it’s a lovely day and you decide to launch a giant helium balloon. Once filled, your balloon is a perfect sphere with a radius of 6.90 m. You consider having the balloon lift a crate of water balloons. What is the maximum weight the filled helium balloon can just lift (solve for the equilibrium condition where upward force equals downward force)? Assume that the membrane of the helium balloon has a mass of 920 kg (this does not include the mass of the helium within nor the mass of the crate). Neglect the buoyant force on the crate of water balloons. Density of He is 0.179 kg/m3. Density of air is 1.29 kg/m3. Volume of a sphere is 4/3 π r3. Weight is in N (not kg)

A lost shipping container is found resting on the ocean floor and completely submerged. The container is 5.9 m long, 2.8 m wide, and 2.3 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloon's radius is 1.7 m, the shipping container just begins to rise towards the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3.

Bowling balls are roughly the same size but come in a variety of weights. Given that the official radius a bowling ball should have is roughly 0.110 m, calculate the weight of the heaviest bowling ball that will float in a fluid of density 1.000 x 10° kg/m³. weight: N

OSU has been given a large model of the solar system which consists of hollow Styrofoam spheres of different sizes representing the Sun and planets. The planets are all connected to the center of the sun by means of steel rods of varying lengths and at varying angles relative to the x-axis as shown above. The steel rods are all 0.5 cm in diameter and are made of steel having a density of 7.88 g/cm3. We’d like to suspend the model from it’s center of mass, but it doesn’t look like the center of mass coincides with the position of the Sun. Find the center of mass of the model (direction and angle) relative to the Sun in the center of the model. The Styrofoam spheres are so much lighter in comparison to the rods, that their mass can be neglected. Hint: calculate the center of mass for the x and y dimensions separately, then combine them to get the final answer