Rutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman
|
|
- Ella Hudson
- 7 years ago
- Views:
Transcription
1 1 of 8 2/29/ :17 PM Signed in as Weida Wu, Instructor Help Sign Out Rutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman Instructor Resources etext Study Area Course Home Assignments Roster Gradebook Item Library 5. Relativistic time dilation and length contraction (Ch. 37) [ Edit ] Overview Summary View Diagnostics View Print View with Answers 5. Relativistic time dilation and length contraction (Ch. 37) Due: 11:59pm on Sunday, February 28, 2016 To understand how points are awarded, read the Grading Policy for this assignment. Postulates of Special Relativity Description: Discuss the postulates of Special Relativity, and show that they contradict Galilean Relativity. Learning Goal: To understand the postulates of special relativity and their relationship to Galilean relativity. Einstein's theory of special relativity is based on two postulates: 1. The principle of relativity: The laws of physics are the same in any inertial coordinate system. For example, by watching the action of the balls on a pool table that is on a ship, you cannot tell whether the ship is at the dock or moving through the water at a constant speed. (You can think of an inertial coordinate system as a nonaccelerating coordinate system. There are actually other subtle conditions, but for now they are not of concern.) 2. The speed of light in vacuum is constant. This says that observers in any inertial coordinate system will measure the same value for the speed of light, independent of the origin of that light. The simplicity of these assumptions belies their brilliance--they directly contradict our intuitive ideas of relativity, yet by accepting them we can easily build a theory of relative motion that is in accord with all observation. We now discuss these ideas more fully, showing where they depart from the previously held ideas about relativity. Consider a pool game being played on a pool table on the deck of an aircraft carrier near the bow (front). Assume that the carrier is moving north at As a result of the initial break, a ball flies over the edge of the table and over the edge of the deck with a horizontal component of velocity directed toward the bow of the ship of What is, the horizontal component of the speed with which this ball strikes the water in front of the ship (i.e., what is the speed of the ball relative to the water)? Express your answer numerically in meters per second. Use ordinary (Galilean) physics. Hint 1. Galilean relativity for velocity addition In Galilean relativity, time and distance are absolute and independent quantities, and velocities therefore add. In particular, the formula for relative velocity addition is (suppressing the vector signs), where is the velocity of the ball relative to the water, is the velocity of the ball relative to the carrier, and is the velocity of the carrier relative to the water. = 30 Part B You have used the ideas of Galilean relativity--that time and distance are absolute and independent quantities and that velocities therefore add. In particular, the formula for relative velocity addition is, where is the velocity of the ball relative to the water, is the velocity of the ball relative to the carrier, and is the velocity of the carrier relative to the water. These ideas are embodied in Isaac Newton's Principia. Newton started this seminal work by stating which of the following? Space is uniform and infinite in extent but time is relative. Space is relative but time is everywhere uniform and the same. Space is uniform and infinite in extent and time is everywhere uniform and the same. Space and time are both relative. Part C
2 2 of 8 2/29/ :17 PM Which of these factors was definitely not a consideration in Einstein's making the postulate that the speed of light is constant for all observers? Maxwell's equations predict that light travels at speed without any reference to the velocity of the reference frame. The Michelson-Morley experiment showed that the round-trip travel time of light did not depend on the motion of the earth through the ether. Measurements of the locations of distant stars showed an annual circular motion consistent with the hypothesis that the earth was moving through a stationary ether in which the star's light wave traveled. Michelson made very accurate measurements of the speed of light. The exact value of the speed of light was immaterial to Einstein except that it had to be a speed beyond practical comprehension. Also, Michelson measured the speed of light after Einstein's work, which was published in Part D We now consider the motion of a flash of light that is emitted from the ship described in. Imagine that there is a flashlight on the pool table that emits a flash of light directed toward the bow of the ship, which is still traveling northward at The light encounters two photodiodes on the table that are spaced exactly 1.00 apart along a north-south