Chapter 9 Gravity (and some Satellite Motion)!
Universal Law of Gravitation
Universal Gravitational Constant (“G”)
Inverse Square Law
Weight and Weightlessness
Satellites – Circles and Ellipses/Energy Considerations
Gravity and Ocean Tides
Gravitational Fields and Black Holes!
Universal Law of Gravitation
Force ~
mass1  mass2
distance2
mass2
Force =
G m1  m2
d
d2
mass1
This force is always attractive and exists between every pair of masses in the
universe!
If d is large we can approximate any object by a point particle at its center of mass.
For a sphere we can do this at any distance (outside the sphere).
THE Universal constant “G”
Where does “G” come from?????
G = 6.67  10-11 N m2/kg2
G m1  m2
Force =
Extremely weak Force!
d2
This law has been verified from ~10-6 m to the largest distances
probed with telescopes.
mercury
One Experimental Method
(von Jolly)
m1
m2
Balance –
Measure F to restore
the balance!
6 TON lead sphere!
Force on an apple as it moves away from the earth
1N
G m1  Mearth
Force =
Force (N)
(Rearth + d)2
- If you know G this
can be used to
measure the mass of
the Earth!
1/4N
0
1
2
3
4
5
distance from the surface of the Earth (in Earth Diameters)
d
Rearth ~ 6400 Km
Mearth ~ 6 1024 Kg
Other influences also decrease as 1/R2 ! (sound, light from a star, etc.)
http://hubblesite.org/gallery/
Answer: 1
Discounting the changes in the fuel, the
gravitational force on the shuttle in orbit is
94% as much as when on Earth’s surface—
nearly the same!
Weight and Weightlessness
More general definition of weight:
The weight of an object is the force the object exerts
against a supporting surface (floor) or a weighing scale.
Weight = m”g”
Net Force =
G Mearth  m
= m a = m “g”
Rearth2
a=g
a = -g
What do the scales read
in each case?
scale
Satellites (cont’d)
Circular Orbits
- 8Km/s tangential speed!
- Near surface, about 90minutes to orbit,
- If further away “g” is less, orbital speed is slower,
they move a longer distance --> so it takes longer!
GPS satellites – about 12 hour orbits
Geosynchronous – about 24 hour orbits.
Moon – 27.3 days for orbit!
Real-time tracking @ http://www.n2yo.com/
Elliptical Orbits
-Move faster than 8km/s
(overshoots a circle)
-Kepler’s Laws!
Ocean Tides
Tides are caused by the rotation of the Earth combined with
differences (about 6.7%)in the gravitational pull between the moon
and the earth on the opposite sides of the earth!
The ocean remain bulges are fixed
while we rotate in and out of them!
Rotation axis
Moon
Pull on
ocean
from
Moon is
smaller
here
Pull on ocean from
Moon is larger here
(not to scale!)
Earth
• 2 high tides and 2 low tides per day!
• Spring tides/Neap tides
Nasa
http://home.hiwaay.net/~krcool/Astro/moon/moontides/
Satellites
An Earth satellite is a projectile that falls around the Earth rather than into it!
8000m (8Km ~5miles)
Earth’s Surface
5m
Because the Earth is spherical, the earth’s surface drops ~5m for every 8000m
tangent to the surface.
If you could throw a ball so that it only dropped 5m after traveling 8Km then the
ball would follow the curvature of the Earth (we are not worried about mountains
here)!
•Remember d = ½ gt2 ? It takes the ball about a second to drop 5m!
So you have to throw it at 8 Km/s so that it orbits the Earth!
• The tangential velocity keeps satellites from colliding
(the moon into the earth, the earth into the sun, etc.)
Gravitational Fields
- We can imagine that any mass (even us!) sets up a gravitational
field of force around is that attracts any “test” mass that is placed
nearby.
We think of the mass as
altering the space around it!
What is the gravitational field like INSIDE the Earth?
What is a “black” hole and should I be worried about particle
accelerators creating them?
For Review
The Universal Law of Gravity
1. In what sense does the moon “fall”?
2. State Newton’s law of universal gravitation in words and in an
equation!
3. What is the gravitational force between two 1Kg masses 1m apart?
4. What is the gravitational force between the Earth and a 1Kg mass?
5. What do we call the gravitational force between the Earth and your
body?
The Inverse Square Law
6. If you travel four times further from the sun the amount of light to
reach you is _________ as much.
Weight and Weightlessness
1. Give an example of when your weight is more than mg and another
when your weight is less than mg. How about zero?
Tides
2. Why do both the sun and moon exert a greater gravitational force on
one side than the other?
