How much vertical weight/height do I need to store 33 kWh of energy? My question is the feasibility of a vertical mechanical weight battery, but unlike previous questions, I wanted to give a precise scenario and see if my math is right (which I doubt)
First, it takes 1.345 watts to lift 1 lb 1 vertical foot in 1 second.
Assume the battery weighs 100 lb per cubic foot, so a block of weight 4 feet per side would weigh 6,400 lbs.
Therefore it would take 8,600 watts (or 8.6 kw) to lift this weight 1 foot (not sure if the "per second" aspect matters).
Now, that it has 8.6 kw of potential energy, I can now power my house at night by dropping the weight slowly.
If a typical home uses 1000 kWh energy per month, thats about 33 kwh per day.
So  if I want my battery to store 33 kwh of power per day, instead of 8.6kw, I either need to quadruple my weight or the lifting height (increase to 4 ft instead of 1 ft lift height).
One main unaccounted factor I can think of is inefficiency of the system, but even at say 50%, I would offset that loss by doubling my height or weight once again.  My thought is a weight battery to store solar, so a second issue would be cloudy days, so maybe double or triple the height/weight again.
Yes, I have already seen that large scale  pilot project with cranes & blocks.
Is my math right? Does this sound feasible?
 A: The power equation you have is causing confusion.  That deals with all sorts of nuances about how you would have to apply the energy, but you're concerned with how large the block must be, and how high it must be raised.  These can be done entirely with energy terms.
One of the extraordinarily nifty thing about energy is that it is conserved.  This ends up meaning that it doesn't matter how you lift the block.  All that matters is where the block ends up.  In particular, the equation you need is
$$E=mgh$$
Where $E$ is the gravitational potential energy you're storing in the block, $m$ is its mass, $g$ is the acceleration of gravity, and $h$ is the height you raise it to.
We can rearrange the equation to $h=\frac{E}{mg}$ to get the height you have to raise the block to as a function of mass.  Given $E=33000\;\text{J}$ and $g=9.8\;\text{m/s}$  (I have converted kJ to J to put everything in base units, just for ease of use), we get $h\approx 3367[\frac{\text m}{\text{kg}}]\cdot\frac{1}{m}$.
If I take your 6,400 pound block, and convert that to kg, I get 2903kg, so you would need to lift the block 1.16m to store 33kJ.  Since you are using English units, I'll convert that to about 3.8 ft.
Or do you?
You'll note that I quietly fixed your energy units.  When you say 33kW, that's a power measure.  If you're measuring energy, as in the first part of the phrase "energy per day", its joules.  I silently just put 33kJ into that equation, just to run the numbers.  However, given that your "33k" number is really close to "30kWh", which is the average consumption of a household per day, my guess is that you really intended to write 33kWh... that is "thirty three kilowatt hours."
No worries, we can run these numbers too!  30kWh can be turned into joules pretty easily.  1 kilowatt-second is 1 joule, so 1 kilowatt-hour must be 3600 kilojoules.  So you really wanted 108,000kJ (same as 108MJ, same as 180,000,000J).
Plugging that number in, we find:
$h\approx 11,020,408[\frac{\text m}{\text{kg}}]\cdot\frac{1}{m}$
And with your 2903kg block, that's $h\approx 3,796[\text m]$
For reference, that's about ten times the height of the Empire State Building.
We're going to need a bigger block.
There are systems which store energy by lifting heavy things.  They tend to lift heavier things than a mere 3 ton block.  The systems I have read about put a multiple-acre inflatable bladder under several meters of sand.  Filling the bladder with water lifts the sand, just like you lifted a block.  However, because it is distributed and stays on the ground, it is much easier to work with.
For another point of view, I found this video of lifting a Ford Raptor using a home lift.  This lift is connected to the house with a standard extension cable, so it is clearly pulling no where near the amperage of a whole house.  Yet it lifts the 6000 pound Raptor much faster than you are talking about lifting the block.
