How do I determine the amount of lift needed to launch an object? So as part of a video I'm working on, I'm trying to launch a 10kg table about 8m into the air.  A machinist friend of mine has provided a solution that involves pneumatic cylinders and a pump to generate the force needed to propel the table.  
What we're trying to calculate is the amount of PSI needed to lift the table. All these calculations don't need to be exact (if it only goes 16m up, then there's no issue)
I don't know where to even start to figure it out. Once gravity gets involved, it throws me off.
Any real help would be appreciated, thanks!
 A: I'm going to assume that you have a pneumatic ram of some kind, and that it features an area $A$ and a stroke length of $l$ which is very short compared to the other distances in this problem. I further assume that you can connect this device to a high pressure reservoir with a volume much larger than $Al$ (making the force on the ram effectively constant over the stroke) at pressure $P$.
Other assumptions:


*

*The object to be lifted has mass $m$

*The target height is $h$

*The ram has very little friction.


Measuring from the starting height our projectile will have potential energy $E_p = mgh$ when it reaches the desired elevation, and if it is at the top of its arc it will have no kinetic energy there. (Here $g$ is the acceleration of gravity $g \approx 9.8 \text{ m/s}^2 \approx 32.2 \text{ ft/s}^2$.
By conservation of energy that means it should have kinetic energy of $mgh$ as it leaves the ram.
The ram provides a constant force $PA$ over a length $l$; by the work energy theorem the kinetic energy of the projectile at launch is $ E_k = PAl = mgh $. With $A$ and $l$ fixed by the geometry of the ram, that leaves us with
$$ P = \frac{mgh}{Al} .$$

If you are working with an experienced machinist I probably don't have to tell you how potentially dangerous this is, but I'm going to anyway.
For any reasonable mass, you are talking about energies that are more than sufficient to main or kill you. Take care, wear your safety goggle, and get behind appropriate cover before running this thing.
Likewise, any high pressure system poses a potential risk to life and limb. You should learn to handle these systems from an expert before cobbling something together on your own.
