the same symbol is used for speed and elocity. You always need to state whether the symbol represents the speed or elocity. Our tram speeds up continually until it reaches the origin, it then slows down and stops at the right end. In the return journey, it continually speeds up until it reaches the origin it then slows down and stops at the left end of the track. The speed and elocity are always changing. Hence, it is more useful to talk around instantaneous alues rather than aerage alues. The instantaneous elocity is a ector quantity whose magnitude is equal to the instantaneous speed and who instantaneous direction is in the same sense to that in which the particle is moing at that instant. The elocity ector is always tangential to the trajectory of the particle at that instant. Remember, speed and elocity are not the same physical quantity een though they hae the same S.I. unit [m.s ].
5 The aerage elocity gien by equation (2) is ag s t If we make the time interal t smaller and smaller, the aerage elocity approaches the instantaneous alue at that instant. Mathematically it is written as limit t 0 s t This limit is one way of defining the deriatie of a function. The instantaneous elocity is the time rate of change of the displacement (3) ds definition of instantaneous elocity dt For rectilinear motion along the x-axis, we don t need the ector notation and we can simply write the instantaneous elocity as (4) dx rectilinear motion dt You don t need to know how to different a function, but you hae to be familiar with the notation for differentiation and be able to interpret the process of differentiation as finding the slope of the tangent to the displacement s time graph at one instant of time figure (3). Fig. 3. The aerage and instantaneous elocities can be found from a displacement s time graph. The slope of the tangent gies the instantaneous elocity (deriatie of a function). The reerse process to differentiation is integration. Graphically, integration is a process of finding the area under a cure. The slope of the tangent to the displacement s time graph is equal to the elocity. The area under a elocity s time graph in a time interal s in that time interal as shown in figure(5). t is equal to the change in displacement When you refer to the speed or elocity it means you are talking about the instantaneous alues. Therefore, on most occasions you can omit the word instantaneous.
6 ACCELERATION Velocity is related to how fast an object is traelling. Acceleration refers to changes in elocity. Since elocity is a ector quantity, an acceleration occurs when an object speeds up (magnitude of elocity increases) an object slows down (magnitude of elocity decreases) an object changes direction (direction of elocity changes) Acceleration is a ector quantity. You don t sense how fast you are traelling in a car, but you do notice changes in speed and direction of the car especially if the changes occur rapidly you feel the effects of the acceleration. Some of the effects of acceleration we are familiar with include: the experience of sinking into the seat as a plane accelerates down the runway, the "flutter" in our stomach when a lift suddenly speeds up or slows down and being thrown side-ways in a car going around a corner too quickly. The aerage acceleration of an object is defined in terms of the change in elocity and the interal for the change a (5) ag definition of aerage elocity t The instantaneous acceleration is the time rate of change of the elocity, i.e., the deriatie of the elocity gies the acceleration (equation 6). Again, you don t need to differentiate a function but you need to know the notation and interpret it graphically as the acceleration is the slope of the tangent to a elocity s time graph as shown in figure (4). The area under the acceleration s time graph in the time interal is equal to the change in elocity in that time interal as shown in figure (5). (6) (7) d a definition of instantaneous acceleration dt d a rectilinear motion dt
7 elocity acceleration a elocity elocity elocity a > 0 t t a < 0 time t time t instantaneous acceleration at time t is equal to the slope of the tangent at time t a t a = 0 elocity is a linear function of time a t posite constant t Fig. 4. Velocity s time graphs for rectilinear motion. The slope of the tangent is equal to the acceleration. For the special case when the elocity is a linear function of time (straight line) the acceleration is constant. s t time t t time t time t Fig. 5. The area under the elocity s time graph in the time interal t is equal to the change in displacement s in that time interal. The area under the acceleration s time graph in the time interal t is equal to the change in elocity in that time interal.
