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# Agenda - PowerPoint PPT Presentation

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.

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• 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

• Measure of Energy “Stored” in a system

• Akin to work

• 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)

• 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

• 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 ConservationEF = 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

• 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.

• Energy ~ Integral of Force

• Field from a point

C = constant (k, G)

S = stuff (Q, M0

r = distance from object emanating field

• 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 GravityCh. 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 GravityCh. 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 VelocityEF = 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 VelocityEF = 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 VelocityEF = 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 -

• When dealing with “points,” what is a good reference for energy?

• Hint: Earth (from outside) looks like point source (G Law)