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Homework Statement
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
Homework Equations
Buoyant Force (Fb) = p (density) * V * g
Density = mass/volume
Fb = Wo = p (density of object) * V (Volume of object) * g
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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