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PHYS 211 Midterm 1 Study Guide

by: Chin Hung Chao

PHYS 211 Midterm 1 Study Guide PHYS 211

Chin Hung Chao
Cal Poly
GPA 3.84

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About this Document

This is just a basic overview study of everything we learn from the lecture in Modern Physics for Professor Fraser's class
Modern Physics
Study Guide
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This 5 page Study Guide was uploaded by Chin Hung Chao on Monday April 11, 2016. The Study Guide belongs to PHYS 211 at California Polytechnic State University San Luis Obispo taught by Fraser in Spring 2016. Since its upload, it has received 30 views. For similar materials see Modern Physics in Physics 2 at California Polytechnic State University San Luis Obispo.


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Date Created: 04/11/16
Spring 2016 PHYS 211­01 Midterm 1 Study Guide  Special Relativity (1905) Describes fast objects, neglecting gravity. Special cases of General Relativity  General Relativity (1916) A theory that describes gravity as the curvature of space time Time is the “fourth dimension”  Newton’s Law 1 2 E= m2 +mgh 1 Special Relativity Modifies: mv 2 2 General Relativity Modifies: mgh Special Relativity (neglects gravity)  Space­time is “flat” like a flat sheet  Objects move in this flat space­time  Light always has speed of c = 3 x 10  m/s no matter what o Note: No object with mass m > 0 can achieve the speed of light, which means  light is massless, m = 0 for light.  Most motion is relative, but not for light General Relativity 8  Light always has speed of c = 3 x 10  m/s  Any dense matter curves the space­time. (Energy and pressure also curves space­time  too)  The curvature of space­time causes gravity  Gravity is not viewed as a force  When curvature is weak enough: Newton’s gravity is a good approximation. Example: Planets orbiting the Sun; the planets move in the curved space­time created by  the Sun  Predicts light bends when it passes near the Sun  Higher density = higher curvature  If any object is squeezed enough, the higher curvature produces a black hole. Light  Light is an electromagnetic wave  c = speed of the wave = speed of light 1 Electromagnetism predicts:  ε μ ; ε0 = 8.85 x 10  C /(Nm ) 2 √ 0 0 ­7 2 2    μ0 = 4π x 10  Ns /C     C = Coulomb Special Relativity Postulates: 1. All laws of physics are the same any inertial frame 2. Speed of light (in vacuum) is always 3 x 10  m/s in any inertial frame Inertial Reference Frame: Not accelerating (constant velocity) frame In an inertial frame:  All clocks are identical, they are in time t simultaneously (synchronized) Event: A physical phenomenon that occurs a definite location and time Time Dilation: Different values of elapsed time (between two events) due to relative  motion Time Dilation Formula:  Δ t=γΔt 0 Δ 0  = “proper” elapsed time  between two events at same location in space 1 γ= 2 v γ  approaches infinity as v approaches light  1− c2 √ speed If v/c << 1: Use binomial approximation: b b If |x| << 1 for (1 + x)  then (1 + x)  = 1 + bx Twin Paradox Time Dilation can causes one of the twin who is traveling in space around the speed of  light to age only a little while the other twin who stays behind on Earth will age a lot. Length Contraction  Moving Length L is observed to (measured) to be shorter than its lengoh L  at rest L 0= rest length; “proper” length 1 L 0 γ= 2 Formula:  L= γ 1− v √ c2 How measured a moving length? 1. Measure distance L at endpoints simultaneously 2. Wait for endpoints to pass a single clock Relativity of Simultaneity: Two events simultaneous in one inertial frame, they are not simultaneous in any other different inertial frame (relative speed v) Lorentz Transformation How to compare measurement s of position (x, y, z) and time t in two different inertial  frame Newton:  x=x +vt Galilean Transformation       x =x−vt x =γ(x−vt) Lorentz Transformation Equations:  y` = y z` = z v           t =γ(t− c2x)   Inverse Transformation Equations:  x=γ(x +vt) y = y` z = z` t=γ(t + v x ) c2 Velocity Transformation Formula for velocity u: ux = object’s velocity in x­direction uy = object’s velocity in y­direction uz = object’s velocity in z­direction v = Frame S` velocity; the moving frame’s velocity ux−v u y uz ux= u y uz= vu x vu x vu x 1− 2 γ(1− 2 ) γ(1− 2 ) c c c Inverse formula: u +v u u ux= x u x y ux= z vu x vu x vu x 1+ 2 γ(1+ 2 ) γ(1+ 2 ) c c c Momentum and Energy p=γmu Momentum Formula:  u = velocity; m = mass of the object Conservation of momentum is still applied in special relativity like in Newton’s  definition of Momentum Momentum is conserved in collisions and explosions E=γmc 2 Energy Formula:  m = mass of object Conservation of energy is still applied in special relativity also When |u| << c ( |u|/c << 1): Use binomial approximation: 2 1 2 Which results in:  E=mc + mu 2 1 2     rest mc ; (Newtonian)  K= m2 2     K=E−E rest(γ−1 mc Can Rewrite Conservation of Energy as: 2 Δ(K totΔ(m c ) tot 2 By using p = γmu and E = γmc , we can create two new formulas: p u 2 2 2 2 = 2 and E =(pc) +(mc ) E c If u = c speed of light: Using the two equations above, m = 0 as the final result, which proves no object with  mass can achieves the speed of light. And light is massless also.


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