8 VELOCITY AS A VECTOR We will consider a number of problems (with solutions) to illustrate a how-to approach to soling problems inoling ectors. It is important to consider the steps and strategies inoled so that you will use similar techniques in answering your examination questions. Remember you want to strie for technical excellence. For many ector problems you need to hae mastered the mathematics of a right angle triangle. For a right angle triangle with sides a, b and c (hypotenuse) and with angles A, B and C = 90 sin A a cos A b tan A a c c b sin A cos A 2 2 tan A sin A cos A 1 a B C b c A Pythagorean theorem Area of triangle = ½ a b c a b Example 1 An aircraft is climbing with a steady elocity of 200 m.s at an angle of 20 o to the horizontal. What are the speeds that the aircraft is moing horizontally and ertically? Solution 1 How-to approach the problem Draw a frame of reference showing the x (horizontal) and y (ertical) coordinate axes. Represent the aircraft as a dot at the origin. Draw the elocity ector Show the components of the elocity ector on a separate diagram with a box around the elocity ector. Use the properties of a right angle triangle to calculate the alues for the x and y components of the elocity. Check you answer sensible, significant figures, units. +y +x? m.s y 200 m.s 20 o = 20 o? m.s x always identifying the unknowns
9 From the right angle triangle 200cos 20 m.s 188 m.s horizontal component x ertical component y units included after all expressions, answers to 3 s.f. o 200sin 20 m.s 68.4 m.s o check: m.s 200 m.s ok x y Example 2 An aircraft is trying to fly due north with a elocity of 200 m.s but is subject to a cross wind blowing from the east at 50 m.s. What is the elocity of the plane with respect to the ground? Solution 2 How-to approach the problem Draw a frame of reference showing the x (WE) and y (SN) coordinate axes. Represent the aircraft as a dot. Draw the elocity ectors for the aircraft w.r.t. the wind and the wind w.r.t. the ground. Add the ectors using the head-to-tail method. Use the properties of a right angle triangle to calculate the resultant elocity. Check you answer sensible, significant figures, units. W N +y S +x E elocity of the plane w.r.t. the air m.s elocity of the wind w.r.t. the ground 2 50 m.s The resultant elocity of the plane w.r.t the ground is Adding the ectors head-to-tail method From the right angle triangle The resultant elocity of the plane w.r.t. the ground is 206 m.s and is flying in the direction 14.0 o W of N.? m.s m.s 206 m.s 50 atan o ? m.s always identifying the unknowns 200 o?
10 Example 3 A motor boat is traelling at 10.0 m.s w.r.t the water. The boat wants to cross from one side to the other of a 400 m wide rier in the shortest possible time but the rier is flowing at a rate of 5.00 m.s? In which direction must the boat point and how long will it take to cross the rier? Solution 3 How-to approach the problem Draw a frame of reference showing the x (perpendicular to the rier) and y (parallel to the rier) coordinate axes. Represent the boat as a dot. Draw the elocity ectors for the boat w.r.t the water and the water w.r.t. the ground. Add the ectors using the head-to-tail method so that the resultant points directly across the rier. Use the properties of a right angle triangle to calculate the elocity of the boat w.r.t. the water. Calculate the time to cross the rier. Check you answer sensible, significant figures, units. For the boat to cross the rier in the shortest time it must trael directly across the rier. So the boat must head up steam so that it will drift down with the flow of the water in the rier. +y +x water flowing in rier m.s boat w.r.t. water m.s? resultant elocity must be directly across the stream (pointing in the +x direction)? m.s o m.s From the right angle triangle o? m.s width of rier x 400 m time to cross rier t?s x x t t m.s 8.66 m.s sin asin o x 400 t s = 46.2 s 8.66 The boat must head up-stream pointed at an angle of 30 o as shown in the diagram. The boat crosses the stream at 8.66 m.s and the shortest time to cross the rier is 46.2 s.
VISUAL PHYSICS ONLINE THE LANGUAGE OF PHYSICS KINEMATICS
VISUAL PHYSICS ONLINE THE LANGUAGE OF PHYSICS KINEMATICS The objects that make up space are in motion, we move, soccer balls move, the Earth moves, electrons move,.... Motion implies change. The description
More informationTHE LANGUAGE OF PHYSICS:
HSC PHYSICS ONLINE THE LANGUAGE OF PHYSICS: KINEMATICS The objects that make up space are in motion, we move, soccer balls move, the Earth moves, electrons move,.... Motion implies change. The study of
More informationUNDERSTAND MOTION IN ONE AND TWO DIMENSIONS
