Force acceleration solution . . .Shipping boxes . . .
Dear Search Engineer: Okay, this is an embarrassing situation, but I need a solution. If I have a particle of mass m falling through height h at the acceleration of gravity (g=9.81 m/s2), what would be the reaction force (as if a bathroom scale were the object the particle would impact) after the particle hit? Assume that the bathroom scale is a solid immovable object. I understand the kinetic energy of the particle, but I can't resolve that in to a resultant force.—F.S., WI
Dear F.S.: Dude, only unasked questions are embarrassing… Here's the deal: The potential energy PE of the object at a given height above the scale is PE=mgh. This is converted into kinetic energy (KE=½mv2) when the object hits the scale at velocity v because of the conservation of energy, KE=PE.
The work done in stopping the object's fall is equal to an average force Favg times the distance the scale deflects d (there is no totally immovable object). This work is equal to the kinetic energy: Favg d=½mv2=mgh
You have to assume d. Another reasonable assumption is the force buildup is somewhat sinusoidal, for a peak force, say, around twice the average force.
Dear Search Engineer: We manufacture sealed boxes for installation on ships. The environment is severe, with temperatures ranging from -30C to +60C, including sun loading. The pressure delta between inside and outside the box causes our seals to be breached. We need a way to equalize the pressure (both directions) without allowing ingress of the outside environment. We tried a gas permeable membrane, but it quickly became clogged with salt accretion from the salt spray. Can you help?—M.S., CA
Dear M.S.: Is there space available, or can total box volume be increased, sufficiently to add a bellows? Imagine a bellows that takes up part of the interior of the box, with one end of it being the floor of the box. Let a small hole through that floor communicate between the outside world and interior of the bellows. As the functional volume of the box pressurizes, the bellows will be forced to contract, with no major rise in pressure at least until the bellows reaches its limit of compression.
The opposite takes place when the pressure is reduced due to cooling or other conditions. The total pressure excursion is reduced, thus cutting differential across the seals. If the bellows can be made with its neutral position at +15C, roughly halfway between full contraction and full expansion, it will do the most good even if it cannot be large enough to eliminate the pressure change entirely. Putting the hole in the "floor" provides some natural protection from rain, snow, dust, etc., and may even provide some self-cleaning.
Material choice might start with electroformed nickel or similar. A more esoteric version would use an evacuated and fully sealed bellows (not communicating with the outside), possibly with a spring arrangement to set "neutral" as desired. Vacuum should be adequately compressible or expandable. This means it can never fully compensate, however, since it uses the increased or reduced pressure to expand or compress the bellows.