Work, Energy & Power Explained | Chapter 6 of University Physics

Chapter 6 bridges Newton’s laws and energy conservation by introducing work, kinetic energy, and power, along with the powerful work-energy theorem for analyzing motion and forces.

Watch the full video summary on YouTube for detailed derivations and examples.

Work: Definition and Calculation

Work occurs when a force causes displacement. For a constant force aligned with motion, use W = F s. When force and displacement form an angle φ, apply the dot product:

W = F s cos(φ)

Work can be positive, negative, or zero. Forces perpendicular to motion (like the normal force on a flat surface) perform no work. To find total work, sum contributions from each force or use the net force in the dot-product formula.

Kinetic Energy & the Work-Energy Theorem

Kinetic energy is the energy of motion, defined by:

K = ½ m v²

The work-energy theorem relates net work to changes in kinetic energy:

W_total = ΔK = ½ m v₂² – ½ m v₁²

This approach lets you determine motion changes without solving for acceleration or time explicitly.

Work by Varying Forces

When force varies with position, compute work via an integral:

W = ∫_x₁^x₂ F(x) dx

For springs (Hooke’s Law, F = k x), the work is:

W = ½ k x² (from 0 to X)

In general, use the line integral form W = ∫ F · dl for forces along curved paths.

Power: Rate of Energy Transfer

Power measures how quickly work is done or energy is transferred. Average and instantaneous definitions are:

• P_avg = ΔW/Δt
• P = dW/dt = F · v = F v cos(φ)

Power’s SI unit is the watt (W = J/s); the non-SI unit horsepower (hp) equals 746 W.

Conclusion

Energy methods—work, kinetic energy, and power—offer elegant alternatives to force-based analyses, especially when applying the work-energy theorem and power relations. Master these tools to simplify complex mechanics problems in fields from engineering to physics research.

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