Short paper due Thursday start of class HW10 on balloons, pressure, gases …. Better to do it this week at problem solving session than to put off, but it’s up to you. This week: Gases and pressure: how tires work, why your sealed Tupper ware explodes in the microwave, The atmosphere: why less oxygen on the top of Longs Peak Balloons - Helium and Hot air … why do these rise? Important physics: Forces, Newton’s Laws (F net = mass x acceleration), Weight = mass in kg x g, Ideal gas law, Pressure Revisit 1010 notes on force and NET force if you need a refresher

Air and pressure Air : Lots of small molecules zooming around. Hit objects and each other … exert a force Force exerted = pressure of air x area OR Pressure = Force/Area A totally flat bike tire (tubeless tire), the air pressure on the inside of the tire is: a. less than the air pressure on the outside b. greater than the air pressure on the outside c. equal to the air pressure on the outside. Answer is c. Rim Tube Pressure on inside, same as pressure on outside Pressure at sea level = 14 lbs of force per square inch Force of air on inside balances outside.

1.Add more gas molecules (Increase N (# of molecules)  Increase P, more collisions with wall/each other every second) 2.Make gas hotter (Increase T (temperature)  Increase P, moving faster, more collisions, hitting harder) 3.Make box smaller (Decrease V (volume)  Increase P, higher density, more collisions with wall/each other every second) Need to raise pressure of tire to make it work. Think about all the different ways to raise pressure of a gas. Work in group, write down 3 ways and why this would increase pressure. Does pressure depend on type of atom? He vs Air say: a. Yesb. No Look at behavior gives “ideal gas law”: Pressure= k * (number of molecules) * (Temperature in K) Volume Boltzmann’s Constant (k): 1.38x Pa m 3 /(atom K) Temperature in absolute scale (Kelvin) 0 C = 273 K room temp = 293 K Density =  particle # atoms/m 3 In Pascals (Pa)

Look at behavior gives “ideal gas law”: Pressure= k * (number of molecules) * (Temperature in K) Volume Boltzmann’s Constant (k): 1.38x Pa m 3 /(atom K) Temperature in absolute scale (Kelvin) 0 C = 273 K room temp = 293 K Density =  particle # atoms/m 3 Does pressure depend on type of atom? He vs Air say: Answer is : b. No Pressure does not depend on type of atom or mass of atom, all differences account for by temperature (Thermal energy). At 273 Kelvin: Heavy atom moving slowly, fewer collisions, more force per collision Lighter atoms moving fast, more collisions, less force per collision

Back to tires Pump in more air: Many more molecules in same space, ADD air until pressure increases by 100 lbs per square inch (psi) (so total inside pressure now 114 psi) Force exerted = pressure of air x area If bike + person weighs 150 lbs, how much area of bike tire is on road: a. less than 1 sq inch b. 1.3 sq inches c. 1.5 square inchesd. 12 sq. inches Inside – Outside air pressure: 100 psi Pressure from road on tire: 100 psi Tire tread

Air and pressure Pump in more air: Many more molecules in same space, ADD air until pressure increases by 100 lbs per square inch (psi) (so total inside pressure now 114 psi) Force exerted = pressure of air x area Where road is in contact with tire, pushes up with pressure of 100 lbs/square inch: Total force upwards must be 150 lbs to balance weight Total force upwards = 150 lbs = area x 100 lbs/in 2 SO area is 1.5 in 2 Inside – outside air pressure: 100 psi Pressure from road on tire: 100 psi Force of road on bike Force of Gravity Force of Gravity (in Newtons) = mass in kg x g = mass in kg x 9.8 m/s 2 F net = Force of road on bike (up) - Force of Gravity (down) = 0 (b/c not falling!) Force of road on bike (up) = Force of Gravity (down)

What will happen if we remove the air from inside the drum? a. Nothing b.The drum will explode c.The drum will implode d.Something else PUMP REMOVE AIR FROM INSIDE Pressure Gauge

To Pump The mighty force of Air Pressure! Initially: Air both inside and out Pressure inside = Pressure outside No Net Force on walls of barrel (of course still have force of gravity) As Air removed:

Add up weight of every air molecule in column: Total weight = 22,700 lbs or = 10,300 kg* 9.8 m/s2 = 101,000 Newtons (LIKE A BIG BUS ON EVERY m 2 !) How much force is air putting on the steel drum? How much does the atmosphere weigh? Sea Level Top of Atmosphere (~50 km) Force Down = Weight of Atmosphere above Force Up ? a.No force up b.Air below is pushing up with force equal to force down c.Air below is pushing up with force less than force down d.Ground is pushing up with force equal to force down Look at 1 meter above sea level Column of Air above ground (1 m 2 ).