3. Gravitational force depends on the inverse _______ of distance.
Tidal force, the difference in gravitational force per unit mass,
depends on the inverse _________ of distance.
4. What’s the difference between spring tides and neap tides?
5. Do tides occur inside the Earth? Are they also greatest during a new
or full moon?
6. Does the moon rotate (spin) on its axis? Does it spin and revolve
about the Earth?
1. When the moon’s long axis is not aligned with the Earth there is a
rotational force, or ________ about the Moon’s center.
Black Holes etc!
2. If the Earth shrank with no change in mass what would happen to the
gravitational force on you if you stayed in the same place as before the
earth started shrinking?
3. How can we detect black holes is they are invisible?
4. What percent of the universe is currently thought to be composed of an
unknown form of matter (dark matter) and an unidentified form of energy
(dark energy).
Exercises
1. Comment on whether the following label should be cause for concern:
CAUTION: the mass of this product pulls on every other mass in the universe!
2. What would be the path of the Moon if somehow all gravitational forces on it
vanished to zero?
3. A friend says that astronauts are weightless in orbit because they are beyond
the pull of Earth’s gravity. Correct your friend!
4. Does the more massive Earth attract the less massive Moon with a force that
is greater/smaller/the same as the force that the Moon attracts the Earth?
5. An astronaut lands on a planet that has twice the mass of Earth and twice the
radius. How does the astronaut’s weight differ from their “Earth” weight?
6. The intensity of light from a central source varies inversely as the square of
the distance. If you lived on a planet only half as far from the Sun as the Earth
how would the light intensity compare with that at the Earth? How about 10
times further away?
Study Guide Exam #2 Momentum, Energy, Rotational Motion and Gravity
(Chapters 6-9)
The exam will be based on the homework Review Questions, Exercises, and Quick
Calculations from these chapters!
The format is the same as the previous exam – multiple choice, true-false, fill in the
blank, write-out the answer type questions, and quick calculations.
Equations that will be provided:
v =d/t, a = v/t, v = at, d = ½ at2, a = F/M
P = mv, Impulse = Ft = mv, W = Fd, P = W/t, PE = mgh, KE = ½ mv2, W = KE,
v = r  , Torque = lever arm  F, F = mv2/R, Angular momentum = I (= mvr
sometimes), F = Gm1m2/d2
You should:
- Be able to define, use the correct units, and do quick calculations (using the
equations provided) of momentum, kinetic energy, gravitational potential energy,
work, power, angular momentum, torque, centripetal force, and angular momentum!
In momentum, you should
o
Understand what impulse is and the relationship of impulse to changes in momentum.
o
Be able to state the Law of Conservation of (Linear) Momentum.
o
Know the difference between an elastic and inelastic collision.
In energy you should
o
Understand the difference between momentum and energy (kinetic and potential (which is a vector and
which is a scalar?)
o
Understand what doing work means and that power is the rate at which work is done.
o
Understand the work energy Theorem (e.g., how far does the car slide before it comes to a stop?)
o
Be able to state the Law of Conservation of Energy!
o
Be able to give examples of different types of energy sources (is hydrogen a source of energy or a way of
storing energy?)
o
Know the basic principle of the operation of a machine.
In Rotational motion you should
o
Understand the difference between tangential and angular velocity.
o
Understand what rotational Inertia means and how it affects the rotational motion of objects.
o
What torque is and how the concept can be applied.
o
Understand center of mass and stability.
o
Know that an object moving in a circle experiences a force toward the center (centripetal).
o
Be able to State the Law of conservation of angular momentum
Chapter 13
Liquids!
Pressure -definition
Pressure in a Liquid
Bouyancy
Archimedes’ Principle
What makes an Object Sink or Float?
Flotation
Pascal’s Principle
Surface Tension and Capillarity
http://en.wikipedia.org/wiki/Liquid
Liquids– Phases of matter (solid,liquid, gas)
- The motion of molecules and how far they stray from one another
defines the phase of a collection of molecules
Unbound
Loosely Bound – matter flows
Strongly Bound – fixed positions
-The temperature of a collection is determined by the average kinetic
energy of the collection and can determine the phase.
Bonus Quiz!
(1) The volume of a completely submerged object is (equal to/less
than/greater than) the volume of the fluid it displaces.
(2) The buoyant force on a completely submerged object in a fluid is (equal
to/less than/greater than) the weight of the fluid it displaces.
True/False
(3) The mass of a completely submerged object is equal to the mass of the
fluid it displaces.
___
Question
(4) The relative densities of ice, water and alcohol are 1.0, 0.9, and 0.8
respectively. Do ice cubes float higher or lower in a mixed alcoholic drink?