axis. What is the time that elapses between when the flash of light encounters the first photodiode and when it strikes the second? Express your answer in seconds to eight significant figures. Remember that an answer such as 1/ will be accepted at its calculated value (if you do not put commas in your answer). Also, the speed of light in vacuum is. Hint 1. How to get time from velocity As always, you can find the time from the equation, where is the distance and is the velocity. = Part E Now imagine that there is a similar set of photodiodes, also spaced 1.00 apart along a north-south axis, mounted on a dock on shore directly ahead of the aircraft carrier. The light from the flashlight on the pool table encounters these two photodiodes. What is the time that elapses between when the flash of light encounters the first photodiode and when it strikes the second? Express your answer in seconds to eight significant figures. Remember that an answer such as 1/ will be accepted at its calculated value (if you do not put commas in your answer). Use for the speed of light in vacuum. Hint 1. How to get time from velocity As always, you can find the time from the equation, where is the distance and is the velocity. = Part F You have now correctly used the key ideas of special relativity. As a consequence of these ideas, what can you conclude? Space is uniform and infinite in extent but time is relative. Space is relative but time is everywhere uniform and the same. Space is uniform and infinite in extent and time is everywhere uniform and the same. Space and time are both relative. Gedanken Conceptual Questions Description: Conceptual questions on observations in different frames of reference. These questions ask students to perform thought experiments similar to Einstein's gedanken experiments. Einstein developed much of his understanding of relativity through the use of gedanken, or thought, experiments. In a gedanken experiment, Einstein would imagine an experiment that could not be performed because of technological limitations, and so he would perform the experiment in his head. By analyzing the results of these experiments, he was led to a deeper understanding of his theory. In each the following gedanken experiments, Albert is in the exact center of a glass-sided freight car speeding to the right at a very high speed relative to you.
3 3 of 8 2/29/ :17 PM Albert has a flashlight in each hand and directs them at the front and rear ends of the freight car. Albert switches the flashlights on at the same time. In Albert's frame of reference, which beam of light travels at a greater speed, the one directed toward the front or the one toward the rear of the train, or do they travel at the same speed? Which beam travels faster in your frame of reference? Enter the answers for Albert's frame of reference and your frame of reference separated by a comma using the terms front, rear, and same. For example, if in Albert's frame of reference the beam of light directed toward the front of the train travels at a greater speed and in your frame of reference the two beams travel at the same speed, then enter front,same. Hint 1. A postulate of Einstein s relativity One of the basic postulates of special relativity is that the speed of light is the same for all observers, regardless of the speed of either the observer or the source of the light. Part B In Albert's frame of reference, which end, front or rear, is struck by light first, or are they struck at the same time? Which end is struck first in your frame of reference? Enter the answer for Albert's frame of reference and your frame of reference separated by a comma using the terms front, rear, and same. For example, if in Albert's frame of reference the beam of light strikes the front first and in your frame of reference the two beams strike at the same time, then enter front,same. Hint 1. Distinguishing between frames of reference It is important to clearly distinguish between the two frames of reference involved in this problem. In Albert s frame, the train is at rest. Albert, the flashlights, the walls, and the ceiling and floor of the train are all completely stationary in this frame of reference. In your frame of reference, the train and everything in it is moving. Albert, the flashlights, the walls, and the ceiling and floor of the train are all moving at exactly the same speed in your frame of reference. Hint 2. Situation in Albert s frame In Albert s frame, the train is completely at rest. The light from the flashlights is emitted directly between the two stationary ends, and one beam moves to the right and the other moves to the left at exactly the same speed, the speed of light. Hint 3. Situation in your frame In your frame, both the front and rear ends are moving to the right at the same constant speed. The light from the flashlights is emitted directly between these two moving ends, and one beam moves to the right and the other moves to the left at exactly the same speed, the speed of light.
