#### Transcript Lecture 15

Agenda • Friday&Monday – Problems Ch. 21-23 • Tuesday – lab 5 & “Curve” Quiz – Can Improve score by 5-20 pts – Or replace quiz 2 (not a popular quiz) • Today – Potential & Potential Energy – Chapters 6&7 Potential Energy • Measure of Energy “Stored” in a system • Akin to work W F dx Gravitational PE [I know, U…] • How much work does it take to raise a mass M to a height H in a gravitational field g? W F dx WG FG dx Mg dy Set Ref. Y = 0 H H 0 0 WG Mgdy Mg dy MgH Negative work done by gravity Implies gravitational energy stored Work done by something else (Outside) Conservative Forces & PE • Energy from Conservative forces can be described in terms of PE • Spring PE (E stored by spring) • Gravitational PE (E stored by gravity) • Electrical PE (E stored in Electric Fields) • Conservative = Path Independent • Conservative = No energy lost • Conservative N.E. to friction “Mechanical” Energy Conservation • Have – Q = DU + W – Heat, internal energy, Mechanical • Most large systems, Heat irrelevant – Thermal energy of a golf ball? Small! • Need to look closer at macroscopic here • WNC = DE = EF – E0 “Mechanical” Energy Conservation EF = E0 + WNC • WNC = DE = EF – E0 • WNC Work done by Non-Conserved – “Outside” or Friction, etc…. • E = Energy = PE + KE – See how thermal might come in? • Wonder of Energy – No Directions – If no WNC, then no cares about path! – Can often ignore everything but initial & final Relativity • No – not the extra cool one • Energy is relative • Can you tell what floor I’m on when I drop something? • Gravitational PE comes into play as relative height change, not absolute height. Potential vs. Fields • Energy ~ Integral of Force • Field from a point S E C 2 r C = constant (k, G) S = stuff (Q, M0 r = distance from object emanating field Potential vs. Fields • Energy ~ Integral of Force • Field from a point C = constant (k, G) S = stuff (Q, M0 r = distance from object emanating field S r2 S P C 2 dr r 1 P CS 2 dr r CS P r E C P Potential Could be gravitational Potential Could be electrical potential (Volts) Examine Gravity Ch. 8? • How fast must something be traveling to escape the pull of the Earth’s gravitational field? • Needed – Gravitational Potential Field – Energy Relationship – Beginning “height” – Final height” Examine Gravity Ch. 8? • How fast must something be traveling to escape the pull of the Earth’s gravitational field? • Needed – Gravitational PE = PEG = -GmME/r – Energy Relationship EF = E0 + WNC • Given an initial velocity, no other “NC” WNC=0 – Beginning “height” RE (~ Surface of Earth) – Final height” Far Away (infinity) Find Escape Velocity EF = E0 + WNC • Initial Energy – KE = 0.5mv2 – PE = -GmME/RE – Negative implies object attracted to earth – As r increases, PE becomes less negative – As r increases, h increases, PE increases (mgh) • WNC = 0 – Only force is gravity • Final Energy – PE = ? – PE = 0 [no earth pull] Find Escape Velocity EF = E0 + WNC • Initial Energy – KE = 0.5mv2 – PE = -GmME/RE • WNC = 0 – Only force is gravity • Final Energy – PE = 0 [no earth pull] – KE=? – KE = 0 [minimum initial energy to escape earth] Find Escape Velocity EF = E0 + WNC • • • • • EF = 0, WNC =0 E0 = 0 E0 = PE0 + KE0 E0 = -GmME/RE + 0.5mv2 = 0 v2 = -2GME/RE • • • • What does escape velocity depend on? How does this relate to electricity? V = kQ/r & PEE = kQ1Q2/r Same method, gravity easier as no + or - Reference for PE • When dealing with “points,” what is a good reference for energy? • Hint: Earth (from outside) looks like point source (G Law) Explore System of Charges