Fall wk 4 – Thus.21.Oct.04
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Welcome, roll, questions
Exercise on rising CO2 levels
Energy and Work
Looking ahead: Winter seminar texts
Energy Systems, EJZ
Measured rising CO2 levels
Intro to Energy, Cassedy & Grossman
Predicting future CO2 levels
You found equations for ppm of CO2 (t in yrs)
(a) Linear rise: L(t) = 8/7 t + 315
(b) Exponential rise: z(t) = 315 (1.005)t
(c) Oscillations: c(t) = 4 cos 2pt
To predict CO2 level in 2100, use (a) or (b).
To predict when CO2 level will reach 550 ppm,
solve (a) or (b) for time.
Energy and work
Mechanical energy = potential + kinetic
Mechanical energy is conserved (Ebefore = Eafter)
• In the absence of dissipative forces
• If the force is conservative (e.g. gravity, elec)
Potential energy depends on the source:
Gravitational, chemical, electrostatic, spring,
others?
Conservation of energy
In a conservative system, energy can change from
kinetic energy  potential energy
K = ½ mv2 
U = mgh
Force = slope of potential energy curve.
Where is the net force=0? Where is it greatest?
Conservative forces
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No dissipation, e.g. friction
Work done = change in kinetic energy
Increase in K = decrease in U
Work is independent of path
Work = force * distance. Which path takes more work?
What is the work done in going around a loop?
Conservation of energy
1. Which kid will be going fastest at the bottom?
A. Paul
B. Kathleen
C. Same
2. Which kid will reach the bottom first?
Energy in oscillations
In an oscillating system, energy can slosh back
and forth between kinetic and potential
Simple harmonic motion
Kinetic energy = ½ mv2
Potential energy = ½ kx2
Candidate Phys7hw1
Ch.7 (p.159) # 2 (meteorite), 3 (proton), 16 (lift), 66 (ski
lift)
Ch.8 (p.187), Q5 (U), Q9 (K), #2 (drop), 3 (bowl), 9
(bowl), 10 (drop), 37 (U,K), 112 (Mt.Everest), 121
(hydro), 125 (waterfall),
(Challenge question: 8.45)
Next week
• Monday:
– required Blog workshop in CAL from 1:00-2:30
– 5-minute Midquarter conferences in Zita’s office
– Energy midterm and Seminar midterm on inQsit – finish
by Friday
• No seminar class (conferences with Sem students)
• Read Energy Appendix B
• Tuesday: Required workshops
– Research planning #2
– Library workshop #2
– Writing workshop at 3:30
• Thus: Present your midquarter Research Proposal
Force and Power
Energy = Force * distance: E = F x
Power = Energy/time:
P = E/t
P = (F x)/t
Velocity = v = x/t
P = F (x/t)
P=Fv
Power = Force * velocity
Energy derivations (extra)
Force = mass * acceleration = m a
a = dv/dt and v = dx/dt, so
F = m dv/dt = m v (dv/dx)
K = Kinetic energy = force * distance =  F dx
K =  [m v (dv/dx)]dx =  m v dv = ½ mv2
Kinetic energy = ½ mv2
We can define a potential energy U in a conservative force:
F = -dU/dx