SUBAREA I. COMPETENCY 1.0 UNDERSTAND MOTION IN ONE AND TWO DIMENSIONS MECHANICS Skill 1.1 Calculating displacement, aerage elocity, instantaneous elocity, and acceleration in a gien frame of reference
More informationVISUAL PHYSICS ONLINE RECTLINEAR MOTION: UNIFORM ACCELERATION
VISUAL PHYSICS ONLINE RECTLINEAR MOTION: UNIFORM ACCELERATION Predict Obsere Explain Exercise 1 Take an A4 sheet of paper and a heay object (cricket ball, basketball, brick, book, etc). Predict what will
More informationPhysics 2A Chapter 3 - Motion in Two Dimensions Fall 2017
These notes are seen pages. A quick summary: Projectile motion is simply horizontal motion at constant elocity with ertical motion at constant acceleration. An object moing in a circular path experiences
More informationChapter 1: Kinematics of Particles
Chapter 1: Kinematics of Particles 1.1 INTRODUCTION Mechanics the state of rest of motion of bodies subjected to the action of forces Static equilibrium of a body that is either at rest or moes with constant
More informationStatus: Unit 2, Chapter 3
1 Status: Unit, Chapter 3 Vectors and Scalars Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication by a Scalar Adding Vectors by Components Unit Vectors Vector Kinematics Projectile
More informationChapter 3 Motion in a Plane
Chapter 3 Motion in a Plane Introduce ectors and scalars. Vectors hae direction as well as magnitude. The are represented b arrows. The arrow points in the direction of the ector and its length is related
More informationDisplacement, Time, Velocity
Lecture. Chapter : Motion along a Straight Line Displacement, Time, Velocity 3/6/05 One-Dimensional Motion The area of physics that we focus on is called mechanics: the study of the relationships between
More informationWould you risk your live driving drunk? Intro
Martha Casquete Would you risk your lie driing drunk? Intro Motion Position and displacement Aerage elocity and aerage speed Instantaneous elocity and speed Acceleration Constant acceleration: A special
More informationLesson 2: Kinematics (Sections ) Chapter 2 Motion Along a Line
Lesson : Kinematics (Sections.-.5) Chapter Motion Along a Line In order to specify a position, it is necessary to choose an origin. We talk about the football field is 00 yards from goal line to goal line,
More informationLesson 3: Free fall, Vectors, Motion in a plane (sections )
Lesson 3: Free fall, Vectors, Motion in a plane (sections.6-3.5) Last time we looked at position s. time and acceleration s. time graphs. Since the instantaneous elocit is lim t 0 t the (instantaneous)
More informationChapter 2 Motion Along a Straight Line
Chapter Motion Along a Straight Line In this chapter we will study how objects moe along a straight line The following parameters will be defined: (1) Displacement () Aerage elocity (3) Aerage speed (4)
More informationMCAT Physics - Problem Drill 06: Translational Motion
MCAT Physics - Problem Drill 06: Translational Motion Question No. 1 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems on paper as 1. An object falls from rest
More informationChapter 2: 1D Kinematics Tuesday January 13th
Chapter : D Kinematics Tuesday January 3th Motion in a straight line (D Kinematics) Aerage elocity and aerage speed Instantaneous elocity and speed Acceleration Short summary Constant acceleration a special
More informationChapter (3) Motion. in One. Dimension
Chapter (3) Motion in One Dimension Pro. Mohammad Abu Abdeen Dr. Galal Ramzy Chapter (3) Motion in one Dimension We begin our study o mechanics by studying the motion o an object (which is assumed to be
More information1. Linear Motion. Table of Contents. 1.1 Linear Motion: Velocity Time Graphs (Multi Stage) 1.2 Linear Motion: Velocity Time Graphs (Up and Down)
. LINEAR MOTION www.mathspoints.ie. Linear Motion Table of Contents. Linear Motion: Velocity Time Graphs (Multi Stage). Linear Motion: Velocity Time Graphs (Up and Down).3 Linear Motion: Common Initial
More informationONLINE: MATHEMATICS EXTENSION 2 Topic 6 MECHANICS 6.6 MOTION IN A CIRCLE
ONLINE: MAHEMAICS EXENSION opic 6 MECHANICS 6.6 MOION IN A CICLE When a particle moes along a circular path (or cured path) its elocity must change een if its speed is constant, hence the particle must
More informationPhysics 1: Mechanics
Physics 1: Mechanics Đào Ngọc Hạnh Tâm Office: A1.53, Email: dnhtam@hcmiu.edu.n HCMIU, Vietnam National Uniersity Acknowledgment: Most of these slides are supported by Prof. Phan Bao Ngoc credits (3 teaching
More informationPhysics 4A Solutions to Chapter 4 Homework
Physics 4A Solutions to Chapter 4 Homework Chapter 4 Questions: 4, 1, 1 Exercises & Problems: 5, 11, 3, 7, 8, 58, 67, 77, 87, 11 Answers to Questions: Q 4-4 (a) all tie (b) 1 and tie (the rocket is shot
