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Physics 1/Work & energy

Work, energy & power

Work, kinetic and potential energy, the work–energy theorem, conservation of mechanical energy, and power. Anchored to OpenStax University Physics Vol. 1, Ch. 7 (§7.1–7.4) and Ch. 8 (§8.1–8.4).

Before you start — give these a try

Attempting first primes your brain for the lesson — even if you miss. Nothing is graded or saved; it's just a warm-up.

A satellite moves in a circular orbit. The gravitational force on it is always directed toward Earth's centre, perpendicular to its velocity. How much work does gravity do over one orbit?

A ball is dropped from rest at 20 m20\ \text{m}. Using energy conservation, what is its speed just before landing (m/s, g=9.8g = 9.8)?

What you’ll be able to do

  • Compute work W=Fdcos⁡θW = Fd\cos\theta and recognise when it is zero.
  • Use the work–energy theorem and conservation of mechanical energy.
  • Relate power to work and time.
1

Work and kinetic energy

Work by a constant force is W=Fdcos⁡θW = F d\cos\theta, where θ\theta is the angle between force and displacement — so a force perpendicular to motion does no work. Kinetic energy is KE=12mv2KE = \tfrac12 m v^2. The work–energy theorem says the net work equals the change in kinetic energy: Wnet=ΔKEW_{\text{net}} = \Delta KE. (OpenStax §7.1–7.4.)

2

Potential energy & conservation

Near Earth, gravitational potential energy is PE=mghPE = mgh. When only gravity (a conservative force) does work, mechanical energy is conserved: KEi+PEi=KEf+PEfKE_i + PE_i = KE_f + PE_f. A ball dropped from height hh reaches v=2ghv = \sqrt{2gh}. (OpenStax §8.1–8.3.)

3

Power

Power is the rate of doing work: P=W/tP = W/t (watts). Lifting the same load faster needs more power, though the work (and energy) is the same. (OpenStax §7.4.)

Work–energy theorem

Wnet=ΔKE=12mvf2−12mvi2.W_{\text{net}} = \Delta KE = \tfrac12 m v_f^2 - \tfrac12 m v_i^2.

Intuition. Net work is just energy transferred into motion — positive work speeds things up, negative work slows them down.
Conservation of mechanical energy

With only conservative forces, KEi+PEi=KEf+PEfKE_i + PE_i = KE_f + PE_f.

Intuition. Energy sloshes between kinetic and potential but the total stays fixed — height buys you speed and vice versa.

Worked examples

Example 1

A 0.50 kg0.50\ \text{kg} ball is dropped from rest at 20 m20\ \text{m}. Using energy conservation, find its speed just before it lands (g=9.8g = 9.8).

  1. 1

    All the potential energy becomes kinetic: mgh=12mv2mgh = \tfrac12 m v^2 (mass cancels).

  2. 2

    So v=2gh=2(9.8)(20)=392v = \sqrt{2gh} = \sqrt{2(9.8)(20)} = \sqrt{392}.

  3. 3

    v≈19.8 m/sv \approx 19.8\ \text{m/s}.

Answer. v≈19.8 m/sv \approx 19.8\ \text{m/s} (independent of the mass).