Answer to Question #84271 in Physics for Daniyan Faruq

Question

A spiral spring loaded with a piece of metal, extends by 10.5cm in air. When the metal is fully submerged in water, the spring extends by 6.8cm. Calculate the relative density of the metal (Assume Hooke's law is obeyed)

Answer 1

The balance of forces condition in air

mg=kx_1

So

gρV=kx_1 (1)

The balance of forces condition in water

mg=kx_2+F_buoyant

So

gρV=kx_2+gρ_w V (2)

Eq. (1) and (2) give

gρV=gρV x_2/x_1 +gρ_w V

Thus

ρ(1-x_2/x_1 )=ρ_w

Finally, the relative density of the metal

ρ/ρ_w =1/(1-x_2/x_1 )=1/(1-6.8/10.5)=2.84