More informationMotion in Two and Three Dimensions
PH 1-A Fall 014 Motion in Two and Three Dimensions Lectures 4,5 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
More informationAlgebra Based Physics. Motion in One Dimension. 1D Kinematics Graphing Free Fall 2016.notebook. August 30, Table of Contents: Kinematics
Table of Contents: Kinematics Algebra Based Physics Kinematics in One Dimension 06 03 www.njctl.org Motion in One Dimension Aerage Speed Position and Reference Frame Displacement Aerage Velocity Instantaneous
More informationMotion in Two and Three Dimensions
PH 1-1D Spring 013 Motion in Two and Three Dimensions Lectures 5,6,7 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
More informationFeb 6, 2013 PHYSICS I Lecture 5
95.141 Feb 6, 213 PHYSICS I Lecture 5 Course website: faculty.uml.edu/pchowdhury/95.141/ www.masteringphysics.com Course: UML95141SPRING213 Lecture Capture h"p://echo36.uml.edu/chowdhury213/physics1spring.html
More informationBrake applications and the remaining velocity Hans Humenberger University of Vienna, Faculty of mathematics
Hans Humenberger: rake applications and the remaining elocity 67 rake applications and the remaining elocity Hans Humenberger Uniersity of Vienna, Faculty of mathematics Abstract It is ery common when
More informationMath 144 Activity #9 Introduction to Vectors
144 p 1 Math 144 ctiity #9 Introduction to Vectors Often times you hear people use the words speed and elocity. Is there a difference between the two? If so, what is the difference? Discuss this with your
More informationSKAA 1213 Engineering Mechanics
SKAA 113 Engineering Mechanic TOPIC 8 KINEMATIC OF PARTICLES Lecturer: Roli Anang Dr. Mohd Yunu Ihak Dr. Tan Cher Siang Outline Introduction Rectilinear Motion Curilinear Motion Problem Introduction General
More informationDynamics ( 동역학 ) Ch.2 Motion of Translating Bodies (2.1 & 2.2)
Dynamics ( 동역학 ) Ch. Motion of Translating Bodies (. &.) Motion of Translating Bodies This chapter is usually referred to as Kinematics of Particles. Particles: In dynamics, a particle is a body without
More information(a) During the first part of the motion, the displacement is x 1 = 40 km and the time interval is t 1 (30 km / h) (80 km) 40 km/h. t. (2.
Chapter 3. Since the trip consists of two parts, let the displacements during first and second parts of the motion be x and x, and the corresponding time interals be t and t, respectiely. Now, because
More informationChapter 2: Motion in Two Dimensions
Chapter Motion in Two Dimensions Mini Inestigation Garbage Can Basketball, page 59 A. Answers may ary. Sample answer When launched from knee height, an underhand upward thrust is used such that the ball
More informationA. unchanged increased B. unchanged unchanged C. increased increased D. increased unchanged
IB PHYSICS Name: DEVIL PHYSICS Period: Date: BADDEST CLASS ON CAMPUS CHAPTER B TEST REVIEW. A rocket is fired ertically. At its highest point, it explodes. Which one of the following describes what happens
More informationNote on Posted Slides. Motion Is Relative
Note on Posted Slides These are the slides that I intended to show in class on Tue. Jan. 9, 2014. They contain important ideas and questions from your reading. Due to time constraints, I was probably not
More informationDYNAMICS. Kinematics of Particles VECTOR MECHANICS FOR ENGINEERS: Tenth Edition CHAPTER
Tenth E CHAPTER 11 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdinand P. Beer E. Russell Johnston, Jr. Phillip J. Cornwell Lecture Notes: Brian P. Self California Polytechnic State Uniersity Kinematics
More informationMotion In Two Dimensions. Vectors in Physics
Motion In Two Dimensions RENE DESCARTES (1736-1806) GALILEO GALILEI (1564-1642) Vectors in Physics All physical quantities are either scalars or ectors Scalars A scalar quantity has only magnitude. In
More informationCHAPTER 3: Kinematics in Two Dimensions; Vectors
HAPTER 3: Kinematics in Two Dimensions; Vectors Solution Guide to WebAssign Problems 3.1 [] The truck has a displacement of 18 + (16) blocks north and 1 blocks east. The resultant has a magnitude of +
More informationPhysics 111. Help sessions meet Sunday, 6:30-7:30 pm in CLIR Wednesday, 8-9 pm in NSC 098/099
ics Announcements day, ember 7, 2007 Ch 2: graphing - elocity s time graphs - acceleration s time graphs motion diagrams - acceleration Free Fall Kinematic Equations Structured Approach to Problem Soling
More information(a)!! d = 17 m [W 63 S]!! d opposite. (b)!! d = 79 cm [E 56 N] = 79 cm [W 56 S] (c)!! d = 44 km [S 27 E] = 44 km [N 27 W] metres. 3.
