A light spring of constant k = 85.0 N/m is attached vertically to a table. A 1.9

Question

A light spring of constant k = 85.0 N/m is attached vertically to a table. A 1.95-g balloon is filled with helium (density = 0.179 kg/m3) to a volume of 4.96 m3 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. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.

Explanation / Answer

Force is given by F= Kx

At equilibilium upward buoyant force = spring force

For Helium

Volume = 4.96m3

density=0.179 kg/m3

Mass = 0.179 * 4.96 = 0.8878 kg

Total mass of the baloon and helium = 0.8878 + 0.00195 kg

=0.88975 kg

So at equilibrium we have

K * L = M* g

85 *L = 0.88975 * 9.8

L=0.1025m (Ans)

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