What comment can you make about a cocktail in which ice cubes lie
submerged at the bottom of the glass! ?
Pressure = Force/Area
- When we talk about fluids and forces we use the concept of pressure.
-You are under a lot of pressure when there is a large force exerted on
you over a small area!
P = F/A
(the unit is called the Pascal, N/m2)
An Elephant versus a pin?
2 blocks of the same mass. Which exerts more pressure on the table?
Pressure in a Liquid
Liquid Pressure = Weight density  Depth
- more dense fluids exert more pressure
- the further the object is submersed the
higher the pressure
Pressure in a Liquid
-
If you are submerged in a liquid the pressure on you depends on 3
things:
(a) Your depth below the surface of the liquid (d).
(b) The density () of the liquid
(c) The acceleration due to gravity (g)! (different on the moon)
P=gd
d
The origin of the force is from the weight
of fluid above the object
Fluid, density = 
In general there may be more than one fluid contributing
to the force (example: pressure on a fish in the gulf
includes the air from the atmosphere above the ocean).
Pressure in a Liquid (cont’d)
Pressure = Force/Area = mg/A
The mass is the density times volume:
m=V= Ad
Pressure = (Ad)g/A = gd
Weight of fluid above A = mg
Volume of fluid above A = Ad
Area = A
Quick Calculation – Water pressure
Calculate the pressure exerted on your head by the surrounding
water when you are 1m below the surface of a swimming pool.
Hints: water = 1g/cm3 or 1000Kg per m3
Pressure in a Liquid (cont’d)
•Liquid pressure does not depend on the volume of the liquid you are
submerged in
-At a given depth below the surface the pressure is the same in the
Atlantic ocean as in a swimming pool (aside from density differences!).
• “Water seeks its own level” (steady-state)
-Since water depends on depth, not volume, water will adjust its depth
in any vessel to maintain the same pressure at any given depth. If it did
not, the pressure difference would cause a flow in the fluid to equalize
the pressures. (water can flow “uphill” to equalize pressures)
Open at the bottom and
Immersed in fluid!
Pressure in a Liquid (cont’d)
• Experimentally, liquid pressure on a submerged object is exerted
in all directions equally at a given depth!
(pressure can act “sideways”, up and down).
• When a liquid presses against a surface there is a net force perpendicular
to that surface. We can look at the pressure dependence of
depth by poking holes in a cup!
Buoyancy
- An upward force on immersed or submerged objects equal to the weight
of the fluid the object displaced.
Block displaces a volume of fluid equal to its volume (V)
d
There is more pressure at the bottom than the top of the
block!
Pressure on the sides cancel. The net result is a force
upward on the block.
Bouyancy (cont’d)
We can show where this upward force comes from:
Difference in pressure across the block (the top to the bottom) = g d
Force up = g d times Area
= g times Volume of Object (V)
= V g
d
d
= Mass of Fluid displaced by the volume of the
object times g
= “Weight of fluid displaced by the objects
immersed volume”
Fluid, density = 
(Does it matter at what depth I place the object?)
Buoyancy (cont’d)
This is Archimedes’ Principle:
An immersed object is buoyed up by a force equal to the weight of the
fluid it displaces.
Check: If an object is placed in water and displaces 1Kg of water, what is
the buoyant force on the object?
Check: Do objects placed in water weigh less than in air? How much?
Check: An object is thrown into a well and sinks deeper and deeper. Does
the buoyant force change?
Quick Calculation – Buoyancy
Estimate the buoyant force on yourself when completely
submerged in a swimming pool. How about only ½ immersed?
Hints: water = 1g/cm3 or 1000Kg per m3
(Volume person ~ 0.1m3)
What makes objects sink or float?
We can find out with Newton’s 2nd Law!
At any given time,
Buoyant Force – Weight = ma
positive
fluidV g - Mg = ma
•If submerged and Weight > Buoyant Force then it will sink!
•If submerged and Weight < Buoyant Force then it will rise
(and may end up partially immersed).
The mass of the object is M = object V
fluidV g - object Vg = ma
OR
fluid- object = (m/Vg) a
What makes objects sink or float?
fluid- object = (m/Vg) a
(submerged object)
The same rule from Newton’s 2nd Law are that a submerged object
- sinks when the density of the object is greater than the fluid
- rises when the density of the object is less than the density
of the fluid
- floats (a=0) when the densities are the same!
Principle of Flotation: A floating object displaces a weight of fluid equal to
its own weight:
Buoyant Force = Weight of Object
Floating object only!
What makes objects sink or float?
Wait. If I put an ice cube in water it floats but part of it is immersed.
Can I figure out how much?