Chapter Reiew, pages 90 95 Knowledge 1. (b). (d) 3. (b) 4. (a) 5. (b) 6. (c) 7. (c) 8. (a) 9. (a) 10. False. A diagram with a scale of 1 cm : 10 cm means that 1 cm on the diagram represents 10 cm in real
More informationDYNAMICS. Kinematics of Particles Engineering Dynamics Lecture Note VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER
27 The McGraw-Hill Companies, Inc. All rights resered. Eighth E CHAPTER 11 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdinand P. Beer E. Russell Johnston, Jr. Kinematics of Particles Lecture Notes: J.
More information(a) Taking the derivative of the position vector with respect to time, we have, in SI units (m/s),
Chapter 4 Student Solutions Manual. We apply Eq. 4- and Eq. 4-6. (a) Taking the deriatie of the position ector with respect to time, we hae, in SI units (m/s), d ˆ = (i + 4t ˆj + tk) ˆ = 8tˆj + k ˆ. dt
More informationPHYS 100: Lecture 3. r r r VECTORS. RELATIVE MOTION in 2-D. uuur uur uur SG S W. B y j x x x C B. A y j. A x i. B x i. v W. v S.
PHYS 100: Lecture 3 VECTORS A C B r r r C = A + B j i A i C B i B y j A y j C = A + B C = A + B y y y RELATIVE MOTION in 2- W S W W S SG uuur uur uur = + SG S W Physics 100 Lecture 3, Slide 1 Who is the
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 4. Home Page. Title Page. Page 1 of 35.
Rutgers Uniersit Department of Phsics & Astronom 01:750:271 Honors Phsics I Fall 2015 Lecture 4 Page 1 of 35 4. Motion in two and three dimensions Goals: To stud position, elocit, and acceleration ectors
More informationNote on Posted Slides. Chapter 3 Pre-Class Reading Question. Chapter 3 Reading Question : The Fine Print. Suggested End of Chapter Items
Note on Posted Slides These are the slides that I intended to show in class on Wed. Jan. 9, 2013. They contain important ideas and questions from your reading. Due to time constraints, I was probably not
More informationReview. acceleration is the rate of change of velocity (how quickly the velocity is changing) For motion in a line. v t
Accelerated Motion Reiew acceleration is the rate o change o elocity (how quickly the elocity is changing) For motion in a line a i t t When an object is moing in a straight line, a positie acceleration
More informationIII. Relative Velocity
Adanced Kinematics I. Vector addition/subtraction II. Components III. Relatie Velocity IV. Projectile Motion V. Use of Calculus (nonuniform acceleration) VI. Parametric Equations The student will be able
More informationNote: the net distance along the path is a scalar quantity its direction is not important so the average speed is also a scalar.
PHY 309 K. Solutions for the first mid-term test /13/014). Problem #1: By definition, aerage speed net distance along the path of motion time. 1) ote: the net distance along the path is a scalar quantity
More informationPearson Physics Level 20 Unit I Kinematics: Chapter 2 Solutions
Pearson Phsics Leel 0 Unit I Kinematics: Chapter Solutions Student Book page 71 Skills Practice Students answers will ar but ma consist of: (a) scale 1 cm : 1 m; ector will be 5 cm long scale 1 m forward
More informationPHYS 1443 Section 004 Lecture #4 Thursday, Sept. 4, 2014
PHYS 1443 Section 004 Lecture #4 Thursday, Sept. 4, 014 One Dimensional Motion Motion under constant acceleration One dimensional Kinematic Equations How do we sole kinematic problems? Falling motions
More informationSo now that we ve mentioned these terms : kinetic, potential, work we should try to explain them more. Let s develop a model:
Lecture 12 Energy e are now at the point where we can talk about one of the most powerful tools in physics, energy. Energy is really an abstract concept. e hae indicators of energy (temperature, elocity
More informationPhysics Department Tutorial: Motion in a Circle (solutions)
JJ 014 H Physics (9646) o Solution Mark 1 (a) The radian is the angle subtended by an arc length equal to the radius of the circle. Angular elocity ω of a body is the rate of change of its angular displacement.
More information1-D Kinematics Problems
x (m) Name: AP Physics -D Kinemics Problems 5. Answer the following based on the elocity s. time graph. 6 8 4-4 -8 - straight cured 4 6 8 a. Gie a written description of the motion. t (s) Object moes in
More informationUnit 11: Vectors in the Plane
135 Unit 11: Vectors in the Plane Vectors in the Plane The term ector is used to indicate a quantity (such as force or elocity) that has both length and direction. For instance, suppose a particle moes
More informationsin! =! d y =! d T ! d y = 15 m = m = 8.6 m cos! =! d x ! d x ! d T 2 =! d x 2 +! d y =! d x 2 +! d y = 27.2 m = 30.0 m tan! =!
