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... Let me take this opportunity to chime in with another
word that could be used to "name that force" ...
hydrostatic pressure (in addition to the previously-
mentioned viscosity). If we make the steady-state
approximation, and a few other approximations, there
will be a pool of water on the bottom of the boxcar,
and the surface of the water will have a slope. The
steady addition of new water will, via viscosity etc.,
maintain this slope. The hydrostatic pressure will
push on all the walls, but because of the slope
there will will be greater force on the back wall,
resulting in deceleration.