Solution Found!

Physics / Classical Mechanics 0 / Chapter 15 / Problem 15.20

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

Change Question

Newton's first law can be stated: If an object is isolated

Chapter 15, Problem 15.20

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Newton's first law can be stated: If an object is isolated (subject to no forces), then it moves with constant velocity. We know that this is invariant under the Galilean transformation. Prove that it is also invariant under the Lorentz transformation. [Assume that it is true in an inertial frame \(\mathcal{S}\), and use the relativistic velocity-addition formula to show that it is also true in any other \(\mathcal{S}^{\prime}\).]

Questions & Answers

QUESTION:

Newton's first law can be stated: If an object is isolated (subject to no forces), then it moves with constant velocity. We know that this is invariant under the Galilean transformation. Prove that it is also invariant under the Lorentz transformation. [Assume that it is true in an inertial frame \(\mathcal{S}\), and use the relativistic velocity-addition formula to show that it is also true in any other \(\mathcal{S}^{\prime}\).]

ANSWER:

Step 1 of 4

Consider the body in inertial frame S moving with speed . Since the frame is inertial,first Netwon’s law holds. If there is no force, we expect no acceleration.The fact is that is true in any other inertial frame under Galilean transformations. Now, let's see if it holds under Lorentz transformation. Let's transform form S with a body of constant speed to moving with relative to .

Study Tools You Might Need

Chapter: 3 Problem: 81P

Introductory Chemistry 5
An iron nail with a mass of 12 g absorbs 15 J of heat. If the nail was initially at \(28\ ^{\circ}\mathrm{C}\), what is its final temperature? Equation Transcription: Text Transcription: 28 deg C

Chapter: 6 Problem: 55P

Introductory Chemistry 5
A sugar crystal contains approximately \(1.8 \times 10^{17}\) sucrose (\(C_{12} H_{22} O_{11}\)) molecules. What is its mass in milligrams? Equation Transcription: . Text Transcription: 1.8 times 10^17

Chapter: 7 Problem: 53P

Introductory Chemistry 5
Is each chemical equation correctly balanced? If not, correct it. (a) \(R b(s)+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{RbOH}(a q)+\mathrm{H}_{2}(g)\) (b) \(2 \mathrm{~N}_{2} \mathrm{H}_{4}(g)+\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2}

Chapter: 2 Problem: 2.12

Sears and Zemansky's University Physics with Modern Physics 13
Figure E2.12 shows the velocity of a solar-powered car as a function of time. The driver accelerates from a stop sign, cruises for 20 s at a constant speed of and then brakes to come to a stop 40 s after leaving the stop sign. (a) Compute the average acceleration during the following time intervals:

Chapter: 11 Problem: 11.27

Chemistry: The Central Science 12
Problem 27E Intermolecular Forces (Section) Ethylene glycol (HOCH2CH2OH), the major substance in antifreeze, has a normal boiling point of 198 C. By comparison, ethyl alcohol (CH3CH2OH) boils at 78 C at atmospheric pressure. Ethylene glycol dimethyl ether (CH3OCH2CH2OCH3) has a normal boiling poi

Chapter: 9 Problem: 9.1.2

Modern Chemistry: Student Edition 2012 1
For each equation, write all possible mole ratios. a. 2HgO(s) 2Hg(l) + O2(g) b. 4NH3(g) + 6NO(g) 5N2(g) + 6H2O(l)

Chapter: 5 Problem: 1

Biology 11
What would happen if a plant cell were placed in an isotonic solution? a hypertonic environment? a hypotonic environment? How would you modify your predictions for an animal cell?

Chapter: 6 Problem: 1

Advanced Engineering Mathematics 10
State the Laplace transforms of a few simple functions from memory.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account