4 4 of 8 2/29/ :17 PM One of the most startling consequences of special relativity is that two events can be simultaneous for one observer, in one frame of reference, but may not be simultaneous for a different observer in a different frame. Thus, saying that two things "happened at the same time" may be true for one person and false for another, but both observers are correct in their statements. Now Albert directs his flashlights at the ceiling and floor of the freight car. The flashlights are located midway between the ceiling and the floor and Albert switches them on at the same time Part C In Albert's frame of reference, which surface, ceiling or floor, is struck by light first, or are they struck at the same time? Which surface is struck first in your frame of reference? Enter the answer for Albert's frame of reference and your frame of reference separated by a comma using the terms ceiling, floor, and same. For example, if in Albert's frame of reference the ceiling is struck by light first and in your frame of reference the floor and the ceiling are struck by light at the same time, then enter ceiling,same. Hint 1. Situation in Albert's frame In Albert s frame, the train is completely at rest. The light from the flashlights is emitted directly between the floor and the ceiling, and one beam moves up and the other moves down at exactly the same speed, the speed of light. Hint 2. Situation in your frame In your frame, the entire train is moving to the right, but no part of the train is moving vertically. The light from the flashlights is emitted directly between the floor and the ceiling, and one beam moves up and the other moves down at exactly the same speed, the speed of light. Albert is playing laser tag in the freight car. Two "assassins" sneak into the freight car with Albert. One is positioned against the front end and the other against the rear end. They each fire a laser at Albert. The two lasers strike Albert at the same time. Part D In Albert's frame of reference, who fired first, the person against the rear end or the person against the front end, or did they fire at the same time? In your frame of reference, who fired first? Enter the answers for Albert's frame of reference and your frame of reference separated by a comma using the terms front, rear, and same. For example, if in Albert's frame of reference the person against the front end fired first and in your frame of reference both "assassins" fired at the same time, then enter front,same. Hint 1. Situation in Albert's frame
5 5 of 8 2/29/ :17 PM In Albert s frame, the train is completely at rest. The two assassins are equally distant from Albert and their laser beams travel at equal speeds. Hint 2. Situation in your frame In your frame, Albert is directly between the assassins and moving to the right. The rear laser beam moves to the right at the speed of light and the front laser beam moves to the left at the speed of light. Therefore, Albert is moving in the same direction as the rear beam and in the opposite direction of the front beam. Which beam will take a larger amount of time to hit Albert? front rear The question states that both beams strike Albert at the same time. Therefore the one that takes a larger amount of time to reach him must have been fired first. This is another example of how two events, the firing of the lasers, can be simultaneous in one frame of reference and not simultaneous in another frame. Time is Relative Description: Consider two events occurring at the same space point in a frame of reference, find their space distance as measured in a moving frame of reference, given the time intervals between the two events measured in both frames of reference. Two events are observed in a frame of reference S to occur at the same space point, with the second event occurring after a time of In a second frame S' moving relative to S, the second event is observed to occur after a time of What is the difference between the positions of the two events as measured in S'? Use for the speed of light in a vacuum.
