2. A sand core used to form the internal surfaces of a brass casting experiences a buoyancy force of 14 kg. The volume of the mold cavity forming the outside surface of the casting = 4500 cm3. What is the weight of the final casting? Ignore considerations of shrinkage. (Sand density = 1.6 g/cm3, brass casting density = 8.62 g/cm3).

weight of final casting is 1134.4 kg

Explanation:

The formula for buoyancy force is;

B=ρ*v*g where

B=Buoyancy force in Newtons=140N

ρ=density of sand = 1.6g/cm³=1600kg/m³

v=volume of sand displaced

g=acceleration due to gravity = 9.8 m/s²

Applying the formula,

140=1600*v*9.806

140=15689.6v

140/15689.6 = v

0.008923 m³=v

This the volume of the displaced body

The volume of the mold cavity forming the outside surface of the casting = 4500 cm³ = 0.0045 m³

Total volume will be : 0.008923 + 0.0045 = 0.01342 m³

Formula for mass of brass = density of brass * total volume

Mass of brass=8620 * 0.01342 = 115.7

Weight of brass = mass of brass*acceleration due to gravity

w=mg

w=115.7*9.806 = 1134.4 kg