1. What change in pressure occurs in a parry balloon that is squeezed to one-third its volume with no change in temperature?
2. Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)
3. A mountain-climber friend with a mass of 80 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that show the volume of the balloon to be about 17 m3 (slightly more than 3 m in diameter for a spherical balloon).
4. On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor down-ward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N.
a. Show that the weight of the displaced air is 20,000 N.
b. Show that the volume of the displaced air is 1700 m3.
5. Consider an airplane with a total wing surface of 1002 m. At a certain speed the difference in air pressure below and above the wings is 4% of atmospheric pressure. Show that the lift on the airplane is 400,000 N.
6. The weight of the atmosphere above 1 m2 of Earth's surface is about 100,000 N. Density, of course, becomes less with altitude. But suppose the density of air were a constant 1.2 kg/m3. Calculate where the top of the atmosphere would be.