Question

Ipe ( pronounced ee-pay ) is a Brazilian hardwood that can be used as a durable (and expensive!) construction material for decks, docks and other outdoor projects.Every cubic foot of ipe weighs 69 pounds. Use dimensional analysis to convert the density of ipe to g/cm^3. How does the density compare to other woods and material on the list above?

Answer 1

The density of an object is by definition the mass over the volume of that object. Therefore the density of Ipe is

`\rho =m/V=69 (lb/ft^3)`
The dimensional analysis goes as

`\ \textless \ \rho\ \textgreater \ =\ \textless \ lb/ft^3\ \textgreater \ =\ \textless \ 0.4535 kg/(0.3048 m)^3\ \textgreater \ =`

`=\ \textless \ 0.4565 kg/0.0283 m^3\ \textgreater \ =16.13 \ \textless \ kg/m^3\ \textgreater \`
Therefore

`\rho =m/V =69 (lb/ft^3)=69*16.13 (kg/m^3)=1113 (kg/m^3)`