Fall wk 4 – Thus.21.Oct.04

• Welcome, roll, questions

• Exercise on rising CO2 levels

• Energy and Work

• Looking ahead: Winter seminar texts

Energy Systems, EJZ

Measured rising CO2 levelsIntro 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 2t

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

• 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 energy1. 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 = 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 mv2

Kinetic energy = ½ mv2

We can define a potential energy U in a conservative force:

F = -dU/dx