Isaac Newton almost single-
handedly discovered the laws of
physics pertaining to mechanics.
But, one concept that he missed
was ENERGY!
So… what is ENERGY? We use
the term in many different ways…..
full of
…. We speak of a person who is “_______
energy
_________.”
energy crisis
….. We speak of an “_____________”, as
natural resources
non-renewable ________________ such as
coal, oil & natural gas become more scarce.
_________________
alternative energy sources
…. We speak of _____________________,
hydroelectric nuclear
such as, ____________ energy, ________
solar wind
energy, _____ energy, _____ energy, etc.
(What are the “pros” and the
“cons” of each type?)
A Physicist’s Definition of Energy
Energy is the capacity or ability to
do work
__________. When work is done,
transferred
energy is ___________ from one form
to another. This transfer can never be
100 % efficient which is why no one
______________,
has been successful at discovering a
“perpetual motion machine”!!
Units of Energy:
In the SI/Metric system, like work, energy is
Joules
measured in _______.
Other common units of energy are the:
BTU
• ______ or British Thermal Unit ( the energy
required to raise 1 pound of water 1° F)
1 BTU 1000 Joules
Kilocalorie
•____________ (the energy required to raise
1 kilogram of water 1°C.)
When food labels speak of “calories”, they
Kilocalories
are actually “____________!”
1 Kilocalorie (a food calorie) 4000 Joules
From a European
Candy Bar…
Where do the calories (energy) that we eat
ultimately come from?
Sun
The _____! Green plants “capture”
energy from the sun in a process called
photosynthesis
______________.
How do scientists measure the calorie
(energy) content in the food we eat?
Bomb Calorimeter
With a “_____________________”….
So how does it work?
The food is dried, ground into a
powder, and placed into the
calorimeter (a strong metal
container surrounded by water).
The calorimeter is then pumped full
of oxygen at high pressure and the
food is ignited! The explosion
results in an energy transfer from
the food into heat. By measuring
the water’s increase in
temperature scientists can
______________,
heat
calculate the _______ generated
calorie
and thus the original __________
content of the food!
From such experiments, scientists have
found that:
•1 gram of fat contains approximately 9 “calories”.
•1 gram of pure alcohol contains
7 “calories”.
•1 gram of protein or carbs contains 4 “calories”.
The average 120 pound person burns about
55 “calories” per hour while RESTING.
Jogging will burn off about 8 TIMES that per
hour! ... Let’s say you eat a Whopper with
cheese for lunch (760 calories!) How long will
it take to “burn off” all the calories?
Examples of Energy Transfer:
Work
1. Bow and Arrow: ______ is
required to pull the bowstring back, a
the person
transfer of energy from __________
stored potential
to ______ (or ________) energy in
the bow. When the bowstring is
released, the energy has been
motion
transferred into the arrow’s _______
kinetic
(or _______ ) energy.
2. Car skidding to a stop:
Kinetic
_______ energy is transferred
into thermal (heat) energy
___________
Heat loss
( _____ _____).
Potential Energy (PE)
Stored energy of position…has the
“potential” to do work….. 2 types:
Gravitational
___________
Spring (elastic)
_______________
Gravitational Potential Energy:
The potential energy given to an object a
height, h, above the “ground” must equal
the work done to lift the object a height, h…
mass, m W=Fd
W = (mg)h
_____
h
mgh
So… PEg = _____
Spring (Elastic) Potential Energy:
“Elastic” = capable of being stretched and then
able to resume former shape.
Examples: Springs, rubber bands, bungee cords,
diving boards (Demo – saw blade!)
What is the relationship between the force, F
applied to a spring & the distance stretched X?
Force (N) X (cm)
1 10
2 20
3 30
4 40
Graph the Data:
Clearly, the force (F) and the
F (N)
directly
“stretch” (X) are _______ related.
4
3
2 Y = mx + b becomes…
1
.1 .2 .3 .4 .5 X (m) F=KX
3/0.3 = 10
K = ___________N/m ….. where K is called the
“spring constant” (the slope)
• Example: if K = 300 N/m, a 150 N force would
0.5 m
stretch the spring _______. Demo:
Car
• The greater the “K”, the stifferthe spring.
_____ Spring
So… how can we calculate the potential
energy stored in a spring?
The energy stored in a spring must be the same
work
as the _______ done to stretch (or compress)
the spring. Since the force in a spring varies as
average
it is stretched, the ________ force must be
used when calculating the work….
W Fav d
1
W KX X
2
1
1
So.. PEspring KX
2 X = distance
W KX 2 stretched or
2 2 compressed
Video: Energy of the Spring
Kinetic Energy (KE): Energy of motion
Until the early 1700’s, scientists believed that
the energy of motion was proportional to the
velocity of an object. But a series of
experiments performed by a Dutch physicist,
Willem Gravesande (1688-1742), seemed to
suggest otherwise.… He dropped spherical lead
masses onto beds of clay from different heights
to see how big of a dent they made in the clay.
