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Unit Plan – Work and Energy
Chapters
Week 9 (begin 10/18)
Monday (PLC day, periods 5 minutes shorter)
MMMM
Go over test
Tuesday
Movie: Elements of Physics, Modern Physics and Cosmology
Wednesday
Lec Work introduction.notebook
Thursday
Finish Lec Work introduction.notebook
Handout Practice Energy Problems
Friday
Lec Energy.notebook
show particle accelerator
Week 10 (begin 10/25)
Monday
MMMM
Stamp Chapter Outline
Finish Lec Energy.notebook
Present problems
Tuesday
Present problems
Wednesday
Present problems
Thursday
Present problems
Friday
Present problems
Lec test review.notebook
Week 11 (begin 11/1) (P/T Th/Fr)
Monday (PLC day, periods 5 minutes shorter)
MMMM
Lec test review.notebook
Review time
Tuesday
Test
Wednesday
Go over test
Go over last test: Test Work and Energy key.notebook
Thursday (20 min period)
Team builder - Apples to Apples
Friday
No school
Smartboard files - blue
Demos - purple
Video - bold turquoise
Web assign - dark red
Jeopardy - brown/red
IP file - yellow/brown
Labs - dark forest green
Week - green
Tests - red
Still not good results….
More on w=fd… NOTHING else matters
Spring & mass problems
Change exam answer key.. # 5 numbers changed
Remember i hat, j hat, k hat. Unit vectors.
Work = F*d = F*s (where s is the scalar value of s)
Work is in Nm (Joules) – not confused with torque
If at an angle, then W = F*s*cosΘ
If angle = 90 then NO WORK done
Work against gravity = Wg = Fh = Fwh = mgh
Dot Product
Scalar product of two vectors:
Given magnitudes and angle between them: A · B = AB cos (A,B)
(page 230 covers in detail)
Given components use: A · B = AxBx + AyBy + AzBz
W = F · s = F * s * cosΘ
i.e. a rocket moving straight from (0,0,0) to (100m,0,25m) with F = (400N)i + (10N)j + (100N)k. The displacement is s = (100m-0)i +
(0-0)j + (25m – 0)k.
What is the work? FscosΘ is difficult since we don’t have Θ.
The work done is W = F · s = (400N)(100m-0) + (10N)(0-0) + (100N)(25m-0) = 42500Nm.
Is Work a vector?
Calculus:
W = F cosΘ s  as we look at small distances, we get
dW = F cosΘ ds  as path curves, friction always opposes the motion, always fighting friction so Θ = 0
so F ∫ ds = Fl  W = fl. Work is force times distance
If you do full circle, fighting friction the whole time, obviously work was done… NONCONSERVATIVE FORCE
Work against friction is always positive
So, since F * s = work, area under a curve applies
WPiPf = ∫ F · ds
Work Diagrams are COMMON
Work in direction of Force is POSITIVE
Meandering in the field: conservative forces (gravity, magnetic, spring, pressure, electrical, etc.) conservative means process is
reversible. Non-conservative are: friction, air resistance, muscles pushing or pulling.
Energy:
Remember Energies: PE, KE, spring KE, discuss
Conservation of E
Try: sample problems
Energy is relative: KE = ½ mv2. Person walking on a train has velocity relative to train, or observer on platform.
PE = mgh … what h?
W = KEf - KEi = ΔKE
W = ΔE in general
PE = -mgΔh
ΔPE = -∫ F · ds
Revisit Ed in space: F=GMm?r^2  W = Fs = ∫F · ds = ∫ Fg cosΘ ds
Walk thru on CD & book derives sideways does not matter, only Δr, so:
WPiPf = -∫ Fg(r) dr = -∫ GmM/r^2 dr = GmM(1/rf – 1/ri)
ΔPE = -W  ΔPE = GmM(1/rf – 1/ri)
(for when you don’t know g)
PEG = -GmM/r  consider magnets: closer together, more potential (PE = mgh is more limited)
Escape Velocity: Ei = KEi + PEi = 1/23mv^2 +(-GmM/R)
Want v = 0 (minimum) and PEG=0 (at r = infinity), and E = constant, so Ei = Ef = 0
 KEi = PEG  1/2mv^2 = GmM/R
 Vesc = (2GM/R)^1/2
P = dW/dt (derivative of Work gives power): W as a function of time.. from F(t) from a(t)…
d(t) = 2t^2 + t +1
v(t) = 4t +1
a(t) = 4
F(t) = m * 4
W(t) = 4m * (2t^2 + t +1)
P(t) = 4m * (4t +1)
 P = F· v (if parallel, then P = F v)
Now try:
d(t) = 3t^3 – 2t^2 + t +1
v(t) = 9t^2 – 4t +1
a(t) = 18t – 4
F(t) = m * (18t – 4)
W(t) = m * (18t – 4) * (3t^3 – 2t^2 + t +1)
Springs:Δ
F = ks
Slope of F-d graph gives k
ΔPE = ½ s (ks) = ½ k s^2
chapter 7-8 7% (12 days)
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Chapter 7: Work and Energy
Topics:
Work Done by a Constant Force - simple examples (zero work examples, etc.) units,
The Scalar Product of Two Vectors - DOT Product with unit vectors defined
Work Done by a Varying Force - graphical definition goes quickly to integration, spring force is
done by integration.
Kinetic Energy and the Work-Energy Theorem - derive net work = delta K, slow down due to friction,
other friction examples.
POWER - differential definition, units
* Energy and the Automobile - discussion of power and energy loss in autos
* Kinetic Energy at High Speeds - relativity, brief
Chapter 8: Potential Energy and Conservation of Energy
Topics:
Potential Energy - starts with gravitational pot energy near earth and W = ∆U units
Conservative and Nonconservative Forces - define, examples with gravity and spring and friction
Conservative Forces and Potential Energy - integration, general and brief
Conservation of Energy - first phrased with no energy added from outside and no nonconservative
forces, lots of conceptual examples
Changes in Mechanical Energy when Nonconservative Forces are Present - now includes changes
in internal energy and stuff like friction, lots of examples
Relationship Between Conservative Forces and Potential Energy - Calculus derivation, theory only.
* Energy Diagrams and the Equilibrium of a System - calculus based max min graph approach,
stable and unstable equilibrium defined this way
Conservation of Energy in General - brief, mention of thermodynamics rule
* Mass-Energy Equivalence - E =m c-squared
* Quantization of Energy - energy levels in atom and in earth orbit of satellite.