6 6 of 8 2/29/ :17 PM Hint 1. How to approach the problem Although the two events are observed to occur at the same location in S, from the point of view of an observer at rest in S' they occur at a space distance that depends on the relative speed of the two frames of reference and the time elapsed between the two events as measured by the observer in S'. Note that the observer at rest in S' will see the source of the event moving with speed. Therefore, to find the difference between the positions of the two events as measured in S', you need to determine the relative speed. To do that, use the relativistic relationship between the time interval measured in S and the one measured in S'. Hint 2. Find the expression for the space distance between the two events If the speed of S' relative to S is, which of the following expressions for the space distance between the two events as measured in S' is correct? Here, and are the time intervals between the two events as measured in S and S', respectively. Hint 3. Find the relative speed What is the speed of the frame of reference S ' with respect to the frame S? Express your answer numerically in meters per second. Hint 1. Time dilation Since the speed of light is the same in all frames of reference (Einstein's postulate), the time interval between two events that are observed to occur at the same space point in a given frame of reference S is not the same in all reference frames. An observer in a frame S' moving with speed relative to S would measure a longer time interval between those two same events because of the relativistic effect of time dilation. The time interval measured in the moving frame S' is. If you know the time interval, also called proper time, and, you can derive an expression for the relative speed. Hint 2. Find the proper time The time interval between two events occurring at the same space point as measured in a particular frame of reference is called the proper time. What is the value of the proper time in this case? Express your answer numerically in seconds. = = 1.70 = = Also accepted: = = = Also accepted: =
7 7 of 8 2/29/ :17 PM Do not be tempted to interpret the distance that you have just calculated as the distance traveled by the moving frame S' in the time elapsed between the two events as measured by an observer in S. An observer in S would measure a distance equal to, where is the relative speed of the two reference frames and is the time between events in S. Exercise 37.5 Description: The negative pion pi^- is an unstable particle with an average lifetime of 2.60 * 10^-8 s (measured in the rest frame of the pion). (a) If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the... The negative pion is an unstable particle with an average lifetime of (measured in the rest frame of the pion). If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the laboratory to be pion expressed as a fraction of. Express your answer using five significant figures.. Calculate the speed of the = Part B What distance, measured in the laboratory, does the pion travel during its average lifetime? Express your answer using three significant figures. = 126 The Empire Strikes Back Description: A space ship marked by an elliptic symbol of given dimensions is moving relative to an observer; find the speed of the space ship needed in order for the observer to measure the symbol as circular. The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is times its minor axis ( in the figure ). How fast, relative to an observer, does an Empire ship have to travel for its markings to be confused with those of a Federation ship? Use vacuum. Express your answer in terms of and. for the speed of light in a Hint 1. How to approach the problem An observer would see a circle on the Empire ship if the major axis and the minor axis of the Empire's symbol appear to be of equal length. Using the relativistic relation for length contraction calculate the length of the major axis of the Empire's symbol as measured by the observer and make it equal to its minor axis. By doing so you will obtain an expression for the speed of the Empire ship. Note that a length perpendicular to the direction of motion is not affected by the relativistic effect of length contraction. So the observer at rest relative to the Empire ship will measure the same length for the minor axis of the Empire's symbol as an observer on the Empire ship. Hint 2. Find the length of the major axis as measured by the observer If the Empire ship is moving at speed relative to an observer, what is the length of the major axis in the Empire's symbol as measured by the observer? denotes the speed of light and is the proper length of the major axis of the Empire's symbol.
8 8 of 8 2/29/ :17 PM Now make this expression equal to the minor axis of the Empire's symbol and solve for the relative speed. Note that the proper length of the minor axis will cancel out. Copyright 2016 Pearson. All rights reserved. Legal Notice Privacy Policy Permissions Support
Rutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 )
1 of 13 2/17/2016 5:28 PM Signed in as Weida Wu, Instructor Help Sign Out Rutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 ) My Courses Course Settings University Physics with Modern Physics,
More informationSome Special Relativity Formulas
Some Special Relativity Formulas 1 Introduction The purpose of this handout is simple: to give you power in using special relativity! Even though you may not, at this stage, understand exactly where all
More informationx 1 ' = x 1 vt 1 x 1 ' = 4.0 m t 1 = 1.0 s x 2 vt 2 ' = 4.0 m t 2 ' = x 2 = 3.0 s x 1 = x 2 x 1 ' + vt 1 ' + vt 2 v (t 1 t 2 ) = x 2 ' x 1 ' = x 2
Physics 2220 Module 16 Homework 01. A firecracker explodes in reference frame S at t 1 1.0 seconds. A second firecracker explodes at the same position at t 2 3.0 seconds. In reference frame S', which moves
More informationEinstein s Theory of Special Relativity Made Relatively Simple!