He found that if a ball hit the clay traveling twice
four
as fast, it left a dent ______ times as deep,
indicating that the energy of motion seems to be
square
proportional to the _________ of the velocity!
How is kinetic energy measured, then?
A derivation....
F ma
Multiply both sides by “d”… F d ma d
1 2
If Vi = 0, d = ?... W ma at
2
W mat
1 2
Rearranging terms….
2
1 2
What is acceleration times time?... W mv
2
Since energy is the capacity to
1 2
do work, 1/2mv2 must be a KE mv
measure of motion energy! 2
Law of Conservation of Energy:
created ________….
Energy can NOT be _______ or destroyed
Only transferred from one form to another.
If there are no external forces (such as
friction) doing work on a system, then ….
PEi KEi PE f KE f
….where i = initial and f = final
If there is friction, then friction does work on
the system (Wf), resulting in “heat loss”…
HeatLoss W ff PEii KEi PE ff KE ff
HeatLoss W PE PE KE
Simulation from “The
Examples: (1) The Pendulum…. Physics Classroom”
website
Demo: Hold against chin and release!
top
PE is maximum at the ____ of the swing.
bottom
KE is maximum at the _______ of the swing
PEtop = KEbottom
Demo: If an obstruction hits the pendulum’s string at the
bottom of its swing, how high will the mass go now?
(2) All the ramps below are 5 m high. Find the
speed of the block at ground level for each case
IF there is NO friction. Find the speed of case 1
by recalling free fall (assume g = 10 m/s2). Think
about energy conservation for Case 2 and 3.
10 10 10
The speed at the bottom depends ONLY on
height
the _________ from which the block fell,
path
NOT on the actual ________ taken.
(3) Which block gets to the
bottom first, assuming no
friction?
A!! Since the velocity at the
d
bottom must be the same,
d/t must be the same…
d
t
(4) A bead slides due to
t
gravity along an upright, Dh
Only ____
frictionless wire. It starts
matters!
from rest at A. How fast is it
10 m/s
traveling at B? ______
10 m/s
D? 10 m/s E? ______
_____
Maximum Speed at _____? C !
Simulation from “The
(5) What happens to the skier once Physics classroom”
he hits level ground with “unpacked website
snow”? Where does the energy go?
stops
He ______ because his kinetic energy is
heat
transferred to ______.
(“W” in the simulation is the “Work of friction”)
(6) In certain windy locations,
the wind is used to generate
electrical power. Does the power
generated affect the speed of the
YES
wind? _____!
If yes, would locations behind the wind-powered
generators be windier or less windy because of
the generators?
Less windy… Energy must be conserved!
Some of the wind’s kinetic energy is
converted into the blades’ kinetic energy
and ultimately into electrical energy.
Wind “Farm” on I-39 between
Bloomington/Normal and Rockford
50.4 MegaWatts of Power (63 wind turbines;
800-kilowatts each), enough for 15,000 homes.
Ann Pataky and Caitlin Meneely, Class of 2007
From The News-Gazette, April 29, 2007
Closest Wind Farm to
us… between
400 MegaWatts of
Gibson City and
Power; enough for
Bloomington/Normal
120,000 homes
Required Wind
Speeds: 12 – 55 mph
(7) The source of energy for hydroelectric
gravitational potential
power generation is _____________________
energy of the water
______________________.
Hoover Dam on
Colorado River
(8) A basic understanding of energy can
help explain why the terrorist acts of 9/11
were so destructive…
(#’s from “Jupiter Scientific” website and AP newspaper article)
Energy Release in Initial Impact:
An MIT analysis determined that the first plane
was traveling 430 mph, and the second 540 mph
(which may help explain why the tower hit second
actually fell first.) Using an approximate number
of 500 mph (225 m/s), and the weight of a Boeing
767, which is 400,000 pounds (180,000 kg), the
kinetic energy can be calculated….
KE 180,000kg225m / s 4.5 x10 J
1 2 9
2
For comparison purposes, 1 TON of TNT is
equivalent to about 4 billion Joules. Since
almost all of the kinetic energy was deposited
into the tower upon impact, then, the equivalent
of a little more than 1 TON of TNT was
released at impact.
Energy Release in Resulting Jet Fuel Fire:
Each jet could carry approximately 24,000 gallons
of jet fuel, but for transcontinental flights, the
tanks are only 2/3 full, so each jet was carrying
about 16,000 gallons of fuel. The energy content
of jet fuel is 130,000 BTUs per gallon. One BTU is
a little more than 1000 J…
2x1012 J _______
So, approximately ________ (2 trillion Joules)
of energy were released in each fire. This is the
525
equivalent of about ____ TONS of TNT. The
heat generated was enough to melt the steel
support, causing the eventual collapse….
