Calculating Buoyant Force on a Helium-Filled Balloon

AI Thread Summary
To calculate the tension in the line holding a helium-filled balloon, first determine the buoyant force acting on the balloon using the formula for buoyancy, which is the weight of the displaced air. The volume of the balloon can be calculated using the formula for the volume of a sphere, and then multiply this volume by the density of air (approximately 1.225 kg/m³) to find the buoyant force. Next, calculate the weight of the helium-filled balloon by adding the mass of the empty balloon to the mass of the helium it contains. Finally, apply the equation: buoyant force minus the weight of the balloon equals the tension in the string. This approach will yield the tension in the line supporting the balloon.
amjber2
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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?
 
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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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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