A.3.2—Work as energy transfer

Work transfers energy

Work done by a force is the energy transferred by that force. For a constant force,

$W=Fs\cos\theta$

where $\theta$ is the angle between force and displacement.

Use the sign

Positive work transfers energy into the object’s relevant store; negative work transfers energy out of it. A force perpendicular to displacement does zero work.

Follow the physical process

Wind can transfer kinetic energy to a turbine through work, while resistive forces can transfer mechanical energy to internal energy of the surroundings.

Common trap

Do not call every force an energy transfer. Check whether the force has a component along the displacement.

[ 2 ]

Describe the energy transfers taking place in a wind generator.

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.

A.3.2—Work as energy transfer

Relate Work to Energy Transfer

Retrieve the A.3 Work, Energy and Power Model

A.3.2 Exam Analysis