Agenda Friday&Monday – Problems Ch 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

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? 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 =  U + W –Heat, internal energy, Mechanical Most large systems, Heat irrelevant –Thermal energy of a golf ball? Small! Need to look closer at macroscopic here W NC =  E = E F – E 0

“Mechanical” Energy Conservation E F = E 0 + W NC W NC =  E = E F – E 0 W NC  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 W NC, 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 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 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 = PE G = -GmM E /r –Energy Relationship  E F = E 0 + W NC Given an initial velocity, no other “NC”  W NC =0 –Beginning “height”  R E (~ Surface of Earth) –Final height”  Far Away (infinity)

Find Escape Velocity E F = E 0 + W NC Initial Energy –KE = 0.5mv 2 –PE = -GmM E /R E –Negative implies object attracted to earth –As r increases, PE becomes less negative –As r increases, h increases, PE increases (mgh) W NC = 0 –Only force is gravity Final Energy –PE = ? –PE = 0 [no earth pull]

Find Escape Velocity E F = E 0 + W NC Initial Energy –KE = 0.5mv 2 –PE = -GmM E /R E W NC = 0 –Only force is gravity Final Energy –PE = 0 [no earth pull] –KE=? –KE = 0 [minimum initial energy to escape earth]

Find Escape Velocity E F = E 0 + W NC E F = 0, W NC =0 E 0 = 0 E 0 = PE 0 + KE 0 E 0 = -GmM E /R E + 0.5mv 2 = 0 v 2 = -2GM E /R E What does escape velocity depend on? How does this relate to electricity? V = kQ/r & PE E = 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