Minimum volume of helium balloon to lift 240 kg load

[mizzy]

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?

 

[rl.bhat]

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.

 

[mizzy]

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??

 

[rl.bhat]

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.

 

[mizzy]

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.

 

[rl.bhat]

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.