Section. Motion in Two Dimensions An Algebraic Approach Tutorial 1 Practice, page 67 1. Gien d 1 = 7 m [W]; d = 35 m [S] Required d T Analysis d T = d 1 + d Solution Let φ represent the angle d T with
More informationdifferent formulas, depending on whether or not the vector is in two dimensions or three dimensions.
ectors The word ector comes from the Latin word ectus which means carried. It is best to think of a ector as the displacement from an initial point P to a terminal point Q. Such a ector is expressed as
More informationThe Dot Product Pg. 377 # 6ace, 7bdf, 9, 11, 14 Pg. 385 # 2, 3, 4, 6bd, 7, 9b, 10, 14 Sept. 25
UNIT 2 - APPLICATIONS OF VECTORS Date Lesson TOPIC Homework Sept. 19 2.1 (11) 7.1 Vectors as Forces Pg. 362 # 2, 5a, 6, 8, 10 13, 16, 17 Sept. 21 2.2 (12) 7.2 Velocity as Vectors Pg. 369 # 2,3, 4, 6, 7,
More informationMOTION OF FALLING OBJECTS WITH RESISTANCE
DOING PHYSICS WIH MALAB MECHANICS MOION OF FALLING OBJECS WIH RESISANCE Ian Cooper School of Physics, Uniersity of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECORY FOR MALAB SCRIPS mec_fr_mg_b.m Computation
More informationPhysics Teach Yourself Series Topic 2: Circular motion
Physics Teach Yourself Series Topic : Circular motion A: Leel 14, 474 Flinders Street Melbourne VIC 3000 T: 1300 134 518 W: tssm.com.au E: info@tssm.com.au TSSM 013 Page 1 of 7 Contents What you need to
More informationReversal in time order of interactive events: Collision of inclined rods
Reersal in time order of interactie eents: Collision of inclined rods Published in The European Journal of Physics Eur. J. Phys. 27 819-824 http://www.iop.org/ej/abstract/0143-0807/27/4/013 Chandru Iyer
More information3. What is the minimum work needed to push a 950-kg car 310 m up along a 9.0 incline? Ignore friction. Make sure you draw a free body diagram!
Wor Problems Wor and Energy HW#. How much wor is done by the graitational force when a 280-g pile drier falls 2.80 m? W G = G d cos θ W = (mg)d cos θ W = (280)(9.8)(2.80) cos(0) W = 7683.2 W 7.7 0 3 Mr.
More informationAP Physics 1 Kinematics 1D
AP Physics 1 Kinematics 1D 1 Algebra Based Physics Kinematics in One Dimension 2015 08 25 www.njctl.org 2 Table of Contents: Kinematics Motion in One Dimension Position and Reference Frame Displacement
More informationPHYS 1441 Section 002 Lecture #6
PHYS 1441 Section 00 Lecture #6 Monday, Feb. 4, 008 Examples for 1-Dim kinematic equations Free Fall Motion in Two Dimensions Maximum ranges and heights Today s homework is homework #3, due 9pm, Monday,
More information6.3 Vectors in a Plane
6.3 Vectors in a Plane Plan: Represent ectors as directed line segments. Write the component form of ectors. Perform basic ector operations and represent ectors graphically. Find the direction angles of
More informationPreliminary Physics. Moving About. DUXCollege. Week 2. Student name:. Class code:.. Teacher name:.
Week 2 Student name:. Class code:.. Teacher name:. DUXCollege Week 2 Theory 1 Present information graphically of: o Displacement vs time o Velocity vs time for objects with uniform and non-uniform linear
More informationKinematics - study of motion HIGHER PHYSICS 1A UNSW SESSION s o t See S&J , ,
1 Kinematics - study of motion HIGHER PHYSICS 1A UNSW SESSION 1 01 s Joe Wolfe s o t See S&J.1-.6, 3.1-3.4, 4.1-4.6 Is this straightforward, or are there subtleties? See Physclips Chs &3 and support pages
More informationUnit 1 Parent Guide: Kinematics
Unit 1 Parent Guide: Kinematics Kinematics is the study of the motion of objects. Scientists can represent this information in the following ways: written and verbal descriptions, mathematically (with
More informationDisplacement, Velocity, and Acceleration AP style
Displacement, Velocity, and Acceleration AP style Linear Motion Position- the location of an object relative to a reference point. IF the position is one-dimension only, we often use the letter x to represent
More informationMagnetism has been observed since roughly 800 B.C. Certain rocks on the Greek peninsula of Magnesia were noticed to attract and repel one another.