Yes. The volume submerged is the volume required such
that the buoyant force is the same as the weight of fluid displaced.
fluidVimmersed g - Mg = Ma = 0
Total mass = object Vtotal
object
Vimmersed
=
Vtotal
fluid
Buoyancy Exercises
1. A block of aluminum with a volume of 10cm3 is placed in a beaker of water
filled to the brim. The same is done in another beaker with a 10cm3 block of
lead. Does lead displace more, less or the same amount of water?
2. A block of aluminum with a mass of 1kg is placed in a beaker of water filled to
the brim. The same is done in another beaker with a 1kg block of lead. Does
lead displace more, less or the same amount of water? (hint: which has the
larger volume for a given mass?)
3. A block of aluminum with a weight of 10N is placed in a beaker of water filled
to the brim. The same is done in another beaker with a 10N block of lead.
Does lead displace more, less or the same amount of water? (hint: which has
the larger volume for a given mass?)
4. If liquid pressure were the same at all depths would there be a
buoyant force on an object submerged in the liquid?
Pascal’s Principle
A change in pressure at any point in an enclosed fluid at rest
is transmitted undiminished to all points in the fluid.
An example is the simple machine, the hydraulic press!
(Machine: a device for multiplying forces or changing the direction of forces.
Energy is conserved.)
Machines!
f
D=Fd
http://en.wikipedia.org/wiki/Hydraulic_press
Surface Tension
-Water molecules like other water molecules (cohesion)!
Why is this a “surface” effect rather than a volume effect?
Because at the surface the molecules are pulled preferentially “down” into
the other water molecules. Molecules below the surface are pulled
everywhere equally!
Capillarity
-Water molecules like molecules other than water molecules also (adhesion)!
Adhesive force = Weight of Fluid lifted
www.digitalfieldguide.com/.../2006/09/page/2/
For Review - Liquids
1. Give 2 examples of a fluid.
2. Distinguish between Force and Pressure
3. If you swim beneath the surface in salt water will the pressure be
(the same/greater/less) than fresh water at the same depth?
4. How does water pressure 1m below the surface of a small pond
compare with 1m below the surface of a huge lake?
5. If you punch a hole in a container filled with water, in what direction
does the water initially flow out?
6. Why does a buoyant force act upward on an object submerged in
water?
7. Why is there no horizontal buoyant force on a submerged object?
8. How does the volume of a completely submerged object compare
with the volume of water displaced?
For Review - Liquids
1. Why does the buoyant force act upward on an object?
2. What is the mass of 1L of water? Weight?
3. If a 1L container of anything is immersed halfway into the water,
what is the volume of water displaced?
4. Is the buoyant force on an object equal to the weight of the object or
the weight of the fluid it displaces?
5. How is the density of a fish controlled? A submarine?
6. What is the principle of flotation?
7. A non-sinking 100 ton ship displaces what weight of water? What is
the buoyant force on the 100 ton ship?
Some Exercises! - Liquids
1. Which do you suppose exerts more pressure on the ground – an
elephant or a lady standing on spiked heels?
2. If water faucets upstairs and downstairs are turned on which do you
suppose will flow faster or do they flow at the same rate?
3. Look at the teapots in exercise 12 of the chapter. The teapot on the
left holds less/more/the same amount as the teapot on the right.
4. If liquid pressure were the same at all depths would there be a
buoyant force on an object submersed in the liquid?
5. Why will a volleyball held beneath the surface have more buoyant
force than if it is floating?
6. A piece of iron placed on a block of wood makes it float lower in the
water. If the iron were instead suspended beneath the wood would
the wood float higher lower or the same?
More exercises..!
7. Will a rock gain or lose buoyant force as it sinks deeper in water?
8. When an ice cube in a glass of water melts does the water level in
the glass rise, fall or remain the same? (What does this say about
the North polar ice cap melting in terms of sea level change?) Does
the answer change if the ice cube has air bubbles in it? How about
sand (*this one is hard!)?
Chapter 14
Gases and Plasmas!
The Atmosphere
Atmospheric Pressure
Barometer
Boyle’s Law
Buoyancy of Air
Bernoulli’s Principle
Plasmas
Our Atmosphere
Why is it spherical and why doesn’t it just drift off into
space?
Gravity versus Kinetic Energy!
The sun provides the kinetic energy and the Earth
provides the gravitational
attraction.
www.whatiscience.com/.../Atmosphere.jpg
Most of the “air” stays very close to the Earth’s surface:
- 99% of our atmosphere is less than 30Km from the surface
and the radius of the Earth is ~6400Km!
Some gas molecules escape but they have to have a very large kinetic energy.
