1. Helium, H 2 and hot-air balloons and submarines have mass. Why don’t they fall down ? What is the force that makes them go up ? The Physics of Balloons and Submarines

2. What is air ? It is a gas (80% N 2 ). consists of lots of molecules/atoms bouncing around in free-fall. Can we catch air ? (Use a balloon!) How can we measure it ? Air has pressure! atoms banging on the walls of container exerts forces on walls Average Force is proportional to the area Define Pressure = Force/Unit area Question: Compare the air pressure inside and outside the balloon. Are they different? A unit Area F

3. Air has density! A volume of air particles has an average mass Density = average mass/unit volume (1.25 kg/m 3 ) Air pressure is proportional to density: denser air: more particles hit surface denser air more pressure

4. The Ideal Gas Law Equation We learned that Pressure of an Ideal Gas is proportional to Particle Density. P  , for fixed temperature T Temperature is a measure of the average kinetic energy of atoms, and is related to the pressure. In fact, Pressure is proportional to Temperature. P  T, for fixed particle density  These relations lead to the ‘ideal gas law equation’ (holds only for non-interacting particles): P = k    T Boltzmann’s constant 1.38 x 10 -23 Pa-m 3 /particle-K Particle density Absolute Temperature (  Kelvin)  C + 273 =  K(Kelvin scale) e.g. 0  C = 273  K

5. Profile of a Helium Balloon in Air or an Air Bubble in Water Unbalanced Pressures exert an overall upward force, forces balloon to move towards lower pressure. High Altitudes (thin air) Low Altitudes (dense air)

6. Why do you float in your swimming pool ? Why does a helium balloon fly when released ? It’s all the same thing, really (water and air are both fluids)…. Let’s do a thought experiment…. A. Consider a spherical volume of H 2 0 stationary in the liquid: W sphere = buoyant force B. Replace the H 2 0 sphere with a solid sphere of equal volume. A Submerged object feels a buoyant force equal to the weight of the volume of liquid displaced ! - Archimedes’s Principle Lower pressure Higher pressure A B

7. It doesn’t matter what material you submerge. For the same volume, they all experience the same buoyant force (BF)! If the submerged body’s weight W > BF, it sinks to the bottom. If the submerged body’s weight W < BF, it rises to the top.

8. The difference in air pressure produces as upward Buoyant Force on things around us. High Altitudes: Low Air density (thin air) -> Low Pressures Low Altitudes: High Air density -> Large Air Pressures Air pushes up more than down. But not all things ‘float’. Why ?

9. A Recipe for Floating Balloons 1. Fill balloon w/ any gas that is lighter than air, e.g. He, H 2, etc. mg = (  He V)g BF =  air Vg Volume V He air 2. Fill the balloon with air and heat it.  He   air mg = (  hot air V)g BF =  air Vg Volume V Hot air air  hot air   air

10. Why a Hot-air Balloon Floats Cool Air denser outside Hot Air less dense inside Note: Outside and Inside pressures are equal (otherwise balloon will expand or contract) Hot-air balloons: contains fewer air particles than if it were cold must therefore be ‘lighter’ (less dense) than the volume of relatively colder air it displaces, making them float

11. Buoyant Force (BF) =  V displaced air g: The larger the balloon, the larger BF