Work, Energy & Power — Work, Energy & Power Applied (Medium)

Quick Recap — Work, Energy & Power

• Work: $W=Fd\cos\theta$ (zero when the force is perpendicular to the displacement). Work–energy theorem: $W_{net}=\Delta KE$.
• Energies: $KE=\tfrac12 mv^2=\dfrac{p^2}{2m}$; gravitational $PE=mgh$; spring $PE=\tfrac12 kx^2$. Total mechanical energy is conserved when only conservative forces act.
• Power: $P=\dfrac{W}{t}=Fv$ (instantaneous). $1$ kWh $=3.6\times10^6$ J.
• Free fall / smooth slope: speed at the bottom of a drop $h$ is $\sqrt{2gh}$ (independent of the path).

Worked mini-example. A 200 N/m spring compressed 0.1 m stores $PE=\tfrac12 kx^2=\tfrac12(200)(0.01)=1$ J.