Some molecules get trapped too.
R =6,400Km
EARTH
EARTH
Atmosphere (not too scale)
It is thinner than this!
The Atmosphere
Composition:
~78% Nitrogen
~21% Oxygen
~0.93% Argon
~0.035% Carbon dioxide
The Atmosphere: The Ocean we swim in!
How much mass is there in 1m3 of air?
1m
1m
air ~ 1.25 Kg/m3
1m
At the surface of the Earth
Roughly, what mass of air is in the lecture room? About 1000 Kg (2,200 lbs)!
This density actually depends on how far you are above Earth’s surface.
air ~ 0.4 Kg/m3
At 10 Km above the surface
(National geographic)
Atmospheric Pressure
Column of air above the block
A block just sitting there
Just like liquids pressure from air is the result of the mass
of the air above you!
Unlike liquids, gases are compressible (can be readily
compressed) and they become less dense the higher you go!
So for gases we DO NOT have
P=gd
Since the density is not constant
(over an appreciable distance)!
Atmospheric Pressure
Pressure = Force/Area = Weight of Air/Area
A column of air about 30Km high (99% of atmosphere)
with an area of 1cm2 has a mass of ~1Kg
Column of air above Area A
Pressure at surface ~10N per square cm
Area = A
= 100,000 N/m2 (~100 KPa)
(the average is actually 101.3 KPa)
How do we survive such a tremendous force??
It is pressure differences that create a net force!
Barometers
Can we make a water barometer to measure the local pressure from the
atmosphere?
Sure, but it will need to be about 10.3 m tall!
Weight of column of water =
Force of the Atmosphere!
Vacuum ( tube is closed at the top)
Air pressure
Air pressure pushes water up the column
Weight of column of water =
Force of the Atmosphere!
(Newton’s 2nd Law again)
Mg = Patmosphere  Area
(water V) g = Patmosphere  A
(water A h)g = Patmosphere  A
(waterh)g = Patmosphere
(It does not depend on the area of the tube!)
Vacuum ( tube is closed at the top)
Atmospheric pressure
Air pressure pushes water up the column: Patmosphere
 Area
Barometers (cont’d)
So the height to which the water rises in a closed vessel tells us the atmospheric
pressure:
Patmosphere
h=
waterg
We can estimate this:
h
~
100,000 N/m2
1000
Kg/m3 
10m/s2
= 10m
More practically we can use a more dense liquid to find Patmosphere.
mercury
If we use mercury (13.6 times as dense) then h
~0.76m and this is easier to have around!
http://home.c2i.net/astandne/help_htm/images/element/mercury.jpg
Boyle’s Law
What happens as an object “floats” or ascends or descends
through the atmosphere?
Pressure  Volume= CONSTANT
Where does this come from?
Pressure is proportional to density:
Does the helium balloon
expand as it rises?
Twice the number of molecules means twice the number of collisions
= twice the force on the walls
We can increase the density by decreasing the volume!
Applied external force to compress
The cube
Density increase due to volume decreasing = Pressure increase
P
V= P  v
And they exactly compensate so the product is constant!
Bouyancy of Air (just like liquids – they are both fluids!)
- An upward force on immersed or submerged objects equal to the weight
of the fluid the object displaced.
Block displaces a volume of fluid equal to its volume (V)
d
There is more pressure at the bottom than the top of the
block! This is where the buoyant force comes from!
Pressure on the sides cancel. The net result is a force
upward on the block.
Air
Buoyancy of Air!
This is Archimedes’ Principle for Air:
An immersed object is buoyed up by a force equal to the weight of the
fluid (air here!) it displaces.
Check: If an object is placed in air and displaces 1Kg of air at the surface of
the Earth, what is the buoyant force on the object? What is the volume of
the object?
Check: Do objects placed in air weigh less than in a vacuum? Does this
depend on altitude?
Check: An object is thrown into a well (of water) and sinks deeper and
deeper and the buoyant force does not change. What happens to an object
dropping through the atmosphere?
Buoyancy of Air!
Recall that we found for liquids:
What makes objects sink or float?
fluid- object = (m/Vg) a
The same rule from Newton’s 2nd Law are that a submerged object
- sinks when the density of the object is greater than the fluid
- rises when the density of the object is less than the density
of the fluid
- floats (a=0) when the densities are the same!
For air this equation applies at a particular altitude!
Bernoulli’s Principle
When the speed of a fluid increases,
internal pressure in the fluid
decreases.
For Fluids in motion not at rest!
FLOW LINES
Each part of a fluid exerts pressure (a force) on another part!
A big air bubble
FLOW LINES
The internal pressure is lower here
The internal pressure is higher here
A manifestation of conservation of energy!
