A light spring of constant k = 96.0 N/m is attached vertically to a table. A 1.9

Question

A light spring of constant k = 96.0 N/m is attached vertically to a table. A 1.96-g balloon is filled with helium (density = 0.179 kg/m^3) to a volume of 5.04 m^3 and is then connected with a light cord to the spring, causing the spring to stretch as shown in the figure below. Determine the extension distance L when the balloon is in equilibrium. I solved the problem and got my answer to be L= 0.571409 Typing this into webassign, it tells me my answer is within 10% of the correct value but wont accept the answer, where did I go wrong with my calculations?

Explanation / Answer

Take Density of air = 1.2 kg/m3

Weight of balloon W = _He*V*g = 0.179*5.04*9.81 = 8.85 N

Buoyant force on balloon B = _air*V*g = 1.2*5.04*9.81 = 59.33 N

Net force on balloon F = B - W = 59.33 - 8.85 = 50.5 N

F = kx

50.5 = 96*x

x = 0.5258 m

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