Fall wk 4 – Thus.21.Oct.04 Welcome, roll, questions Exercise on rising CO 2 levels Energy and Work Looking ahead: Winter seminar texts Energy Systems, EJZ

Measured rising CO 2 levels Intro to Energy, Cassedy & Grossman

Predicting future CO 2 levels You found equations for ppm of CO 2 (t in yrs) (a)Linear rise: L(t) = 8/7 t (b)Exponential rise: z(t) = 315 (1.005) t (c)Oscillations: c(t) = 4 cos 2  t To predict CO 2 level in 2100, use (a) or (b). To predict when CO 2 level will reach 550 ppm, solve (a) or (b) for time.

Energy and work Mechanical energy = potential + kinetic Mechanical energy is conserved (E before = E after ) 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 mv 2  U = mgh Force = slope of potential energy curve. Where is the net force=0? Where is it greatest?

Conservative forces 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 mv 2 Potential energy = ½ kx 2

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 = F v 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 mv 2 Kinetic energy = ½ mv 2 We can define a potential energy U in a conservative force: F = -dU/dx