A scale reads 136 N when a piece of copper is hanging from it. What does it read (in N) when it is lowered so that the copper is submerged in water?

Question

A scale reads 136 N when a piece of copper is hanging from it. What does it read (in N) when it is lowered so that the copper is submerged in water?

Answer 1

F_w = ρ_CuVg which is mg and V is the volume of the solid. F_W is the weight

The apparent weight, F_W' = F_W - F_B = ρ_CuVg - ρ_wVg (the buoyant force = weight of water displaced by the volume of the solid.

Combining the two equations and eliminating V:

F_W^' = (ρ_Cu-ρ_w)g(F_W/ρ_Cug) = (1- ρ_w/ρ_Cu)F_W

The only things needed are the densities of water and Cu in the same units - the actual units don't matter for the final form of the equation.

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