1. A light spring of force constant k = 162 N/m rests vertically on the bottom of a large beaker of water (Figure a). A 5.32-kg block of wood (density = 650 kg/m3) is connected to the spring, and the block-spring system is allowed to come to static equilibrium (Figure b). What is the elongation ΔL of the spring in cm?
2. A helium-filled balloon, whose envelope has a mass of 0.29 kg, is tied to a 3.9-m long, 0.051-kg string. The balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium, as in the figure below. Determine the value of h. Hint: Only that part of the string above the floor contributes to the load being supported by the balloon. (The density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3.)