1.1 Magnetic ields Magnetism has been obsered since roughly 800.C. Certain rocks on the Greek peninsula of Magnesia were noticed to attract and repel one another. Hence the word: Magnetism. o just like
More informationPurpose of the experiment
Impulse and Momentum PES 116 Adanced Physics Lab I Purpose of the experiment Measure a cart s momentum change and compare to the impulse it receies. Compare aerage and peak forces in impulses. To put the
More informationDefinitions In physics we have two types of measurable quantities: vectors and scalars.
1 Definitions In physics we have two types of measurable quantities: vectors and scalars. Scalars: have magnitude (magnitude means size) only Examples of scalar quantities include time, mass, volume, area,
More informationFOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem
WEEK-6 Recitation PHYS 3 FOCUS ON CONCEPTS Section 7. The Impulse Momentum Theorem Mar, 08. Two identical cars are traeling at the same speed. One is heading due east and the other due north, as the drawing
More informationRoberto s Notes on Linear Algebra Chapter 1: Geometric vectors Section 8. The dot product
Roberto s Notes on Linear Algebra Chapter 1: Geometric ectors Section 8 The dot product What you need to know already: What a linear combination of ectors is. What you can learn here: How to use two ectors
More informationPhysics General Physics. Lecture 3 Newtonian Mechanics. Fall 2016 Semester. Prof. Matthew Jones
Physics 22000 General Physics Lecture 3 Newtonian Mechanics Fall 2016 Semester Prof. Matthew Jones 1 Review of Lectures 1 and 2 In the previous lectures we learned how to describe some special types of
More informationOn my honor, I have neither given nor received unauthorized aid on this examination.
Instructor(s): Field/Furic PHYSICS DEPARTENT PHY 2053 Exam 1 October 5, 2011 Name (print, last first): Signature: On my honor, I hae neither gien nor receied unauthorized aid on this examination. YOUR
More informationApplications of Forces
Chapter 10 Applications of orces Practice Problem Solutions Student Textbook page 459 1. (a) rame the Problem - Make a sketch of the ector. - The angle is between 0 and 90 so it is in the first quadrant.
More informationUnderstanding. 28. Given:! d inital. = 1750 m [W];! d final Required:!! d T Analysis:!! d T. Solution:!! d T
Unit 1 Review, pages 100 107 Knowledge 1. (c). (c) 3. (b) 4. (d) 5. (b) 6. (c) 7. (d) 8. (b) 9. (d) 10. (b) 11. (b) 1. True 13. True 14. False. The average velocity of an object is the change in displacement
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Graitation. Each of fie satellites makes a circular orbit about an object that is much more massie than any of the satellites. The mass and orbital radius of each satellite
More informationDescribing motion: Kinematics in two dimension
Describing motion: Kinematics in two dimension Scientist Galileo Galilei Issac Newton Vocabulary Vector scalars Resultant Displacement Components Resolving vectors Unit vector into its components Average
More informationMathematical review trigonometry vectors Motion in one dimension
Mathematical review trigonometry vectors Motion in one dimension Used to describe the position of a point in space Coordinate system (frame) consists of a fixed reference point called the origin specific
More informationPHYSICS Kinematics in One Dimension
PHYSICS Kinematics in One Dimension August 13, 2012 www.njctl.org 1 Motion in One Dimension Return to Table of Contents 2 Distance We all know what the distance between two objects is... So what is it?
More informationChapter 1. The Postulates of the Special Theory of Relativity
Chapter 1 The Postulates of the Special Theory of Relatiity Imagine a railroad station with six tracks (Fig. 1.1): On track 1a a train has stopped, the train on track 1b is going to the east at a elocity
More informationVectors and Kinematics Notes 1 Review
Velocity is defined as the change in displacement with respect to time. Vectors and Kinematics Notes 1 Review Note that this formula is only valid for finding constant velocity or average velocity. Also,
More informationKinematics of Particles
nnouncements Recitation time is set to 8am eery Monday. Participation i credit will be gien to students t who uploads a good question or good answer to the Q& bulletin board. Suggestions? T s and I will
More informationPosition, Speed and Velocity Position is a variable that gives your location relative to an origin. The origin is the place where position equals 0.
