A balloon and a springfind extension

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To determine the extension distance L of a helium-filled balloon connected to a spring, the weight of the balloon must be calculated correctly. The initial approach mistakenly considered the balloon's weight as the force acting on the spring. Instead, the upward force on the spring should be the difference between the balloon's weight and the buoyant force from the displaced air. The correct equilibrium condition requires accounting for both forces to find the extension of the spring accurately. Understanding these forces is crucial for solving the problem correctly.
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Homework Statement



A light spring of constant k = 85.0 N/m rests vertically on a table (as shown in part a) of the figure below). A 2.25 g balloon is filled with helium (density = 0.180 kg/m3) to a volume of 5.95 m3 and is then connected to the spring, causing it to stretch as shown in part b). Determine the extension distance L when the balloon is in equilibrium.

Homework Equations



F= k\Deltax
F=\rhoA

The Attempt at a Solution



so i tried to find the weight of the balloon by multiplying Volume of the balloon to the density to the density and then adding it to the mass of the balloon and multiplying it to 9.8m/s2. this answer of 10.51785 i divided by k (85N/m) and got an answer of 0.124 m..this was wrong ..can someone tell me what is wrong with this thinking
 

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What's wrong with this thinking is that the weight of the balloon is NOT the force that is pulling UP on the spring to stretch it. You need to figure out with what force your balloon is being pushed upward.
 
would it be the difference of the weight of the balloon and the air that it displaces to stretch the spring upward??
 

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