📚 Reference: Halliday, Resnick, Krane — Physics (4th ed.), Vol 1, Chapter 7. Independent treatment; no text or figures from the book are reproduced. Numbers, constants, and scenarios are original or from public-domain sources.
What this chapter is about
You know how forces and accelerations connect (Chapter 5), and how to describe motion (Chapter 2). Now comes a powerful shift in perspective: instead of tracking forces at each instant, we ask what forces accomplish over a distance. That accomplishment is work. And work, in turn, is energy transfer — the bridge between mechanics and thermodynamics.
This chapter rewires your physics intuition. Rather than asking "what is the acceleration?", we ask "how much energy changes?", and often the problem becomes much simpler.
Sections
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7.1 — Work done by a constant force — definition of work \( W = \mathbf{F} \cdot \mathbf{d} = Fd \cos \theta \), the dot product, positive/negative/zero work, units (joule).
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7.2 — Kinetic energy and the work–energy theorem — \( KE = \frac{1}{2}mv^2 \), proof that \( W_{\text{net}} = \Delta KE \), applications to collision and motion problems.
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7.3 — Work by variable forces; springs — Hooke's law \( F = -kx \), elastic potential energy \( PE_{\text{spring}} = \frac{1}{2}kx^2 \), integration of work \( W = \int F \, dx \).
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7.4 — Gravitational potential energy and conservative forces — \( PE_{\text{gravity}} = mgh \) (near Earth) and \( PE = -\frac{GMm}{r} \) (general), conservative vs non-conservative forces, path independence.
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7.5 — Mechanical energy and its conservation — total mechanical energy \( E = KE + PE \), when is it conserved, role of friction and air resistance, energy dissipation.
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7.6 — Power and energy transfer — power \( P = \frac{dE}{dt} = \mathbf{F} \cdot \mathbf{v} \), average power, watt as a unit, applications (motors, human metabolism, electricity).
Key concepts to master
- Work is not effort — it's force times displacement in the direction of that force; a perpendicular force does zero work.
- Kinetic energy is always non-negative; \( KE = \frac{1}{2}mv^2 \) depends on speed magnitude, not direction.
- Potential energy stores the work done against a force, ready to be released later.
- Conservation of mechanical energy holds only when friction and air resistance are absent.
- Power is how fast energy transfers; high power = fast change, low power = slow change.
- Real-world systems lose mechanical energy to heat, sound, and deformation — never perfectly conserve.
Prerequisites and connections
- From Chapter 2: kinematics, velocity, acceleration — you need \( v(t) \) to calculate kinetic energy.
- From Chapter 5: Newton's second law (\( \mathbf{F} = m\mathbf{a} \)) — work is the integral of force over distance.
- From Chapter 6: friction and normal forces — mechanical energy is lost to friction as heat.
- Bridge to Chapter 8: momentum and collisions will give a complementary view of interaction (energy is only half the story).
Applications you'll see
- Vehicles: stopping distance scales with \( v^2 \) because \( \frac{1}{2}mv^2 = W_{\text{friction}} \).
- Sports: in jumping or throwing, we're maximizing the work we do on an object.
- Electric motors: convert electrical energy to mechanical work; the efficiency depends on power dissipation.
- Power grids: power = voltage × current; appliances rated in watts tell you how fast they consume energy.
Reading suggestion
Begin with §7.1 and §7.2 in order — they establish the foundation. §7.4 and §7.5 are the conceptual heart; energy conservation is one of the most powerful tools in physics. §7.3 (springs) is a worked-out example of variable forces that prepares you for calculus-based mechanics. §7.6 (power) is often skipped but essential for engineering and real-world problems.
Supplementary materials
- Flashcards (§7 flashcards): 25 key terms and formulas for active recall.
- Q&A / FAQ (§7 Q&A): 20 conceptual questions addressing common student misconceptions.
- Worked problems (coming soon): step-by-step solutions bridging §7.1–§7.6 concepts.
- Practice problems (coming soon): 25+ exercises from basic to advanced.
Next chapter: Chapter 8 — Momentum and Collisions (coming soon)
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