Increased kinetic energy for any given part of the fluid
means less pressure is exerted from molecules within that part.
For Review -Gases
The Atmosphere and Atmospheric Pressure
1. What is the energy source for the motion of gases in the
atmosphere? What prevents the atmosphere from flying off into
outer space?
2. How high would you have to go in the atmosphere would you have
to go for ½ of the mass to be below you?
3. What is the cause of atmospheric pressure?
4. What is the mass of a cubic meter of air at room temperature?
5. What is the mass and weight of a column of air 1cm squared in area
extending from sea level to the upper atmosphere?
6. What is the pressure at the bottom of the column of air referred to in
the previous question?
For Review -Gases
Barometer
6. How does the pressure at the bottom of a 76cm column of mercury
in a barometer compare with air pressure at the bottom of the
atmosphere?
7. How high would you have to go in the atmosphere would you have
to go for ½ of the mass to be below you?
8. When you drink liquid with a straw why is it more accurate to say the
liquid is pushed up the straw rather than sucked up the straw? What
does the pushing?
9. Why will a vacuum pump not operate for a well that is more than
10.3m deep?
10. Why is it that an aneroid barometer is able to measure altitude as
well as atmospheric pressure?
For Review -Gases
Boyle’s Law and Buoyancy of Air
11. By how much does the density of air increase when it is
compressed to ½ its volume?
12. What happens to the air pressure inside a balloon when it is
squeezed to ½ its volume at constant temperature?
13. What is an ideal gas?
14. A balloon that weighs 1N is suspended in air drifting neither up nor
down. (a) How much buoyant force acts on it? (b) What happens if
the buoyant force decreases? Increases?
15. Does air exert a buoyant force on all objects in air or only on
objects such as balloons that are very light for their size?
16. What happens if you release a helium balloon into the atmosphere?
Some Exercises! -Gases
1. Why is the pressure in an automobile’s tires slightly greater after the
car has been driven several kilometers (or miles).
2. When an air bubble rise in water what happens to its mass, volume,
and density?
3. When boarding an airplane you bring a bag of chips and, while you
are in flight, notice that the bag of chips puffs up. Explain why this
happens.
4. We can understand how pressure depends on depth by staking
bricks. The pressure below the bottom brick is the weight of the full
stack and ½ way up the stack only ½ the bricks above contribute to
the pressure. Why should we consider compressible bricks to
explain atmospheric pressure?
5. The “pump” in a vacuum cleaner is merely a high speed fan. Would
a vacuum cleaner pick up dust from a rug on the moon? Explain.
Some Exercises! -Gases
6. Your friend says that the buoyant force of the atmosphere on an
elephant is significantly greater than the buoyant force of the
atmosphere on a small balloon. What do you say?
7. Two Identical balloons of the same volume are pumped up with air to
more than atmospheric pressure and suspended on the ends of a
stick that is horizontally balanced. One of the balloons is punctures.
Is the balance of the stick upset? If so, which way does it tip?
8. The force of the atmosphere on a 10m2 window is about a million N.
Why doesn’t the window break? Why might the window shatter
when a strong wind blows past the window?
9. What provides the lift to keep a Frisbee in flight?
Chapter 22
Electrostatics
Electrical Forces
Electric Charges
Conservation of Charge
Coulomb’s Law
Conductors and
Insulators/Superconductors
Charging – Friction/Induction
Charge Polarization
Electric Field and Potential
Electric Energy Storage
mcdermott.chem.columbia.edu/bioph
ys/intro_ima...
-Electrostatics
The study of stationary (not moving) Electric Charges.
-Electrodynamics
The study of moving charges.
q2
q1
Where does electric charge come from and why must matter be (almost) electrically
neutral?
- There are two types of charge and we call them negative and positive
- Opposite charges attract, like charges repel! Why, we don’t know.
The origin of charge in our daily wanderings is from two elementary particles:
the electron and up and down quarks
(which combine to form the +1 proton and neutral neutron)
Electric Charges: the origin of electricity and magnetism
Nucleus (~ 10-15 m) with one proton (and zero, 1 or
more neutrons)
Electron
( < 10-18 m)
+
-
Schematic of a Hydrogen atom
r ~ 10-10 m
Every atom is
(1) Composed of a positively charged nucleus of protons (q =+1) and neutrons (q =0)
(2) Negatively charged Electrons (-1) “orbit” the nucleus at fixed distances.
(3) Mproton ~ 1800 Melectron
(4) Atoms usually have equal numbers of negative and positive charges
(Ordinary) matter is composed of lots (1023) of atoms and is almost perfectly neutral!
