Final answer:
To determine the volume of the balloon needed to lift the load, we can use the principle of buoyancy. The volume can be calculated using the equation buoyant force = weight of displaced air = density of air × volume × g. Substituting the given values, the volume comes out to be approximately 2.20 m³.
Step-by-step explanation:
We can use the principle of buoyancy to determine the volume of the balloon needed to lift the load. The buoyant force exerted on the balloon is equal to the weight of the displaced air. We can calculate the buoyant force using the equation:
Buoyant force = weight of displaced air = density of air × volume × g
where the density of air is 1.29 kg/m³ and g is the acceleration due to gravity (9.8 m/s²).
Given that the weight of the load is 30 kg, we can equate the buoyant force to the weight of the load:
Weight of load = buoyant force = density of air × volume × g
Rearranging the equation to solve for volume:
Volume = weight of load / (density of air × g)
Substituting the given values, we get:
Volume = 30 kg / (1.29 kg/m³ × 9.8 m/s²)
Volume = 30 / (1.29 × 9.8) m³
Volume ≈ 2.20 m³