A light spring of constant k = 90.0 N/m is attached vertically to a table. A balloon (with empty mass 2.50 g) is filled with a mixture of helium (density = 0.179 kg/m3 ) and air (density = 1.29 kg/m3 ) to a volume of 4.00 m3 and is then connected to the spring, causing the spring to stretch. If the spring stretches by 1.0 cm, find the required density of the gas mixture, and find how much helium and air you need to produce that mixture.

U-shaped tube, open to air on both ends, contains oil. Water is poured into the left arm until the water column is 10 cm deep. What is the height of the oil column (in cm) when the system is in equilibrium? The density of oil is 801 kg/m3

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)

At a given instant, the blood pressure in the heart is 1.4 x 10^4 Pa. If an artery in the brain is 0.49m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.