Question

Liquid 1: Water (density: 1g/cm³)

Water displaced = 156 mL

mass of object was found to be 156 g

Liquid 2: Saltwater (density: 1.02 g/cm³)

water displaced: 158.4 mL

Mass of object was found to be 161.568 g

Use what you know about Archimedes’ Principle: specifically the equations  and , where the wsubscript refers to the liquid the object floats on and the o subscript refers to the object itself. Derive a formula that relates the densities of the object and the fluid it floats on, as well as the depth that the object submerges in water relative to its height. That is, find how the ratios of the object’s and water’s densities are relate to how much of the object is submerged in the water. Since the object floats, we will know that the whole object cannot be submerged underwater. Write out the formula below and find the density of the object.

Answer 1

According to Archimedes principle, when a body is fully or partially immersed in a fluid, weight of fluid displaced=upthrust=apparent loss=buoyant force

When the body floats, weight of body=weight of fluid displaced (upthrust)

Vg=g.........(1)

V=total volume of body

=its density

g=9.8m/s2

=volume of body submerged

=density of fluid

If A is end area and H is total height of body

its volume V=AH

Let h=height of body submerged in fluid, voume submerged  =Ah

Equation (1) becomes,

Vg=g

AH=Ah

H=h

/=h/H

Denisty of object () =h/H