  A folded chain, with one end fixed at the ceiling and the other end released
from the same elevation, is commonly modeled as an energy-conserving system in
one-dimension. However, the analytical paradigms in previous literature is
unsatisfying: The theoretical prediction of the tension at the fixed end
becomes infinitely large when the free end reaches the bottom, contradicting to
the experimental observations. Furthermore, the dependence of the total falling
time on the link number demonstrated in numerical simulations is still
unexplained. Here, considering the horizontal kinetic energy and the geometry
of each link, we derived analytical solutions of the maximal tension as well as
the total falling time, in agreement with simulation results and experimental
data reported in previous studies. This theoretical perspective shows a simple
representation of the complicated two-dimensional falling chain system and, in
particular, specifies the signature of the chain properties.
