The force is not only or exactly a function of the strength of interconnection of particles, so that
- can exert any force anywhere, in the fog
isn't that simple to answer. An example of weakly interconnected media which can exert different forces is the water. The pressure at depth, understandable, but we also use water to cut metals(not exactly directly, but even without abrasive in it water jets are strong enough to easily cut flesh and stuff)
So in terms of interaction, with a human body as they suggest some bridge between VR and reality - you may not necessarily need a strong interconnection of your actuators to achieve sufficient results as limits of what you need is the strength of another participant - the human body.
The strength also depends on the density of the stuff.
For 0.2 t/m3, they mantion 1000PSI which is about 6.9MPa.
Generally, It is a believable strength for such a structure, and about 50 times less than aluminum strength, as an example.
It is more than enough to simulate any environment a human may interact, and tensile strength for muscle tissue isn't that high, and well below the number(even I failed to sort out Google results to find the numbers, even I do remember seeing some, but it needs to dig through different pdf's. It is one of the subjects for different biomedical studies.)
So as a simulation the stuff is good enough, even if for sure we could suggest some improvements in that regard from a position of our time - like a direct supply of visual information to eye's, without the needs to have sparse fog density to mix for air and be transparent and stuff.
The highest imaginary tensile strength mentioned in the fog pdf is 6000PSI which is about 42MPa.
And if we imagine a non-simulating setting, considering the Lucy scenario, it is, most likely, not enough. Not that is it not enough, it may be not enough if the stuff applied in a direct fashion, hard to describe but nothing stops the thing to use some shards of materials, by gripping/wrapping around them and use them as a tool, and then if they can have 42MPa strength for action it may lead to very powerful scenarios, far from invisible force, but with respectable destructive strength.
A diamond shard(let's be exotic with examples), some cone with 1cm2 base and 3cm height, will be 1 cubic centimetre, thus 3.51g mass.
Applying 42MPa to the base(pushing), for a distance 1m of acceleration "track", will result in it having a velocity of 1540 m/s
Even a lesser 6.9MPa strength, may lead to 620 m/s
You really can play a walking gun machine with those guys.
Manila rope has about 69MPa strength and a lot of stuff can be done with that alone.
But all that isn't a Lucy scenario, you need something better for that
I present you a Smart Matter - strains of carbon nanotubes joint like muscles, not those piny grapples of micrometer stuff, but micrometer diameter threads with 100+GPa strength and arbitrry length(meters, 10's m and more). So it 2/3 nanostructures(two dimensions are nano, one is macro)
It can do whatever it is imagined fog can do, but better, and in a bit different way. Just like a side note, I do not have a better description of that stuff than the link, but it at least something.
So generally if you need to imagine some force, take a number like 40MPa at its dense state and then % the density of those things in the place multiplied by that number multiplied by the surface area of where it pushes.
7-40MPa is a reasonable strength for the potential fog material.
But exact numbers - we won't have them until we design the stuff, or build it.