Work, Energy and Power
What this domain tests
Work, Energy and Power tests the work–energy theorem, conservative versus non-conservative forces, potential energy, power, and elastic and inelastic collisions.
Core rules
- Work W = ∫F·ds; for a constant force W = Fs cosθ.
- Work–energy theorem: W_net = ΔK = ½mv² − ½mu².
- Conservative force: work is path-independent and W = −ΔU. Gravity U = mgh; spring U = ½kx².
- Power P = dW/dt = F·v.
- In collisions momentum is conserved; kinetic energy is conserved only in elastic collisions.
Worked example
A block slides from rest down a frictionless incline of height 5 m. Taking g = 9.8 m/s², mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 5) = √98 ≈ 9.9 m/s. The incline angle and path length do not matter because gravity is conservative. If friction acts, W_friction = −f × path length must be included in the work–energy equation.
Traps
Assuming normal force does work when it is perpendicular to motion; using conservation of mechanical energy when friction is present; treating momentum conservation as automatic in every collision; confusing power with energy; forgetting that in a perfectly inelastic collision kinetic energy is lost even though momentum is conserved.