Conservation of Charge
Charge can be neither created nor destroyed only transferred
from one object to another.
Atoms can lose an electron but some other atom must acquire that charge!
A positively charged hydrogen ion = a proton! (and maybe a neutron or 2)
+
-A charge imbalance occurs when electrons are
transferred from 1 object to another.
-Electrons furthest away from the nucleus are loosely bound
and can be “set free” if they are given some energy.
Where is my electron! ?
-Real materials (like hair, plastic, metals) hold onto their
Electrons with different strengths.
Conservation of Charge (cont’d)
-Preference for holding onto their electrons:
Silk > Glass > Rubber > Plastic > Hair
-Ease with which they give up their electrons:
Hair > Plastic > Rubber > Glass > Silk
A Comb transfers electrons from your hair to the comb!
Hair becomes positively charged!
Comb becomes negatively charged
There is an actual difference of integer numbers
of electrons, like 123,766,218,196 electrons.
www.abcgallery.com/R/renoir/renoir127a.jpg
Coulomb’s Law
Force ~
charge1  charge2
distance2
charge2
Force =
k q1  q2
d
d2
charge1
Another inverse square law! This one can be attractive or repulsive.
This time, however, the proportionality constant k is
k = 9,000,000,000 Nm2/C !!!
Coulomb’s Law (cont’d)
Electrical force between two stationary charges:
Force =
k q1  q2
d
q2
d2
k = 9  109 N m2/C2
q1
What is a “Coulomb” of charge? 1 electron has a charge of 1.6 10-19 C.
So 1 C = 6.25 billion billion (6.25 1018) electrons worth of charge!
-For direct current this is about the amount of charge passing through a 100W bulb
in 1s (~100 joules of energy).
Even for highly charged objects the charge imbalance is only 1 part in a trillion.
Conductors and Insulators
All materials can be classified by the ease with which they conduct electric charge
Conductor: electrons in outer atomic shells are “free to wander.”
Relation to thermal conductivity.
- metals
Insulator: electrons in outer atomic shells are not “free to wander” and
Good conductor
Ease with which
electrons are
Moved about
Copper, Iron
Semi-conductors (germanium, silicon)
Wood, plastic, rubber, glass
Insulator
Semi-Conductors: materials that can be made to
behave like a conductor or like an insulator.
Most of our current technology relies
on semiconductors sandwiched together
which are used to control the flow of
charge! (transistors)
Some semiconductors can also conduct
when light is shone on them.
members.tripod.com/~ComputerLab/
micropro.jpg
In general their resistance to the flow of
electrons can be altered by heat, light,
magnetic fields, etc.
Super-Conductors: materials that conduct
perfectly (usually at a very low temperature!)
Charging- the transfer of electrons by physical contact or induction
Direct contact
-
-----
-
-
Gains a net charge
by touching a
charged object.
Initially uncharged
(Hollow metal sphere)
Induction
+
------
+
+
-
+
-
Initially uncharged
+
+
Touch the sphere!
Net positive charge
remains
Charge Polarization
The re-arrangement of charges in a material in response to an external
Net charge.
In conductors, the electrons can move
In insulators, the atoms or molecules themselves become polarized!
-
+
-
Rearrangement of charge within
The molecule (net charge =0)
Negative charge
Outside the molecule
Some molecules have an intrinsic uneven distribution of charge (like water!) and we
say these are “polar” molecules.
Electric Field: The force per unit charge at some location in space.
The direction is defined by the direction of the force
a positive “test” unit charge would feel at that point!
E = Fe/(+q)
E
Fe =
-
k q1  q2
d2
A source of Net charge (-)
+q
+q
Therefore, for a given source of charge, an electric
Field is defined everywhere in space.
Electric Field: The force per unit charge at some location in space.
http://buphy.bu.edu/
~duffy/PY106/2e.GIF
son.nasa.gov/tass/images/electric_fields2.jpg
Electric Field: The force per unit charge at some location in space.
Energy is stored in the electric field and energy can be transported
by the electric field! (over very long distances).
Electric Shielding: Because electric forces can be attractive or repulsive we can
shield objects from any external electric field!
For any conductor all of its net
charge (If any) resides on the
surface.
The charge is distributed so that
the electric field inside the
conductor is zero
Everywhere!
Metal wire cage
(Faraday cage)
-a conducting
Surface.
No electric fields allowed in here!
www.physics.gla.ac.uk/.../E3/pfarad1.gif
Electric Potential:
The electric potential energy per unit charge.
Just like 2 masses can have a gravitational potential energy
associated with their relative positions, 2 charges can have an Electrical
Potential energy associated with their relative positions!
