#### 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
```