The mass of the canister filled with gasoline is 21.5 kg. The weight of the canister filled with water is 29 kg. What is the weight of an empty canister?
Data: m1 (mass of a can with gasoline) = 21.5 kg; m2 (mass of the water canister) = 29 kg.
Constants: ρ1 (gasoline density) = 710 kg / m3; ρ2 (water density) = 1000 kg / m3.
1) Mass of a can of gasoline: m + V * ρ1 = m1 and V = (m1 – m) / ρ1.
2) The mass of the canister with water: m + V * ρ2 = m2 and V = (m2 – m) / ρ2.
3) Mass of an empty canister: (m1 – m) / ρ1 = (m2 – m) / ρ2.
(m1 – m) * ρ2 = (m2 – m) * ρ1.
(21.5 – m) * 1000 = (29 – m) * 710.
21.5 – m = 20.59 – 0.71m.
0.29m = 0.91.
m = 0.91 / 0.29 ≈ 3.14 kg.
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