Physics 26: 6-11 General Relativity

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 27: Sections 6 to 11

Study Points

Section 6: In the four-dimensional view of the universe, three space and one time dimensions are equivalent and necessary to locate an object with reference to a point.
Section 7: Because time and distance are modified at relativistic speeds, dependent concepts such as velocity, momentum, and energy must also be modified. At relativistic speeds (v > 0.1c), p = γ m₀v where m₀ is the rest mass of an object.
Section 8: Note that when v = c, the relativistic mass m_rel = m₀γ becomes m₀/0: an undefined value. This indicates that an object with actual mass can never move at light speed.
Section 9: Einstein showed that relativistic kinetic energy = γm₀c² - m₀c² = (γ -1) m₀c². For a particle at rest in a given reference frame, E = m₀c². Mass can be converted to energy and energy can be converted to mass.
Section 10: If v is the speed of an object A with respect to an observer O, and u' is the speed of an object with respect to moving object A, the velocity observed y O is u = (v + u') / ( 1 + vu'/c²)
Section 11: According to the correspondence principle, classical mechanics is a special case of general relativity, valid where the difference between general relativity predictions and its own are too small to be observed.

Key Equations

Principles	Equation	Variables
Relativistic momentum	$p = \frac{mv}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = γ mv$	p: momentum m: rest mass v: velocity γ: Lorenz factor
Rest mass vs relativistic mass	$m_{relativistic} = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$	m: relativistic mass m₀: rest mass v: velocity
Relativistic kinetic energy:	${KE}_{relativistic} = \frac{m c^{2}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = (γ - 1) m c^{2}$	m: rest mass
Adding relativistic velocities:	$u = \frac{v + u'}{1 + vu'/ c^{2}}$	v: speed of rocket relative to stationary observer u': speed of secondary rocket relative to moving observer u: speed of secondary rocket relative to stationary observer

Web Lecture

Read the following weblecture before chat: General Relativity, Space, and Time

Study Activity

Use the Fermilab Interactive exercise for Orbits in Strongly Curved Spacetime to explore what happens when you change the mass of a black hole orbited by a small satellite. Read the introduction and descriptions, then run the simulator by varying the mass, angular momentum, and radius of the black hole.

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Measuring Relativity with GPS Data (Two Week lab)

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Physics

Chapter 26: 6-11 Assignment