Calculating Buoyant Force on a Helium-Filled Balloon

[amjber2]

buoyant forces

I was having trouble with this problem. please let me know how to approach this. thanks.

An empty rubber balloon has a mass of 0.0135 kg. The balloon is filled with helium at a density of 0.181 kg/m3. At this density the balloon is spherical with a radius of 0.400 m. If the filled balloon is fastened to a vertical line, what is the tension in the line?

 

[gunblaze]

You should show some of ur workings b4 we can help. Alright, just a little clue to get u started. Upthrust- weight= tension of string.

 

[kyle8921]

To approach this problem, we can use the formula for buoyant force, which is Fb = ρVg, where ρ is the density of the fluid (in this case, helium), V is the volume of the object (in this case, the balloon), and g is the acceleration due to gravity. We can also use the formula for the volume of a sphere, which is V = (4/3)πr^3, where r is the radius of the sphere.

First, we can calculate the volume of the balloon by plugging in the given radius into the volume formula:

V = (4/3)π(0.400 m)^3 = 0.268 m^3

Next, we can calculate the buoyant force by plugging in the density of helium (0.181 kg/m^3), the volume of the balloon (0.268 m^3), and the acceleration due to gravity (9.8 m/s^2):

Fb = (0.181 kg/m^3)(0.268 m^3)(9.8 m/s^2) = 0.470 N

Since we know that the buoyant force is equal to the weight of the displaced fluid, we can also say that the tension in the line is equal to the weight of the filled balloon minus the buoyant force:

T = (0.0135 kg)(9.8 m/s^2) - 0.470 N = 0.109 N

Therefore, the tension in the line is 0.109 N. This means that the line is pulling upwards on the balloon with a force of 0.109 N to counteract the buoyant force.