Hot air balloon buoyancy homework

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To determine the density of the hot air in a hot air balloon with a mass of 291 kg and a volume of 809 m³, the buoyant force must be equated to the total weight of the balloon and its cargo. The buoyant force is calculated using the density of outside air (1.29 kg/m³) and the volume of the balloon, resulting in a force of 1.29 kg/m³ multiplied by 9.8 m/s² and 809 m³. The weight of the hot air inside the balloon is expressed as the product of its density and the same gravitational force and volume. After calculations, the density of the hot air is found to be 0.93 kg/m³. This demonstrates the relationship between buoyancy and the densities involved in maintaining the balloon's altitude.
mikep
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A hot air balloon plus cargo has a mass of 291 kg and a volume of 809 m3. The balloon is floating at a constant height of 6.25 m above the ground. The density of the outside air may be assumed to be 1.29 kg/m3. What is the density of the hot air in the balloon?
can someone help me with this problem? i know that i need to use the buoyant force but I'm not sure how to relate the height with the density
 
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I think the height is mentioned only to indicate the balloon is not tethered to the ground and the fact that the height is a constant means the balloon is not accelerating.
 
oh ok. so how would you find the density? i tried 291/809 = 0.36kg/m^3 but that wasn't correct
 
Equate the buoyant force to the weight of the balloon, cargo and the air (whose density you do not know) contained in that volume. The buoyant force is the weight of the displaced air and whose density you do know.
 
so Fb = 1atm + (d)(9.8N/kg)(809m^3) = (1.29kg/m^3)(9.8N/kg)(809m^3) is that right?
 
The buoyant force is

F_b = 1.29 kg/m^3 \times 9.8 m/s^2 \times 809 m^3

and the weight of the hot air is

W_{hot} = \rho_{hot} \times 9.8 m/s^2 \times 809 m^3
 
so the F_b = W_{hot} + W_{balloon} ?

W_{balloon} = (291kg)(9.8N/kg)

\rho_{hot} = 0.93kg/m^3
 
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Way to go, Mike!
 
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