Week 2 Physics Notes—Action–Reaction, Work–Energy, & Universal Gravitation

Course Logistics & Administrative Reminders

• All HW/quiz info lives under the “Syllabus / Course-Outline” tab; download or bookmark the calendar.
  • Each week lists the exact textbook problem numbers to submit.
• Submission workflow ⟶ Assignments → HW → “Add Comment” → attach file
  • Acceptable formats: $\text{PDF}$, $\text{DOC/DOCX}$, $\text{PNG/JPEG}$.
  • Avoid iPhone “live-photo” $\text{HEIC}$ files (incompatible with the instructor’s Windows PC).
  • If platform glitches, email the files directly.
• Quizzes
  • One attempt, modest time-limit (≈3–4× the time actually required).
  • Take only after consulting the posted HW-solution keys.
• Grading cadence: HW 1 being returned; HW 2 + Quiz 1 due Sunday night.

Review of Newton’s Three Laws

(Quick recap to set context)

• 1st Law – Inertia: Natural state is constant $\vec v$ (including $0$) unless a net $\vec F$ acts.
• 2nd Law – Acceleration: $\vec F_{\text{net}} = m \vec a$.
• 3rd Law – Action/Reaction: Every force occurs in equal-magnitude, opposite-direction pairs on different objects.

Newton’s Third Law – Detailed Exploration

• Forces as interactions
  • Require two bodies: e.g.
  • Person leans on wall ⟶ hand pushes wall, wall pushes hand.
  • Gravity: Earth pulls person downward, person pulls Earth upward (immeasurable because $m<em>{\text{Earth}} \gg m</em>{\text{person}}$ so $a_{\text{Earth}} \approx 0$).
• Key wording
  • “Action force” = force that initiates the interaction (definition is arbitrary but useful bookkeeping).
  • “Reaction force” = simultaneous, equal-magnitude, opposite-direction partner.
• Examples
  • Soccer kick: $F<em>{\text{foot→ball}} = 1500\,\text N$ implies $F</em>{\text{ball→foot}} = -1500\,\text N$ (why your foot stings).
  • Hammer/nail, tires/road traction, walking, rocket thrust (engine pushes exhaust ⟶ exhaust pushes rocket).
  • Cannon + cannonball: forces identical, accelerations differ: $a<em>{\text{ball}} = F/m</em>{\text{ball}} \gg a_{\text{cannon}}$.
  • Bug vs car windshield: same force, but bug’s $m\rightarrow0$ ⇒ catastrophic $a$.
  • Two equal-mass skaters push off ⟶ equal & opposite speeds (same $m$, same $|\vec v|$).
• Systems & internal vs external forces
  • Define your “system” to simplify bookkeeping.
  • Only external forces determine $\vec a_{\text{system}}$.
  • Apple–orange–sled cartoon: within a combined system, internal action/reaction pairs cancel; only outside agents (e.g. friction) change the system’s momentum.
• Vector decomposition refresher
  • Break any $\vec F$ into horizontal/vertical components via trig; component magnitudes control motion along incline planes, tension problems, etc.
  • Inclined-plane story: weight $mg$ resolves into $mg\sin\theta$ (down-slope) + $mg\cos\theta$ (normal-force partner). As $\theta$ ↑, $mg\cos\theta$ ↓ so object starts sliding.

Work, Energy & Power

Fundamental Definitions

• Energy = ability to do work; scalar; conserved.
  • Cannot be created/destroyed, only transformed (First Law of Thermodynamics).
• Work $W$: $W = F d$ (force component parallel to displacement).
  • Scalar; units $\text{N·m} = \text J$ (Joule, after James Joule).
  • Zero work if $d=0$ despite muscular effort (pushing on an immovable wall).
• Power $P$: rate of doing work, $P = \dfrac{W}{t}$ (units Watt $1\,\text W = 1\,\text{J·s}^{-1}$; kilowatt $=10^3$ W).

Mechanical Energy Forms

1. Gravitational Potential Energy$PE_g = m g h$
   • Depends only on vertical height difference (path-independent).
   • Examples: water towers, pile-drivers, lifted cement bags.
2. Elastic Potential Energy (bow, spring, rubber band) – stored due to deformation.
3. Kinetic Energy$KE = \frac12 m v^2$
   • $KE \propto v^2$ ⟶ doubling speed quadruples energy.

Work–Energy Theorem

$W_{\text{net}} = \Delta KE$

• Speeding up vehicle: engine does work to increase $KE$.
• Braking: friction does negative work converting $\Delta KE$ mostly to heat (and a little sound).
  • Doubling speed ⟶ stopping distance quadruples for same max braking force.

