How Much Helium Is Needed to Lift a 340kg Balloon?

[pat666]

Homework Statement

How much helium (density 0.18) is requires to lift a 340kg balloon. density of air is 1.28

Homework Equations

The Attempt at a Solution

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i don't know why i keep getting the wrong answer
buoyant force required is 340g which = rho g V
and i keep getting 1888.89m^3 which i can see is way to big, what i can't see is what is wrong with my procedure?

 

[Maybe_Memorie]

In the question you have 340 kg, but in the answer you have 340 g. Which is it?

 

[pat666]

g is gravity(force) sorry the balloon is 340Kg

 

[Maybe_Memorie]

What is the correct answer supposed to be?

I'm getting an answer of $$V = 232.8767 m^3$$, but there is a high chance I'm wrong.

 

[rl.bhat]

If V is the volume of the balloon, then the weight of the balloon with helium will be

W = (340 + V/0.18)g

Weight of the displaced air = (V/0.18)*1.28*g

So 340 + V/0.18 = (V/0.18)(1.28)

Now solve for V.

 

[pat666]

thanks rl.bhat, maybe memorie the correct answer is 309m^3 if you were interested

 

[pat666]

rl.bhat when i solve that equation you gave me i get 218.6m^3 which is still significantly different to what my textbook say..////??

 

[Doc Al]

The buoyant force equals the weight of the displaced air. Set that equal to the weight of the empty balloon plus the helium. Then you can solve for V.

 

[pat666]

so F_b=w_air+w_helium
340g=1.28*9.81x+0.18*9.81x
that comes out to 232.877m^3 which is what someone previously said. maybe the answer in the textbook is wrong??

 

[Doc Al]

so F_b=w_air+w_helium

No, set the buoyant force equal to the weight of balloon + helium.

340g=1.28*9.81x+0.18*9.81x
that comes out to 232.877m^3 which is what someone previously said. maybe the answer in the textbook is wrong??

No, the textbook is fine. For some reason you are setting the buoyant force equal to 340g. That's incorrect. (340g is the weight of the empty balloon.) Write an expression for the buoyant force in terms of the volume (what you call x).

 

[pat666]

ok i still don't get this at all. w_air + w_helium = rho*g*v? if that's right what is the fluid on the right side of the equation?

 

[Doc Al]

w_air + w_helium = rho*g*v? if that's right what is the fluid on the right side of the equation?

Why are you adding the weights of air and helium?

rho_air*g*V is the buoyant force (the weight of displaced air).

Set that equal to the weight of the balloon (which is given) plus the helium (express that in terms of V).

 

[pat666]

THANKS Doc Al i finally have the correct answer although i don't understand why it works. I thought that the buoyant force the helium had to provide would be equal to the force due to gravity so that it could float up?

 

[Doc Al]

I thought that the buoyant force the helium had to provide would be equal to the force due to gravity so that it could float up?

It does! But the buoyant force must lift both the helium and the empty balloon.

 

[pat666]

ok i sort of get that, THANKS AGAIN ill consult my textbook and see if i can't make some more sense of it.. thanks