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A.3.4—Work by constant force

Syllabus
First assessment 2025
Objective
—
Level
HL

Calculate Work by a Constant Force

Constant-force work

For a force FF acting through displacement ss,

W=Fscos⁡θW=Fs\cos\theta

Only the component parallel to displacement transfers energy by work.

Area under a force–distance graph

For a variable force, the area under an FF-against-ss graph gives work. A negative area represents work against the chosen displacement direction.

Check the angle

Use the angle between force and displacement, not the angle between the force and an unrelated axis unless the component has first been resolved.

Worked example from local Question Bank row 39177

A kite pulls a ship with force 2.50×105 N2.50\times10^5\,\mathrm{N} at 39∘39^\circ to its 1.00 km1.00\,\mathrm{km} displacement. Convert 1.00 km=1.00×103 m1.00\,\mathrm{km}=1.00\times10^3\,\mathrm{m}, then

W=Fscos⁡θ=(2.50×105)(1.00×103)cos⁡39∘=1.94×108 J≈1.9×108 JW=Fs\cos\theta=(2.50\times10^5)(1.00\times10^3)\cos39^\circ=1.94\times10^8\,\mathrm{J}\approx1.9\times10^8\,\mathrm{J}

Only the force component along the ship's displacement transfers energy.

A.3.4 Exam Analysis

Assessment in practice

1–3 marks
How it is assessed

The evidence asks what the area under a force–distance graph represents and includes an electric-field work calculation.

Command terms

State / Calculate

What earns marks

Use W=Fs cosθ for a constant force or the area under the force–distance graph for a variable force. State what the area represents and keep the sign and units of work consistent.

Watch for

Using the force magnitude without the parallel component or interpreting graph area as force rather than work.

Representative question

Question 1

[Maximum number: 1]

State what is represented by the area under the graph.

Retrieve the A.3 Work, Energy and Power Model

Account for energy

Define the system, identify energy stores and describe transfers. Work done by a force transfers energy; total energy is conserved even when mechanical energy is not.

Use the mechanical model

E_k= rac12mv^2,\quad \Delta E_{p,g}=mg\Delta h,\quad E_{p,elastic}= rac12k(\Delta x)^2

Conserve their sum only when resistive transfers are absent or included explicitly.

Use rates and ratios

P= rac{\Delta E}{\Delta t}=Fv,\qquad \eta= rac{E_{useful}}{E_{input}}= rac{P_{useful}}{P_{input}}

Fuel energy density connects available input energy to a chosen volume.

Final checks

Check the system boundary, signs of work and potential-energy changes, the reference height, extension from natural length, and whether the quantity is energy, power, efficiency or energy density.