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The weight doesn't have to "free fall" for this to work. It could be a huge boulder that's lifted a few centimeters per hour. And then it can be dropped a few centimeters per hour when needed.
Run the numbers.
How heavy a boulder? 10,000kg?
Potential energy is mass x height, so 10,000kg x 1,400m which is 14MJ of energy. Sounds like a lot, right?
One Joule is a watt flowing for a second and 1,000 watts flowing for 3,600 seconds is 1kWh. 3,600,000 Joules or 3.6MJ. So our 10 ton rock up a 1.4km shaft only stores 4kWhs? 60¢ of electricity?
Everything is linear here, so even having a 100 ton rock will only get us to half a EV battery.
Edit: if you're wondering where the other 90 cents went, this example won't produce two megawatts. It would only produce about 700 kilowatts.
Thanks for doing the math and for expanding.
The way I see it is: if I gather all the electricity I use to power my appliances in a week and just for one home - my home (fridge, heat, washing machines, vacuum cleaner, lightbulbs, laptop), and use it to lift that rock, how high will that rock get?
Also, I wasn't even picturing a rock that small (10,000 kgs in water can be stored half a bedroom of a midsized apartment. Let's just assume that it would take about the same volume in "rock.") I was picturing a rock that's 10m by 10m by 100m tall. More like 10,000,000 kgs.
You missed a factor of ten from the gravitational field strength, but still not great. Their heat batteries work better when it comes to heating, but that is mostly limited to just that.
Oh yes, mgh not mh. You're right