Einstein s Theory of Special Relativity Made Relatively Simple! by Christopher P. Benton, PhD Young Einstein Albert Einstein was born in 1879 and died in 1955. He didn't start talking until he was three,
More informationSpecial Relativity. Photo by Philippe Halsman. Used with permission from Mrs. P. Halsman.
Albert Einstein and the Miracle Year Special Relativity The year 1905 is often referred to as the Annus Mirabilis (or year of miracles). In this year, Albert Einstein, a 23-year old with an undergraduate
More information1 of 7 9/5/2009 6:12 PM
1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationPhysics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings
1 of 11 9/7/2012 1:06 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library
More informationHow To Understand General Relativity
Chapter S3 Spacetime and Gravity What are the major ideas of special relativity? Spacetime Special relativity showed that space and time are not absolute Instead they are inextricably linked in a four-dimensional
More informationThe Neo-classical Theory of Relativity
Toronto, Canada December 29, 2013 Second Edition 2013, Revision 2.1 The Neo-classical Theory of Relativity by Valentin T. Danci Introduction to the Neo-classical Theory of Relativity... 3 1. The conceptual
More informationExperiment 2 Free Fall and Projectile Motion
Name Partner(s): Experiment 2 Free Fall and Projectile Motion Objectives Preparation Pre-Lab Learn how to solve projectile motion problems. Understand that the acceleration due to gravity is constant (9.8
More informationForce 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 informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around
More informationVELOCITY, 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 informationForces. When an object is pushed or pulled, we say that a force is exerted on it.
Forces When an object is pushed or pulled, we say that a force is exerted on it. Forces can Cause an object to start moving Change the speed of a moving object Cause a moving object to stop moving Change
More informationphysics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves
Chapter 20 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide
More informationDeformation of the Bodies by the Result of Length Contraction: A new Approach to the Lorentz Contraction
1 Deformation of the Bodies by the Result of Length Contraction: A new Approach to the Lorentz Contraction Bayram Akarsu, Ph.D Erciyes University Kayseri/ Turkiye 2 Abstract It has been more than a century
More informationThe Theory of Relativity
The Theory of Relativity 1. THE SPECIAL THEORY In 1905, his annum mirabilis, Einstein revolutionized physics with, among other things, his special theory of relativity. With it he completely overturned
More informationWeb review - Ch 3 motion in two dimensions practice test
Name: Class: _ Date: _ Web review - Ch 3 motion in two dimensions practice test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which type of quantity
More informationFEGYVERNEKI SÁNDOR, PROBABILITY THEORY AND MATHEmATICAL
FEGYVERNEKI SÁNDOR, PROBABILITY THEORY AND MATHEmATICAL STATIsTICs 4 IV. RANDOm VECTORs 1. JOINTLY DIsTRIBUTED RANDOm VARIABLEs If are two rom variables defined on the same sample space we define the joint
More informationACTIVITY 6: Falling Objects
UNIT FM Developing Ideas ACTIVITY 6: Falling Objects Purpose and Key Question You developed your ideas about how the motion of an object is related to the forces acting on it using objects that move horizontally.
More informationNEWTON S LAWS OF MOTION
Name Period Date NEWTON S LAWS OF MOTION If I am anything, which I highly doubt, I have made myself so by hard work. Isaac Newton Goals: 1. Students will use conceptual and mathematical models to predict
More informationNewton s Laws. Physics 1425 lecture 6. Michael Fowler, UVa.
Newton s Laws Physics 1425 lecture 6 Michael Fowler, UVa. Newton Extended Galileo s Picture of Galileo said: Motion to Include Forces Natural horizontal motion is at constant velocity unless a force acts:
More information9. Momentum and Collisions in One Dimension*
9. Momentum and Collisions in One Dimension* The motion of objects in collision is difficult to analyze with force concepts or conservation of energy alone. When two objects collide, Newton s third law
More informationChapter 4: Newton s Laws: Explaining Motion
Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More informationPhysics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5
Solutions to Homework Questions 5 Chapt19, Problem-2: (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat
More informationPhysics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationNewton s Law of Universal Gravitation
Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.