+
h
PE =mgh
h
PE ~ q1q2/h
-
Surface of Earth
Gravitational Potential
Electric Potential
If we release the mass it will gain KE.
If we release the + charge (and “hold” the – charge) the + charge will gain KE!
Electric Potential:
The electric potential energy per unit charge.
The electric potential energy is the energy associated with the position of a
Charge in an electric field.
If I bring two similar sign charges together I must do work (because the
force is repulsive).
By doing so I increase the Electric potential energy associated with the charges.
+
+
q
+
+
d
+
If the charge q is doubled then the
Electric potential energy is doubled.
But the amount of potential energy
per electron will remain the same ->
this is the electric potential.
It is defined by the electric field
Electric Potential :
The electric potential energy per unit charge.
The Unit = the VOLT = 1 Joule per Coulomb
A 1 Volt battery generates 1 Joule of energy for every Coulomb of charge
passing through the battery.
The difference in electrical potential between 2 points (in space)
is called the voltage between those points.
Potential
1
Potential
2
d
Voltage = Potential 2 – Potential 1
If the force on any charge is different at
1 than at 2 then there is a voltage
difference between these two points
Electric Energy Storage- Capacitors
Simple parallel plate capacitor:
-Charge is distributed to each plate,
the amount determined by the battery voltage
and the capacitance of the device.
- Roll up it up and we have a cylindrical
capacitor used in almost every electronic device
for energy storage
- release of large amounts of charge in
a short time (large energy transfer- dangerous!)
Cameras, PCs, TVs, etc.
Amount of charges stored = C * Voltage, C =
"capacitance of the device“
Units of capacitance are coulombs per volt
Review Questions:
1. Why does the gravitational force between Earth and the Moon predominate
over electrical forces?
2. How does the charge of one electron compare to that of another electron. Are
two electrons different? How does the electron charge compare with the
charge of a proton?
3. How do the numbers of protons in the nucleus compare with the number of
electrons that orbit the nucleus?
4. What is an ion? Give an example of a positive and negative ion.
5. What is meant by saying charge is conserved?
6. What is meant by saying charge is quantized?
7. What particle has exactly one quantum unit of charge? How about charge 1/3?
8. How does 1 Coulomb of charge compare with the charge of a single electron?
Review Questions (cont’d):
9. How is Coulomb's Law similar to Newton's Law of Gravitation? Different?
10. Why are metals god conductors of heat and electrons?
11. What are materials such as glass and rubber good insulators?
12. How is a semiconductor different than a conductor or insulator?
13. What happens to electrons during any charging process?
14. Example of charging by friction?
15. Example of charging by contact?
16. Example of charging by induction?
17. What do we use lightning rods?
18. How does electric polarization differ from an electrically charged object?
Review Questions (cont’d):
19. What is an electric dipole?
20. How is the magnitude and direction of the electric field defined?
21. Why is there no electric field at the center of a charged solid spherical
conductor (e.g., a steel ball)?
22. When charges mutually repel and distribute themselves on the surface of a
conductor what effect occurs inside the conductor?
23. How much energy is given to 1C of charge that flows through a 1.5V battery?
24. A balloon may be charged to several thousand volts! Does this mean it
transfers several thousand joules?
25. Where is the energy stored in a capacitor?
Exercises!
1. Why do clothes often cling together after being in the clothes dryer?
2. When combing your hair you transfer electrons from your hair onto the comb.
Is your hair positively or negatively charged? How about the comb?
Can you create a large electric potential between the hair and comb?
3. The tires for trucks transporting gasoline and other flammable fluids are electrically
conducting. Why?
4. Strictly speaking, when an object acquires a positive charge by electron transfer,
what happens to its mass?
5. When you double the distance between a pair of charged particles what happens to
the force between them? Does the change in force depend on the sign of the charges?
Their magnitude?
6. When you double the charge on both particles in a pair what effect does this have
on the force between them?
Exercises (cont’d)!
7. Compare the electrostatic force on an electron by a proton in a hydrogen atom
with the force of gravitional acctraction between them.
8. Measurements indicate that there is an electric field surrounding the Earth. The
magnitude, E = 100N/C, and it points toward the center of the Earth. Given this, can
you say whether the Earth has a net negative, zero, or positive charge?
9. How can a charged atom attract a neutral atom.
10. Two Pieces of plastic, a full ring and half ring are net positively charged; the 1/2
ring has 1/2 the total charge of the full ring.
At the center of the ring the electric field is largest for which one?
11. Why may it be dangerous to touch the terminals of a high voltage capacitor on a
device after the device is turned off (unplugged and not connected to any batteries
or other power source)?