Column of Air above 1 m 2 of the ground. Add up the weight of every air molecule in column: Total weight = 22,800 lbs or =10,300 kg * 9.8 m/s 2 = 101,000 Newtons How much does the atmosphere weigh? Sea Level Top of Atmosphere Force Down = Weight of Atmosphere above Force Up ? b.Force up MUST equal Force down otherwise column above would fall. Air pushes up with force. Pressure = Force/Area = 101,000 N / 1m 2 = 22,800 lbs / 1550 in 2 = 14.7 lbs/in 2 Look at 1 meter above sea level

Column of Air (1 m 2 ). Weight = 22,800 lbs = 101,000 Newtons What about in Boulder? Sea Level Top of Atmosphere Force Down = Weight of Atmosphere ABOVE (Less than at sea level… about 80% above us, 20% below us) So Force Up is Less: Air pushes up with less force than at sea level Pressure = Force/Area Air Pressure in Boulder LESS than at Sea Level Look at Boulder

What are the forces acting on cube of air? a. just gravity down b. gravity down, air pressure pushing equally on all sides. c. gravity down, air pressure from all sides but bigger on bottom than top. d. gravity down, air pressure from all sides but bigger on top than bottom. e. only air pressure GROUND Consider cube of air defined by these imaginary borders:

What are the forces acting on cube of air? c. gravity down, air pressure from all sides but bigger on bottom than top. GROUND Also air pressure pushing against front and back of cube. Air pressure greater here because more air above! F air pressure W air in cube (Weight of Air in cube) Remember back, Phys1010… F net = ma. If air parcel is stationary, then a.F air pressure > W air in cube b.F air pressure < W air in cube c.F air pressure = W air in cube d.No way of knowing.

GROUND Air pressure greater here because pressure must support more air above! F air pressure W air in cube = Mass of air x g = Volume x density of air x g Remember back, Phys1010… Newton’s 2 nd Law. If air parcel is stationary (no acceleration), then c.F air pressure = W air in cube Newton’s 2 nd Law:F = ma Sum of Forces = Net Force = mass * acceleration = m a Called, F buoyancy F buoyancy on cube = mass of air in cube x g F buoyancy on cube = volume of cube x density of air x g

PAYLOAD (~3 Large Paper Clips) #1 Air #2 He #3 AIR How does F buoyancy compare for each balloon? A. F buoyancy for #1 > #2 > #3 B. F buoyancy for #2 > #1 > #3 C. F buoyancy for #1 = #2; & both larger than #3 D. F buoyancy for #2 > #3 > #1 E. F buoyancy for #1 = #3; & both smaller than # 2.

#1 Air PAYLOAD (~3 Large Paper Clips) #2 He #3 AIR How does F buoyancy compare for each balloon? C. F buoyancy #1 = #2 and both are larger than #3. Balloons #1 and #2 have the same volume. #3 is smaller volume! F buoyancy = upward force from pressure of air surrounding balloon = mass of air displaced by balloon * gravity = (density of air * volume of balloon) * gravity F buoyancy Weight Balloon + He + string Weight Balloon + Air + string Weight Balloon + Air + string + paperclips Calculating F buoyancy for Balloon #1 density of air at sea level = 1.25 kg/m 3 density of air in boulder = 1 kg/m 3 Volume = 4/3 pi r 3 = 4/3 pi (0.15 m) 3 = m 3 F buoyancy = Volume * density * g = (0.014 m 3 )(1 kg/m 3 )(9.8 m/s 2 ) = 0.14 N = 0.03 lbs