physics question - static fluids

Question

You need to determine the average density of an irregularly shaped, non-uniform object. You have a spring scale. When you hang the object motionlessly from the scale, you measure a mass of 12.7 kg. When you entirely submerge the object in water (with the scale still outside of the water), the reading on the scale is 8.5 kg. What is the average density of the object? Use units of kg/m^3. (If you don't remember the density of water from the lecture then you will need to look it up.)

Answer 1

Mass of object - apparent mass of object = density of water x volume of object. I'm going to replace "volume of object" with V_o for simplicity from here on.

12.7 kg - 8.5 kg = 1000 kg/m³ x V_o [note this is the density of water in kg/m^3 and is the idealized value, if your teacher wants you to use a more precise value or different units check the lecture as it says]. Do the subtraction to get to the next step.

4.2 kg = 1000 kg/m³ x V_o divide both sides by 1000 kg/m³

4.2 kg / 1000 kg/m³ = V_o do the division

0.0042 m³ = V_o [kg divided by kg/m³ will result in the kg's cancelling and leave you with 1/1/m³ which rearranges to m³].

Now that we know the volume of the object we can solve for the density, because Density = mass/Volume.

Density = 12.7 kg / 0.0042 m³ = 3,023.8 kg/m³