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Lesson 19 · Energy of height
Height is a deposit
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Height is a deposit

Lift something and you have banked energy in it. The account balance is U=mghU = mgh — read aloud, U equals m g h. UU is the gravitational potential energy in joules, mm is the mass in kilograms, hh is the height in metres, and g=9.8 m/s2g = 9.8\ \mathrm{m/s^2} is the acceleration the planet supplies for free. It is not a new idea, either: mgmg is the weight FgF_g, and Fg×hF_g \times h is a force times the distance you carried it — the very work you priced in lesson one.

The part students skip, and examiners never do: h is measured from a zero you choose. The floor, the bench, the valley floor, sea level — any of them will do, and none of them is more correct than another. What matters is that you name your zero and then never move it mid-problem. Potential energy has no absolute value; only changes in it are physical, which is why a question that fails to state a reference level is an incomplete question. On this paper the zero is always given to you.

mhU

U=mghU = m g h

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

W=mgW = m g

  • WW= Weight (force)
  • mm= Mass (mass)
Weight (W = mg) solver →