What is the tension in the rope holding a helium-filled balloon at a party?

[awertag]

Homework Statement

Bozo the clown brings an empty birthday balloon with a mass of 0.0120 kg to your party. Bozo fills the balloon with helium of density 0.181 kg/m3. The filled balloon is a perfect sphere with a radius of 0.500 m. Bozo ties the balloon to a rope and holds is so that it is vertical. What is the tension in the rope?

Homework Equations

Ft= tension force
Fb=buoyant force
π=pi
4πr^3=volume of sphere

The Attempt at a Solution

i tried Fnet=0 = Fb-Ft-mg

Ft=Fb-mg=(densityfluid)(Vdisplaced)(g) - (m)(g)

[(4π(.5)^3)(9.8)] - [(.012)(9.8)] ==> Ft=2.6687 N which is obviously not correct, as I'm asking this question.

Any good help is greatly appreciated!

-aea

 

[Doc Al]

4πr^3=volume of sphere

Double check this formula.

The Attempt at a Solution

i tried Fnet=0 = Fb-Ft-mg

That's good.

Ft=Fb-mg=(densityfluid)(Vdisplaced)(g) - (m)(g)

[(4π(.5)^3)(9.8)] - [(.012)(9.8)] ==> Ft=2.6687 N which is obviously not correct, as I'm asking this question.

What's the density of the displaced fluid? What's the total mass of the balloon plus its contents?

 

[awertag]

well the density is given = .181 kg/m^3. But I see what you're saying: the total mass is .012 PLUS the mass of helium...so I would find that with density (.181) times volume (1.5708) so mass total equals .2963 kg?

 

[Doc Al]

well the density is given = .181 kg/m^3.

That's the density of the helium. But the buoyant force equals the weight of the displaced fluid. What's the density of the displaced fluid?

But I see what you're saying: the total mass is .012 PLUS the mass of helium...so I would find that with density (.181) times volume (1.5708) so mass total equals .2963 kg?

Right idea, but wrong volume.

 

[awertag]

oHH okay so the density of air which is 1.29 kg/m^3.
But why is the volume wrong?

 

[awertag]

oh gosh never mind, i see the volume is 4/3 pi r cubed haha :) thanks ill try it now

 

[awertag]

But now i get a final answer with a negative force, so that can't be right...

 

[awertag]

Ok I've finally gotten it! Thank you so much. Have a great day :)