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Lesson 21 · The energy swap
The swap — and the mass that cancels
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The swap — and the mass that cancels

Drop something, and stored energy becomes motion energy: mgh=12mv2mgh = \tfrac{1}{2}mv^2. Now watch the mm on both sides — it cancels. Solve, and v=2ghv = \sqrt{2gh} (v equals root two g h): the landing speed does not care what the mass is. Galileo dropped that fact off a tower four centuries ago, and it still lands.

These are two-step problems: bank the energy at the top, cash it at the bottom. Write the middle answer down with its units before moving on — and estimate first. One order-of-magnitude guess costs five seconds and catches almost every slipped root and missing g.

mv0vW

W=12m(v2−v02)W = \tfrac{1}{2} m \left(v^{2} - v_0^{2}\right)

  • WW= Net work (energy)
  • mm= Mass (mass)
  • vv= Final speed (speed)
  • v0v_0= Initial speed (speed)
Work–Energy Theorem solver →
mvKE

Ek=12mv2E_k = \tfrac{1}{2} m v^{2}

  • EkE_k= Kinetic energy (energy)
  • mm= Mass (mass)
  • vv= Speed (speed)
Kinetic Energy solver →
mhU

U=mghU = m g h

  • UU= Potential energy (energy)
  • mm= Mass (mass)
  • hh= Height (length)
Gravitational Potential Energy (U = mgh) solver →