A light spring of constant k = 95.0 N/m is attached vertically to a table (figure (a)). A 2.70-g balloon is filled with helium (density = 0.179 kg/m3) to a volume of 4.00 m3 and is then connected to the spring, causing the spring to stretch as shown in figure (b). Determine the extension distance L when the balloon is in equilibrium. (The density of air is 1.29 kg/m3.)

Question

A light spring of constant k = 95.0 N/m is attached vertically to a table (figure (a)). A 2.70-g balloon is filled with helium (density = 0.179 kg/m3) to a volume of 4.00 m3 and is then connected to the spring, causing the spring to stretch as shown in figure (b). Determine the extension distance L when the balloon is in equilibrium. (The density of air is 1.29 kg/m3.)
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Damon · Accepted Answer

mass balloon = .0027 kg buoyancy net up force = g [ 4 (1.29-.179) -.0027 ] = g (4.44) = 43.6 N using g = 9.81 m/s^2 F = k x 43.6 = 95 x x = .459 N