### 作业部分要求：

1. A 100lb weight is suspended by three cables as shown in the figure. The ratios of the
stiffness of the cables are: AP:BP:CP = 2k:k:3k, i.e. cable AP and CP are respectively 2x and
3x the stiffness of cable BP. Before the load is applied, all three cables are unloaded and
the geometry is as shown.

(20 pts) Assuming the cables are very stiff and the displacements are therefore small,
determine the forces in the three cables in terms of stiffness value k and the weight W(=
100).
(20 pts) Assuming the springs are not stiff, and therefore the displacements are not
necessarily small, develop a set of equations for the displacement of the mass and the
forces in the cables.

2. Metal castings can sometimes develop a gap between the
casting and mold as the molten metal hardens. The result
can be a substantially altered cooling process.
(20 pts) Set up a simple heat-transfer model that would let
you look at the effect of the gap on the cooling process.
Assume the casting and mold are square in shape, with an
air gap of thickness δ as shown in the figure. The mold sits
in some ambient room temperature. State clearly all
assumptions and develop a corresponding model of the
heat transfer problem.
(10 pts) Assuming that the casting is aluminum, the mold is diatomaceous earth and the
gap is filled with air, see if you can arrive at and summarize some insight into the effect of the gap and its size on the heat transfer process.