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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bobpursley · Answer

bouyant force=weight of air displaced-weight of balloon. = denAir*4m^3-densityH3*4m^3 -.027(9.8) = 4(1.29kg-.179kg) - .027g=4*1.11 N-.027*9.8N stretch=force/k=bouyantforceabove/95N/m