More informationSPEED, VELOCITY, AND ACCELERATION
reflect Look at the picture of people running across a field. What words come to mind? Maybe you think about the word speed to describe how fast the people are running. You might think of the word acceleration
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationProblem Set V Solutions
Problem Set V Solutions. Consider masses m, m 2, m 3 at x, x 2, x 3. Find X, the C coordinate by finding X 2, the C of mass of and 2, and combining it with m 3. Show this is gives the same result as 3
More informationLAB 6: GRAVITATIONAL AND PASSIVE FORCES
55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction
More informationMagnetic Fields and Their Effects
Name Date Time to Complete h m Partner Course/ Section / Grade Magnetic Fields and Their Effects This experiment is intended to give you some hands-on experience with the effects of, and in some cases
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2014
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday
More informationReview Chapters 2, 3, 4, 5
Review Chapters 2, 3, 4, 5 4) The gain in speed each second for a freely-falling object is about A) 0. B) 5 m/s. C) 10 m/s. D) 20 m/s. E) depends on the initial speed 9) Whirl a rock at the end of a string
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More information2After 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 informationSPATIAL COORDINATE SYSTEMS AND RELATIVISTIC TRANSFORMATION EQUATIONS
Fundamental Journal of Modern Physics Vol. 7, Issue, 014, Pages 53-6 Published online at http://www.frdint.com/ SPATIAL COORDINATE SYSTEMS AND RELATIVISTIC TRANSFORMATION EQUATIONS J. H. FIELD Departement
More informationLecture 16. Newton s Second Law for Rotation. Moment of Inertia. Angular momentum. Cutnell+Johnson: 9.4, 9.6
Lecture 16 Newton s Second Law for Rotation Moment of Inertia Angular momentum Cutnell+Johnson: 9.4, 9.6 Newton s Second Law for Rotation Newton s second law says how a net force causes an acceleration.
More informationA Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion
A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. Dr Tay Seng Chuan
Ground Rules PC11 Fundamentals of Physics I Lectures 3 and 4 Motion in One Dimension Dr Tay Seng Chuan 1 Switch off your handphone and pager Switch off your laptop computer and keep it No talking while
More informationFriction and Gravity. Friction. Section 2. The Causes of Friction
Section 2 Friction and Gravity What happens when you jump on a sled on the side of a snow-covered hill? Without actually doing this, you can predict that the sled will slide down the hill. Now think about
More informationExam 1 Review Questions PHY 2425 - Exam 1
Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1H Rev Ques.doc - 1 - Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationEinstein and Relativity Theory
3637_CassidyTX_09 6/14/02 12:08 PM Page 405 C H A P T E R9 Einstein and Relativity Theory 9.1 The New Physics 9.2 Albert Einstein 9.3 The Relativity Principle 9.4 Constancy of the Speed of Light 9.5 Simultaneous
More informationThe University of Texas at Austin. Gravity and Orbits
UTeach Outreach The University of Texas at Austin Gravity and Orbits Time of Lesson: 60-75 minutes Content Standards Addressed in Lesson: TEKS6.11B understand that gravity is the force that governs the
More informationChapter 7 Newton s Laws of Motion
Chapter 7 Newton s Laws of Motion 7.1 Force and Quantity of Matter... 1 Example 7.1 Vector Decomposition Solution... 3 7.1.1 Mass Calibration... 4 7.2 Newton s First Law... 5 7.3 Momentum, Newton s Second
More informationG 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 information1. 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 information6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the
More informationCentripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.
Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationLESSON 17: Balloon Rockets ESTIMATED TIME Setup: 5 10 minutes Procedure: 5 10 minutes
LESSON 17: Balloon Rockets ESTIMATED TIME Setup: 5 10 minutes Procedure: 5 10 minutes DESCRIPTION Apply the concepts of pressure and Newton s laws of motion to build simple rockets. OBJECTIVE This lesson
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationPhysics 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 informationGravitation and Newton s Synthesis
Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass
More informationLecture L17 - Orbit Transfers and Interplanetary Trajectories
S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L17 - Orbit Transfers and Interplanetary Trajectories In this lecture, we will consider how to transfer from one orbit, to another or to
More informationPHY1020 BASIC CONCEPTS IN PHYSICS I
PHY1020 BASIC CONCEPTS IN PHYSICS I Jackson Levi Said 14 lectures/tutorials/past paper session Project on one of the interesting fields in physics (30%) Exam in January/February (70%) 1 The Course RECOMMENDED
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationPhysics Kinematics Model
Physics Kinematics Model I. Overview Active Physics introduces the concept of average velocity and average acceleration. This unit supplements Active Physics by addressing the concept of instantaneous
More informationE/M Experiment: Electrons in a Magnetic Field.
E/M Experiment: Electrons in a Magnetic Field. PRE-LAB You will be doing this experiment before we cover the relevant material in class. But there are only two fundamental concepts that you need to understand.
More informationNewton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of
Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed
More informationName Class Date. true
Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized
More informationLAB 6 - GRAVITATIONAL AND PASSIVE FORCES
L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies
More informationWaves-Wave Characteristics
1. What is the wavelength of a 256-hertz sound wave in air at STP? 1. 1.17 10 6 m 2. 1.29 m 3. 0.773 m 4. 8.53 10-7 m 2. The graph below represents the relationship between wavelength and frequency of
More informationAstronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose
More informationWelcome back to Physics 211. Physics 211 Spring 2014 Lecture 04-1 1. ask a physicist
Welcome back to Physics 211 Today s agenda: Rotations What s on the exam? Relative motion Physics 211 Spring 2014 Lecture 04-1 1 ask a physicist Why are neutrinos faster than light (photons)? I thought
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationThe Universal Laws of Gravitation. Copyright 2012 Joseph A. Rybczyk
The Universal Laws of Gravitation Copyright 2012 Joseph A. Rybczyk Abstract Close examination of Newton s universal law of gravitation and Galileo s discovery that all objects fall to Earth at the same
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 12 Electricity and Magnetism Magnetism Magnetic fields and force Application of magnetic forces http://www.physics.wayne.edu/~apetrov/phy2140/ Chapter 19 1 Department
More informationWork, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work!
Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work! 1. A student holds her 1.5-kg psychology textbook out of a second floor classroom window until her arm is tired; then she releases
More informationCopyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass
Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of
More informationLicensed to: ichapters User
Physics for Scientists and Engineers with Modern Physics, Chapters 39 46, Seventh Edition Raymond A. Serway and John W. Jewett, Jr. Physics Acquisition Editor: Chris Hall Publisher: David Harris Vice President,
More informationLesson 39: Kinetic Energy & Potential Energy
Lesson 39: Kinetic Energy & Potential Energy Total Mechanical Energy We sometimes call the total energy of an object (potential and kinetic) the total mechanical energy of an object. Mechanical energy
More information6. Vectors. 1 2009-2016 Scott Surgent (surgent@asu.edu)
6. Vectors For purposes of applications in calculus and physics, a vector has both a direction and a magnitude (length), and is usually represented as an arrow. The start of the arrow is the vector s foot,
More information1.3. DOT PRODUCT 19. 6. If θ is the angle (between 0 and π) between two non-zero vectors u and v,
1.3. DOT PRODUCT 19 1.3 Dot Product 1.3.1 Definitions and Properties The dot product is the first way to multiply two vectors. The definition we will give below may appear arbitrary. But it is not. It
More information1 of 9 2/9/2010 3:38 PM
1 of 9 2/9/2010 3:38 PM Chapter 23 Homework Due: 8:00am on Monday, February 8, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More information3 Some Integer Functions
3 Some Integer Functions A Pair of Fundamental Integer Functions The integer function that is the heart of this section is the modulo function. However, before getting to it, let us look at some very simple
More information2 Newton s First Law of Motion Inertia
2 Newton s First Law of Motion Inertia Conceptual Physics Instructor Manual, 11 th Edition SOLUTIONS TO CHAPTER 2 RANKING 1. C, B, A 2. C, A, B, D 3. a. B, A, C, D b. B, A, C, D 4. a. A=B=C (no force)
More informationInterference. Physics 102 Workshop #3. General Instructions
Interference Physics 102 Workshop #3 Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by
More informationNewton s Laws of Motion, Reference Frames and Inertia
Newton s Laws of Motion, Reference Frames and Inertia Chris O Loughlin 2 December 2011 Abstract The validity of Newton s Laws of Motion depends on the type of reference frame they act in. They are valid
More informationIn order to describe motion you need to describe the following properties.
