• 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 (Fnet = 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.
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.
Rim
Tube
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.
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)
Look at behavior gives “ideal gas law”:
Pressure= k * (number of molecules) * (Temperature in K)
Volume
In Pascals (Pa)
Boltzmann’s
Constant (k):
1.38x10-23 Pa m3/(atom K)
Density = particle
# atoms/m3
Temperature
in absolute scale (Kelvin)
0 C = 273 K
room temp = 293 K
Does pressure depend on type of atom? He vs Air say:
a. Yes
b. No
Look at behavior gives “ideal gas law”:
Pressure= k * (number of molecules) * (Temperature in K)
Volume
Boltzmann’s
Constant (k):
1.38x10-23 Pa m3/(atom K)
Density = particle
# atoms/m3
Temperature
in absolute scale (Kelvin)
0 C = 273 K
room temp = 293 K
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
Inside – Outside
air pressure:
100 psi
Tire tread
Pressure from
road on tire:
100 psi
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 inches
d. 12 sq. inches
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 of
road on
bike
Force of
Gravity
Force exerted = pressure of air x area
Inside – outside air
pressure: 100 psi
Pressure from
road on tire:
100 psi
Force of Gravity (in Newtons) = mass in kg x g = mass in kg x 9.8 m/s2
Fnet = 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)
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/in2 SO area is 1.5 in2
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
Pressure
Gauge
REMOVE AIR FROM INSIDE
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:
To Pump
How much force is air putting on the steel drum?
How much does the atmosphere weigh?
Top of
Atmosphere
(~50 km)
Column of Air
above ground
(1 m2).
Sea Level
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 m2!)
Look at 1 meter
above sea level 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
How much does the atmosphere weigh?
Top of
Atmosphere
Column of Air above 1 m2 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/s2 = 101,000 Newtons
Look at 1 meter
above sea level
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.
Sea Level
Pressure = Force/Area
= 101,000 N / 1m2
= 22,800 lbs / 1550 in2
= 14.7 lbs/in2
What about in Boulder?
Top of
Atmosphere
Column of Air
(1 m2).
Weight
= 22,800 lbs
= 101,000 Newtons
Look at Boulder
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
Sea Level
Air Pressure in Boulder
LESS than at Sea Level
Consider cube of air
defined by these
imaginary borders:
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
What are the forces acting on cube of air?
c. gravity down, air pressure
from all sides but bigger on bottom than top.
F air pressure
Air pressure greater here
because more air above!
W air in cube
(Weight of Air in
cube)
Also air pressure
pushing
Remember back, Phys1010… Fnet = ma. If
against front and
air parcel is stationary, then
back of cube.
a. F air pressure > W air in cube
GROUND
b. F air pressure < W air in cube
c. F air pressure = W air in cube
d. No way of knowing.
Newton’s 2nd Law: F = ma
Sum of Forces = Net Force = mass * acceleration = m a
Called, F buoyancy
F air pressure
Air pressure greater here
because pressure must
support more air above!
GROUND
W air in cube=
Mass of air x g =
Volume x density of air x g
Remember back, Phys1010… Newton’s 2nd Law. If
air parcel is stationary (no acceleration), then
c. F air pressure = W air in cube
F buoyancy on cube = mass of air in cube x g
F buoyancy on cube = volume of cube x density of air x g
#1
Air
#2
He
PAYLOAD
(~3 Large Paper Clips)
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.
#3
AIR
#1
Air
F buoyancy
Weight
Balloon + Air
+ string +
paperclips
#2
He
F buoyancy
Weight
Balloon + He
+ string
#3
AIR
F buoyancy
Weight
Balloon + Air
+ string
How does FPAYLOAD
buoyancy compare for each balloon?
Paper
Clips)
C. F buoyancy (~3
#1 Large
= #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
Calculating F buoyancy for Balloon #1
density of air at sea level = 1.25 kg/m3 density of air in boulder = 1 kg/m3
Volume = 4/3 pi r3= 4/3 pi (0.15 m)3 = 0.014 m3
Fbuoyancy = Volume * density * g = (0.014 m3)(1 kg/m3)(9.8 m/s2) = 0.14 N = 0.03 lbs