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A.3.5—Work-energy change

Syllabus
First assessment 2025
Objective
—
Level
SL

Relate Resultant Work to Energy Change

Work–energy theorem

The net work done by the resultant force on a system equals its change in kinetic energy:

Wnet=ΔEkW_{net}=\Delta E_k

Use force–distance area

For a variable resultant force, the signed area under the force–distance graph gives the work and therefore the kinetic-energy change.

Include all resultant forces

Friction, applied forces and gravity may each do work. Add their signed contributions before relating the result to the final kinetic energy.

Worked example from local Question Bank row 31356

A constant net force of 100 N100\,\mathrm{N} moves an object from rest through 2.0 m2.0\,\mathrm{m} until its speed is 10 m s−110\,\mathrm{m\,s^{-1}}.

Wnet=Fs=(100)(2.0)=200 JW_{net}=Fs=(100)(2.0)=200\,\mathrm{J}
200=ΔEk=12m(10)2−0200=\Delta E_k=\frac12m(10)^2-0
m=4.0 kgm=4.0\,\mathrm{kg}

The positive net work is exactly the object's kinetic-energy gain.

Common trap

Do not use the work of one force as the net work unless all other force contributions are zero or already included.

A.3.5 Exam Analysis

[ 3 ]

A force of 14.0 N acts on the box for 0.35 m as shown. The force is then removed and the box continues to move. The box comes to rest after a further displacement d.

Determine d.

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.