Chapter 2 One Dimensional Kinematics How would you describe the following motion? Ex: random 1-D path speeding up and slowing down In order to describe motion you need to describe the following properties.
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationDifference between a vector and a scalar quantity. N or 90 o. S or 270 o
Vectors Vectors and Scalars Distinguish between vector and scalar quantities, and give examples of each. method. A vector is represented in print by a bold italicized symbol, for example, F. A vector has
More informationNewton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009
Newton s Laws Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Imaginary Cannon Newton was familiar with Galileo s analysis of projectile motion, and decided to take it one step further. He imagined
More informationAcceleration of Gravity Lab Basic Version
Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration
More informationPhysics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.
Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a
More informationPhysics Section 3.2 Free Fall
Physics Section 3.2 Free Fall Aristotle Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension
Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Conceptual Questions 1) Suppose that an object travels from one point in space to another. Make
More informationLaser Calibration Check
Laser Calibration Check Checking Calibration of the Y- and X-Axes 1. Set up the tripod 30 m (100 ft) from a wall and make sure the tripod head is leveled. 2. Attach the laser to the tripod with the handle
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationNatural Science I: Einstein's Universe Fall 2013 Meyer 121
Natural Science I: Einstein's Universe MAP-UA-0204-010 Fall 2013 Meyer 121 Tuesday and Thursday 2:00 3:15 p.m. Dr. Burton Budick Office Meyer 705 Office Phone: (212)-998-7683 E-mail: bb2@nyu.edu Office
More informationLecture 4: Newton s Laws
Lecture 4: Newton s Laws! Laws of motion! Reference frames! Law of Gravity! Momentum and its conservation Sidney Harris This week: continue reading Chapter 3 of text 2/6/15 1 Newton s Laws & Galilean Relativity!
More informationNotes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.
Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the
More informationACCELERATION DUE TO GRAVITY
EXPERIMENT 1 PHYSICS 107 ACCELERATION DUE TO GRAVITY Skills you will learn or practice: Calculate velocity and acceleration from experimental measurements of x vs t (spark positions) Find average velocities
More informationSpeed, velocity and acceleration
Chapter Speed, velocity and acceleration Figure.1 What determines the maximum height that a pole-vaulter can reach? 1 In this chapter we look at moving bodies, how their speeds can be measured and how
More informationAP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light
AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light Name: Period: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Reflection,
More informationAdvanced Topics in Physics: Special Relativity Course Syllabus
Advanced Topics in Physics: Special Relativity Course Syllabus Day Period What How 1. Introduction 2. Course Information 3. Math Pre-Assessment Day 1. Morning 1. Physics Pre-Assessment 2. Coordinate Systems
More informationThe Special Theory of Relativity
Chapter 1 The Special Theory of Relativity 1.1 Pre-History of concepts about light It is interesting to note that so much of our understanding of the physical universe is based on our interpretations of
More information