Calculate Minimum Volume for Balloon Lift Off w/ Helium & Load

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To determine the minimum volume necessary for a helium balloon to lift off, the weight of the displaced air must equal the total weight of the balloon and its load. The balloon's mass is 80 kg, and it needs to lift an additional 240 kg, totaling 320 kg. The buoyant force is calculated using the density of air (1.29 kg/m^3) and the volume of the balloon. The volume of helium required can be derived from the equation that relates the mass of displaced air to the combined weight of the balloon and load. Clarification is needed on the relationship between the volume of air and the volume of the balloon, as they are equal when the balloon is filled with helium.
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Homework Statement


A balloon is to be filled with helium(density = 0.178kg/m^3) while the air outside has density of 1.29km/m^3. The mass of the empty balloon is 80.0kg and it is to lift a load of 240kg. What minimum volume is necessary for the lift off? Assume that the balloon material and the load occupy negligible volumes.


Homework Equations



density = M/V

The Attempt at a Solution



I'm not quite sure how to start with this question. Can someone help me please?
 
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The balloon will float when the weight of the displaced air is equal to the weight of the balloon with load.

Volume of the balloon = mass of the balloon/density of helium.
 
hmmm. not quite getting it.

This is archemides' principle right? so wouldn't the equation be:

density of balloon/ density of gas = volume of gas/ volume balloon??
 
Mass of the displaced air = Ma = (240 + 80 + VHe* ρHe) kg.

volume of the air = Ma/ρa = ... = Volume of the balloon.

So Vb*ρa = (240 + 80 + VHe* ρHe) kg

Ηere volume of the balloon is equal to the volume of He.
 
k...just want to clarify. The balloon will float when the mass of the displaced air is equal to the weight of the balloon plus the load.

therefore,
Ma = (240 + 80)kg including helium??

how come is volume of air = volume of balloon?

sorry...a bit confused. I'm not great with this kind of physics.
 
mizzy said:
k...just want to clarify. The balloon will float when the mass of the displaced air is equal to the weight of the balloon plus the load.

therefore,
Ma = (240 + 80)kg including helium??

how come is volume of air = volume of balloon?

sorry...a bit confused. I'm not great with this kind of physics.

(240 + 80)Kg is mass without helium. Mass of the displaced air is equal to the (mass of helium + 240 + 80) kg. Balloon will float only when it is filled with the helium. Since the balloon material and the load occupy negligible volumes, volume of the helium = volume of the air.
 

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