Conservation of Energy in Practice

• Bow-and-arrow: draw work $\rightarrow$ 50 J $PE<em>{elastic}$ ⟶ release gives 40 J $KE</em>{arrow}$ + 10 J heat/sound.
• Pile driver: $PE_g$ at top entirely becomes $KE$ at impact (then heat, sound, deformation).
• Energy bookkeeping simpler than $\vec F$ analysis because scalars (no cancellation).

Momentum vs Kinetic Energy (important contrast)

• Momentum $\vec p = m \vec v$ (vector, can cancel; linear dependence on $v$).
• Kinetic energy scalar; quadratic in $v$; cannot cancel.

Simple Machines & Mechanical Advantage

• Energy in = Energy out: $F<em>{in} d</em>{in} = F<em>{out} d</em>{out}$ (ideal, friction-free).
• Lever: rigid bar + fulcrum — trade distance for force. Long arm multiplies force; short arm multiplies speed/distance.
• Pulley / Block-and-Tackle
  • Single fixed pulley changes force direction only.
  • n-rope segments ⟶ load force $=\dfrac{F_{\text{pull}}}{n}$, but you pull $n$× the distance.
• Inclined Plane, Wheel-and-Axle, Screw operate on same work-equivalence principle.
• Efficiency $\eta = \dfrac{Useful\, Work<em>{out}}{Energy</em>{in}}$ (always <1).
  • Typical steam or gas power plant $\eta\lesssim 0.7$; waste heat sometimes repurposed (district heating, historic Edison plant, warm-water manatee refuge).

Biological & Alternative Energy Contexts

• Food energy ➝ cellular $ATP$ ➝ motion/heat; metabolic pathways only ~10–20 % efficient.
• Ecological “10 % rule” across trophic levels (producer → herbivore → carnivore…).
• Solar influx: more energy reaches Earth in 1 h than total human annual consumption.
• Other sources: nuclear fission (enormous energy density), fuel cells (H₂/O₂ ↔ H₂O + electricity), geothermal/fracking‐enhanced reservoirs.

Universal Gravitation & Weightlessness

Newton’s Synthesis

• Same law explains falling apple and Moon’s orbit.
• Law: $F = G \dfrac{m<em>1 m</em>2}{r^2}$ with $G = 6.67\times10^{-11}\, \text{N·m}^2\text{/kg}^2$.
  • Always attractive; inverse-square in $r$.
  • Doubling one mass doubles $F$; doubling both masses quadruples $F$; doubling separation halves $F$ by $\tfrac14$.
• Gravity weakest of four fundamental forces yet dominates astronomically because it never cancels.

Mass, Weight & Apparent Weight

• Weight $W = mg$ (local) = gravitational force exerted by Earth.
• Elevator thought-experiments:
  • Accelerating up ⟶ scale reads $W+ma$ (heavier).
  • Accelerating down ⟶ scale reads $W-ma$ (lighter).
  • Free-fall ⟶ scale reads $0$ (weightless; $g$ still acts!).
• Astronauts in orbit are in continuous free-fall, hence apparent weightlessness.

Gravitational Field Model

• Field $\vec g(\vec r)$ gives force per unit mass at each point.
  • Outside spherical mass: $|\vec g| = G\dfrac{M}{r^2}$ (identical $r^{-2}$ behaviour).
  • Inside uniform Earth: $|\vec g| \propto r$ (linear) ⟶ zero at centre.
  • Hypothetical “tunnel through Earth” gives ~42 min end-to-end oscillation (≈18 min surface-to-centre).

Tides

• Differential lunar gravity raises bulges on near & far sides of Earth ⟶ two high & two low tides per ~24 h.
  • Sun adds secondary effect: spring tides (new/full moon, larger range) vs neap tides (quarter moons, smaller range).

General Relativity & Exotic Predictions

• Einstein: mass/energy warps spacetime; bodies follow curved geodesics.
• Black holes: collapse beyond “event horizon” where escape velocity > c; predicted then observed.
• Potential wormholes: spacetime tunnels linking distant regions/universes (speculative; no empirical confirmation).
• Cosmic destiny:
  • Gravity vs mysterious “dark energy” driving accelerated expansion.
  • Scenarios: eternal expansion (heat death), decelerating then recollapsing “Big Crunch”, or other.

Grand Summary Cheat-Sheet

• Three laws + energy conservation underpin most everyday mechanics.
• Action/reaction forces equal & opposite on different bodies; accelerations differ when masses differ.
• Work–energy: $W=Fd$, $\Delta KE = W_{\text{net}}$; Power $=W/t$.
• Energy bookkeeping often simpler than force diagrams – scalars, no vector cancellation.
• Machines trade force for distance; efficiency < 100 % due to inevitable heat losses.
• Universal gravitation unifies terrestrial and celestial phenomena; weightlessness arises from free-fall, not absence of gravity.
• Modern view (GR) treats gravity as spacetime curvature, predicting black holes, gravitational waves, and fueling cosmological puzzles.