Does weight scale as the cube of size?

[peteski]

As a matter of fact, yes.   Everything has to scale down by a factor of 1/160 in order for any of this to make any sense.
In an N Scale world, everything is 1/160 of life size, including atomic particles.  The world itself, and every particle of it,
is 1/160th of life size.

Wow... this whole thing suddenly took a veer off into very existential territory.

If that was possible, we could have N scale models made with the same materials as the 1:1 scale counterparts and with scale wall thickens. We could also have real 1:160 diesel engines, alternators and traction motors powering our N scale locos!  Or utilize scale steam in our N scale steam locos. 

[nkalanaga]

Ron:  Yes, mass and volume both scale as the cube of the linear ratio.  If the density remains the same, the mass and volume have to remain proportional.  Of course, as we've established, N scale cars don't have the same density as real ones, due to different thicknesses of different materials, but your math is right.

As for scaling the atoms, a 1:160 reduction won't significantly affect the electron shells.  From www,chegg.com, as reported by Google, "The diameter of a copper atom is approximately 2.28e-10 m", so an American copper penny is about 3,000,000 atoms thick.  Reduced 1:160 that is still about 20,000 atoms, which is well into the range of "bulk materials" for physics purposes.

[railnerd]

http://xkcd.com/878/

[Scottl]

FTW

[cv_acr]

The subject line pretty much says it.  Since weight is a function of volume, if an N Scale box car
weighs 24g, would that logically mean we should consider it to be  24 x 160 x 160 x 160 grams, which
works out to about a  "scale" 217,000 lbs?

Oh man, I am so happy with this thread. I've lost track of how many times I've seen the "scale weight" conversation on other forums, and it always starts with some shmuck coming to the determination that the "scale" weight of their boxcar is on the order of 20,000 lbs because that's what the prototype weight divided by the scale factor is. Really hard to get some people to understand the whole cube thing for some reason.

[cv_acr]

In this country we have a bad habit of conflating weight with mass.  Mass is independent of location in space, but weight is dependent upon the local gravitational acceleration.  Weight is therefore m*g.  Now, students of Newton will immediately recognizes this as a form of m*a, where a = g (acceleration in this case due to the Earth's gravity).  Hence, weight, by Newton's second law, is really a force.

True, but in any context that we're likely to be having this discussion (at least until we colonize Mars and still building model railroads there) the local gravitational acceleration is a fixed constant (which you have essentially noted yourself by noting the "g" term (9.8m/s²).

Of course we have force-plate type scales that read off units in either pounds (imperial weight/force units) or kilograms (metric mass units), and balance (mass) scales that read off pounds (force unit), so is it any wonder that no one without a science background really understands what weight actually is when weight/mass are used so interchangeably?

But I digress.  Scaling weight the same way as we scale length is only possible if the density of the material remains constant.  I think you'll agree that an N scale car probably has considerably different density than a real, steel one.  Even when the car is empty, you can calculate an average density for both, and I think you'll find them quite different.

If you (theoretically) use the same materials and reduce all dimensions (including thickness) by the scale factor, then the material densities are unchanged so the scale mass does work out.

Of course we don't use the same materials for a number of obvious reasons, but you can at least figure out the target mass if you wanted to scale it.

It's the physics that don't really scale; our hands can exert far greater proportional forces that the scaled down materials can withstand, the force accelerations don't reduce to "scale" proportions, bumps and irregularities are proportionally far rougher than full scale and track and wheel operating tolerances proportionally much cruder. IMO reliable smooth operation trumps exact scale weight/mass.

[nkalanaga]

Chris:  Your last paragraph is the key.  For a truly scale layout to work, the track would also have to be to scale, including all of the bumps and dips.  Most model track, no matter how good it looks, would fail FRA inspection.

[rschaffter]

Velocity is inversely proportional to the scale factor
Volume, and thus mass, is inversely proportional to the scale factor cubed.
Momentum is inversely proportional to the scale factor to the 4th power (mv)
Kinetic Energy (and thus Power)  is inversely proportional to the scale factor to the 5th power ((m v^2)/2)

However, rolling friction is inversely proportional to the scale factor squared (mgb/r), which, combined with the proportionally lower momentum,  is why our cars don't roll as well as the prototype, and we thus can't easily do hump yards and flying switches...