Flashcards — Chapter 7 🃏

Work and Energy — the bridge between forces and transformations! Master work, kinetic energy, potential energy, and power with these cards. ⚡

🎮 How it works

• 🎴 Study Mode — Cards one at a time. Think, then see the answer.
• ⚡ Quick Quiz — 10 questions in 20 seconds. Score, streak, and competition!

---

---

📋 Card deck: Key terms & formulas

Section §7.1 — Work by constant force

1. Work (W) — force applied in direction of motion × distance; \( W = \mathbf{F} \cdot \mathbf{d} = Fd\cos\theta \) (joule, J)
2. Dot product — \( \mathbf{A} \cdot \mathbf{B} = AB\cos\phi \); commutative, distributive
3. Unit of work — joule (J) = newton·meter (N·m) = kg·m²/s²
4. Positive work — force has component in direction of motion; \( \theta < 90° \)
5. Negative work — force opposes motion; \( \theta > 90° \)
6. Zero work — force is perpendicular to displacement; \( \theta = 90° \)

Section §7.2 — Kinetic energy & work–energy theorem

7. Kinetic energy (KE) — energy of motion; \( KE = \frac{1}{2}mv^2 \) (joule, J)
8. Work–energy theorem — net work equals change in kinetic energy; \( W_{\text{net}} = \Delta KE = KE_f - KE_i \)
9. Stopping distance — proportional to \( v^2 \); doubling speed quadruples stopping distance
10. Total work — sum of work by all forces; \( W_{\text{total}} = W_1 + W_2 + \cdots \)

Section §7.3 — Variable forces & springs

11. Hooke's law — restoring force in a spring; \( F = -kx \) (spring constant \( k \) in N/m)
12. Elastic potential energy (spring) — \( PE_{\text{spring}} = \frac{1}{2}kx^2 \) (joule)
13. Work by variable force — \( W = \int F \, dx \) (area under \( F \)–\( x \) graph)
14. Spring constant \( k \) — stiff spring has large \( k \); stretching or compressing by same \( |x| \) gives same energy

Section §7.4 — Gravitational potential energy & conservative forces

15. Gravitational PE (near Earth) — \( PE_{\text{gravity}} = mgh \) (height \( h \) above reference point)
16. Gravitational PE (general) — \( PE = -\frac{GMm}{r} \) (zero at \( r = \infty \); bound objects have negative PE)
17. Conservative force — work done is independent of path; potential energy can be defined (e.g., gravity, spring)
18. Non-conservative force — work depends on path (e.g., friction, air resistance)
19. Potential energy difference — \( \Delta PE = -W_{\text{conservative}} \) (work against the force)

Section §7.5 — Mechanical energy & conservation

20. Total mechanical energy — \( E = KE + PE \) (sum of kinetic + potential energy)
21. Conservation of mechanical energy — \( E_i = E_f \) (or \( KE_i + PE_i = KE_f + PE_f \)) when no non-conservative forces act
22. Friction dissipates energy — \( \Delta E_{\text{mech}} = -W_{\text{friction}} = -f \cdot d \) (lost to heat, sound)
23. Non-conservative work — \( W_{\text{non-cons}} = \Delta E = E_f - E_i \) (energy dissipation or input)

Section §7.6 — Power

24. Power (P) — rate of energy transfer; \( P = \frac{\Delta E}{\Delta t} \) or \( P = \frac{dE}{dt} \) (watt, W = J/s)
25. Instantaneous power — \( P = \mathbf{F} \cdot \mathbf{v} = Fv\cos\theta \) (product of force and velocity components)

---

📊 Topics covered

• Work — dot product, constant force, positive/negative/zero
• Kinetic energy — \( \frac{1}{2}mv^2 \), work–energy theorem
• Variable forces & springs — Hooke's law, elastic PE, integration
• Gravitational PE — near Earth and general form
• Conservative vs non-conservative — path independence
• Mechanical energy — conservation, dissipation
• Power — rate, average, instantaneous

---

What's next:

👉 §7.7 — Worked problems (step-by-step examples)
👉 §7.8 — Practice problems (exercises)
👉 §7.9 — Q&A (FAQs on common misconceptions)

⇧ Back to chapter