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After watching https://www.youtube.com/watch?v=mmrwdTGZxGk I wondered what kind of device I would have to build in order to store enough energy to run a house for one day.

Let's consider a 100% efficiency of the energy storage system for simplicity.

A standard 40 feet container:

  • Has a mass of 3700 kilograms
  • Measures 12.035 x 2.35 x 2.385 meters (exterior)
  • Has an internal volume of 67.5 m³

Let's say we fill this container with steel (volumetric mass density of 7800 kg / m³).

The mass of steel is: $$m = \rho * V = 7800 * 67.5 = 526500 \textrm{ kg} $$ The total mass of the filled container is 526500 + 3800 = 530200 kg (530 tons)

I need to store 10 kWh of energy using gravity. I have

$$E = m *g * h $$

  • E being the energy (in Joules)
  • m being the mass (in kilograms)
  • g being the gravitational acceleration
  • h being the height of the object in meters (or the difference of height)

10 kWh corresponds to 36 000 000 Joules.

$$h = \frac{E}{m * g} = \frac{36000000}{526500 * 9.81} = 6.92 \textrm{ m}$$

This results in a height of 6.92 meters. Is my computation correct?

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closed as off-topic by Aaron Stevens, alephzero, rob Feb 7 at 15:24

This question appears to be off-topic. The users who voted to close gave these specific reasons:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – rob
  • "This question appears to be about engineering, which is the application of scientific knowledge to construct a solution to solve a specific problem. As such, it is off topic for this site, which deals with the science, whether theoretical or experimental, of how the natural world works. For more information, see this meta post." – Aaron Stevens, alephzero
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  • $\begingroup$ With the same formulas and a container filled with water: 51.7 meters, filled with wet sand: 29.3 meters, granite: 20.5 meters. I can't find a volumetric mass / price graph so it's hard to tell what's the best material for a mass / price compromise. $\endgroup$ – Victor Lamoine Feb 7 at 14:33
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    $\begingroup$ In its present form (v2), this is a check-my-work question. $\endgroup$ – rob Feb 7 at 15:25
  • $\begingroup$ Agreed, I will post again into a more appropriate place. $\endgroup$ – Victor Lamoine Feb 7 at 15:29