A.3 Work, energy and power

UNIT SYLLABUS

SL/HL 8 hours

Energy is physics' universal currency, and this unit teaches you the accounting rules. Work is the mechanism that transfers energy ($W = Fs\cos\theta$ — only the force component along the motion counts). Mechanical energy comes in three interchangeable forms — kinetic, gravitational potential and elastic potential — and when resistive forces are absent, their total is conserved. Energy methods often crack problems that would be miserable with forces alone: no vectors, no components, just a before-and-after balance sheet. Power and efficiency then connect the physics to engines, motors and the real-world cost of wasted energy.

Guiding Questions

? How are concepts of work, energy and power used to predict changes within a system?
? How can a consideration of energy transfers simplify problems that forces make difficult?

✓ What the IB expects you to master

Apply the principle of conservation of energy and represent energy transfers on a Sankey diagram.
Calculate work done by a constant force as $W = Fs\cos\theta$ and interpret work as energy transferred.
Recognise that the work done by the resultant force equals the change in the system's energy.
Use the three forms of mechanical energy: $E_k = \frac{1}{2}mv^2 = \frac{p^2}{2m}$ , $\Delta E_p = mg\Delta h$ , and $E_H = \frac{1}{2}k(\Delta x)^2$ .
Apply conservation of mechanical energy when friction and resistance are absent, and account for the energy dissipated when they are not.
Calculate power as $P = \Delta W/\Delta t = Fv$ and efficiency as useful output over total input (energy or power).
Compare fuel sources by their energy density.

1 Key Formulas

Work done

W = Fs\cos\theta

Kinetic energy

E_{k} = \tfrac{1}{2}mv^{2} = \frac{p^{2}}{2m}

Gravitational PE (near surface)

\Delta E_{p} = mg\Delta h

Elastic potential energy

E_{H} = \tfrac{1}{2}k(\Delta x)^{2}

Power

P = \frac{\Delta W}{\Delta t} = Fv

Efficiency

\eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}}

2 Exam Preparation & Topic Explanations

Choosing energy methods over forces

When a question involves speeds at two positions and the path between them is curved or complicated, energy conservation is almost always the intended route: kinematics equations only work for constant acceleration along a straight line.

Write a clear energy balance: initial mechanical energy = final mechanical energy + energy dissipated. That single line often scores method marks even if arithmetic slips.

Pro Exam Strategy

Work–energy problems don't care about the path when only gravity acts — height change is everything.
$P = Fv$ is the fastest route for constant-speed problems: driving force equals resistance.
Watch for the word "smooth" (no friction — mechanical energy conserved) versus "rough" (include dissipation).
Energy density questions compare fuels: energy per kilogram or per cubic metre, a favourite for data-response questions.

3 MCQ Practice

Q1. A porter carries a heavy suitcase horizontally at constant velocity across a level floor. The work done on the suitcase by the supporting force is:

Positive
Negative
Zero
Cannot be determined

Q2. A pendulum bob is released from a height $h$ above its lowest point. Ignoring air resistance, its speed at the lowest point is:

$\sqrt{gh}$
$\sqrt{2gh}$
$2\sqrt{gh}$
$gh$

Q3. A motor rated at 1.5 kW raises a 60 kg load at a steady $2.0\ \text{m s}^{-1}$ . What is the efficiency of the system?

4 Short Answer Questions

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