Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 2.8000 kg when weighed in air. The density of air is 1.29 kg/m3, and the density of aluminum is 2.7×103kg/m3.

Question

Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 2.8000 kgkg when weighed in air. The density of air is 1.29 kg/m3kg/m3, and the density of aluminum is 2.7×103kg/m32.7×103kg/m3.

Express your answer to five significant figures and include the appropriate units.

Answer 1

The displaced volume of air V_air= V_AL= (M_al,true/ρ_Al), you can calculate Buoyancy force=V =

Then, as in the air on the aluminum piece exerted Buoyancy force its weight in air is gM_{al, true} – F _buoyancy=g2.8kg;

 gM_{Al, true} – gM_{Al, true}(ρ_air/ρ_Al) =g2.8kg; solving for M_{Al, true}=2.8 kg/( 1- ρ_air/ρ_Al)= 2.7986 kg