Question

A 50 mm square hole is to be produced in a casting of length 30 mm. The density of core used is 4.5 g/cc and density of molten metal used during casting process is 8 g/cc. If the surface area of the core print used is 0.05$m^2$, the cross sectional area of the chaplet used is

• A. $746m{m}^2$
• B. zero
• C. $240m{m}^2$
• D. $507m{m}^2$

Answer 1

The correct option is C $240m{m}^2$

${\rho }_c=4.5g/cc,{\rho }_L=8g/cc{A}_{cp}=0.05m^2,A_{chaplet=?}{V}_c=50\times 50\times 300\times {10}^{-9}=7.5\times {10}^{-4}{m}^3\text{Unsupported load}=V_c\times g\times ({\rho }_m-{\rho }_c)-350A_{cp}=7.5\times {10}^{-4}\times 9.81\times (8-4.5)\times \frac{{10}^{-3}}{{10}^{-6}}-350\times 0.05=8.25N$

Now, for every 1 Newton of unsupported load, 29 mm${}^2$ cross section area chaplet must be used,

$\therefore A_{chaplet}=8.25\times 29\approx 240m{m}^2$