Position, Speed and Velocity Position is a variable that gives your location relative to an origin. The origin is the place where position equals 0. The position of this car at 50 cm describes where the
More informationθ Vman V ship α φ V β
Answer, Key { Homework 3 { Rubin H Landau 1 This print-out should hae 9 uestions. Check that it is complete before leaing the printer. Also, multiple-choice uestions may continue on the next column or
More informationLesson 6: Apparent weight, Radial acceleration (sections 4:9-5.2)
Beore we start the new material we will do another Newton s second law problem. A bloc is being pulled by a rope as shown in the picture. The coeicient o static riction is 0.7 and the coeicient o inetic
More informationChapter 11 Collision Theory
Chapter Collision Theory Introduction. Center o Mass Reerence Frame Consider two particles o masses m and m interacting ia some orce. Figure. Center o Mass o a system o two interacting particles Choose
More informationStudent Exploration: Vectors
Name: Date: Student Exploration: Vectors Vocabulary: component, dot product, magnitude, resultant, scalar, unit vector notation, vector Prior Knowledge Question (Do this BEFORE using the Gizmo.) An airplane
More informationChapter: Newton s Laws of Motion
Table of Contents Chapter: Newton s Laws of Motion Section 1: Motion Section 2: Newton s First Law Section 3: Newton s Second Law Section 4: Newton s Third Law 1 Motion What is motion? Distance and Displacement
More informationLinear Momentum and Collisions Conservation of linear momentum
Unit 4 Linear omentum and Collisions 4.. Conseration of linear momentum 4. Collisions 4.3 Impulse 4.4 Coefficient of restitution (e) 4.. Conseration of linear momentum m m u u m = u = u m Before Collision
More informationAH Mechanics Checklist (Unit 1) AH Mechanics Checklist (Unit 1) Rectilinear Motion
Rectilinear Motion No. kill Done 1 Know that rectilinear motion means motion in 1D (i.e. along a straight line) Know that a body is a physical object 3 Know that a particle is an idealised body that has
More information2/18/2019. Position-versus-Time Graphs. Below is a motion diagram, made at 1 frame per minute, of a student walking to school.
Position-versus-Time Graphs Below is a motion diagram, made at 1 frame per minute, of a student walking to school. A motion diagram is one way to represent the student s motion. Another way is to make
More informationMOTION IN 2-DIMENSION (Projectile & Circular motion And Vectors)
MOTION IN -DIMENSION (Projectile & Circular motion nd Vectors) INTRODUCTION The motion of an object is called two dimensional, if two of the three co-ordinates required to specif the position of the object
More informationLecture #8-6 Waves and Sound 1. Mechanical Waves We have already considered simple harmonic motion, which is an example of periodic motion in time.
Lecture #8-6 Waes and Sound 1. Mechanical Waes We hae already considered simple harmonic motion, which is an example of periodic motion in time. The position of the body is changing with time as a sinusoidal
More informationChapter 3 Homework Packet. Conceptual Questions
Chapter 3 Homework Packet Conceptual Questions 1) Which one of the following is an example of a vector quantity? A) mass B) area C) distance D) velocity A vector quantity has both magnitude and direction.
More informationHW Chapter 3 Q 14,15 P 2,7,812,18,24,25. Chapter 3. Motion in the Universe. Dr. Armen Kocharian
HW Chapter 3 Q 14,15 P 2,7,812,18,24,25 Chapter 3 Motion in the Universe Dr. Armen Kocharian Predictability The universe is predictable and quantifiable Motion of planets and stars description of motion
More informationMotors and Generators
Physics Motors and Generators New Reised Edition Brian Shadwick Contents Use the table of contents to record your progress through this book. As you complete each topic, write the date completed, then
More informationChapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion
Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors
More informationPhysics Chapter 3 Notes. Section 3-1: Introduction to Vectors (pages 80-83)
Physics Chapter 3 Notes Section 3-1: Introduction to Vectors (pages 80-83) We can use vectors to indicate both the magnitude of a quantity, and the direction. Vectors are often used in 2- dimensional problems.
More informationjfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt
Phone : 0 903 903 7779, 98930 58881 Kinematics Pae: 1 fo/u fopkjr Hkh# tu] uha kjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k fla ladyi dj] lrs foifr usd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks
More informationLABORATORY VI. ROTATIONAL DYNAMICS
LABORATORY VI. ROTATIONAL DYNAMICS So far this semester, you hae been asked to think of objects as point particles rather than extended bodies. This assumption is useful and sometimes good enough. Howeer,
More informationTeacher Content Brief
Teacher Content Brief Vectors Introduction Your students will need to be able to maneuver their Sea Perch during the competition, so it will be important for them to understand how forces combine to create
More information