(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 1.10 g balloon is filled with helium gas until it becomes a 20.0 cm-diameter sphere.

What maximum mass can be tied to the balloon (with a massless string) without the balloon sinking to the floor?

Density of Air: 1.28 kg/m^3

Density of Helium gas : 0.18 kg/m^3

Volume of a sphere: V = 4/3*pi*r^3

g = 9.80 m/s^2

2. Relevant equations

Buoyant Force (Fb) = p (density) * V * g

Density = mass/volume

Fb = Wo = p (density of object) * V (Volume of object) * g

3. The attempt at a solution

Fb = Weight of the object + Mg (M is the mass to be solved)

(1.23)(4/3*pi*(0.1m)^3)(9.8) = (0.18)(4/3*pi*(0.1m)^3)(9.8) + M(9.8)

M = 4.40 * 10^-3kg

I am uncertain of whether the buoyant force is the force of air pushing upwards on the balloon, or whether it is the helium gas in the balloon. Nonetheless, I used air as the density to solve for the buoyant force.

Another possibility would be that:

T = Fb - mg

T = (1.23)(4/3*pi*(0.1m)^3)(9.8) - (0.0011kg)(9.8)

T = 0.0397 N

Therefore mass of the object = 0.0397N / 9.8 = 4.05 * 10^-3

I am doubtful of which solution is correct and if either solution is actually correct.

Thank you in advance.

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# Homework Help: Helium Baloon question

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