Energy Released in the tower’s collapse:
The gravitational potential energy stored in the
standing skyscraper was primarily converted into
kinetic energy of flying debris, heat, and sound
energy. Each tower weighed about 600,000 tons,
which is roughly 550 million kg. The height of
each tower was approximately 400 m….
The “h” in the formula PE = mgh is actually
half
______ the height of the building. Why?
Must use the height of the CG (center of gravity)
___________________________________
6
PE 550 x10 kg 9.8m / s 2
200 m 1x10 12
J
250 tons
This is an energy equivalent of _________of TNT.
Summary: Event Energy Released
Initial Impact 1 ton of TNT
Jet Fuel Fire 525 tons of TNT
Collapse 250 tons of TNT
Total for one tower 776 tons of TNT
For both towers, the total energy release was the equivalent of
1550 TONS of TNT, which is approximately 1/13th the destructive
power of the atomic bomb dropped on Hiroshima in 1945!
(9) Calculation of a Car’s Stopping Distance:
Initially: Finally:
Vi Vf = 0
d
kinetic
The energy transfer here is from ________
heat loss or Wfriction
energy to _________________.
KEi HeatLoss W f
1 m 2
mvi F f d for d… d vi
2 Solving
2 2F
f
m 2 m 2 1 2
d vi vi
2 mg vi
2g
2F
f
The relationship between the stopping distance
and the initial velocity is NOT linear! Instead, d is
square
proportional to the ________ of the initial velocity.
m 2 m 2 1 2
d vi vi
2 mg vi
2g
2F
f
The relationship between the stopping distance
and the initial velocity is NOT linear! Instead, d is
square
proportional to the ________ of the initial velocity.
Example: If the average stopping
distance for cars traveling 20 mph is
21 feet, what is the predicted stopping
distance for a car traveling 40 mph?
doubled
The speed has __________, but since the distance
square of the speed
is proportional to the ____________________, the
quadruple 21 x22=84 ft
stopping distance will __________ (_____________)
82
(Actual measured average stopping distance for this speed is ___ ft!!)
What would the predicted
required stopping distance be
for a car traveling 80 mph?
Compared to the original speed of
quadrupled
20 mph, the speed has __________,
16
so the stopping distance will be _____
21 x 42=336 feet!!
times greater (_________________).
328
(Actual measured average stopping distance for this speed is ____ ft!!)
Or… compared to 40 mph, the speed
has doubled so the stopping
________,
84 x 22=336 feet
distance will be _________________.
(10) The Physics of Roller Coasters:
Most roller coasters begin with a
motor pulling the coaster up a very
high lift hill, which gives the coaster
potential energy
a large _________________. The
coaster then traverses the track
simply under the influence of
gravity converting its potential
_______,
kinetic
energy into ________, and then
repeating this process numerous
times. However, it can never reach
that initial height of the lift hill again.
friction
Why? __________!
Even though friction makes the ride slow over time, the
ride is still exciting towards the end, because the
reduced
radius of the twists and turns is _________! (tighter curves)
_______
Example: The “Batman” ride at 6 Flags, St. Louis
i (a) Assuming no friction
h=25.6 m and that the coaster
essentially starts from
PE = rest at the top of the lift
0 line
f hill, calculate the speed
at the bottom of the first
drop.
PEi KEi PE f KE f
mgh 1 mv 2
2
9.8m / s 25.6m 2
2 1 v2
v 22.4m / s 50mph
(b) According to
Six Flags, the radius
at the bottom is
R
R = 20 m. What
acceleration would a
rider feel at the
bottom? How many
G-Forces is that?
ac
v
22.4m / s
2 2
R 20m
ac 25m / s 2.6 g' s
2
3.6 G Forces would read at that point!)
(What a “spring accelerometer”
i f
h=25.6 m (c) Again, assuming
h=18.1 m no friction, calculate
PE =
0 line the speed of the
coaster at the top of
the loop.
PEi KEi PE f KE f
mghi mgh f 1 mv2
2
9.8m / s 25.6m 9.8m / s 18.1m 2
2 2 1 v2
9.8m / s 25.6m 18.1m 2
2 1 v2
v 12m / s OR: mgDh 1 / 2mv 2
(d) Assuming no friction,
and that it begins from
Demo!
rest, calculate the
minimum height, h, for a mg
roller coaster to JUST h
barely make it around a
circular loop of radius, R. R
In order to use the conservation of energy, we must first know the
velocity at some point. We can use circular motion to find the min.
velocity at the top of loop since the coaster would no longer be
touching the track there…. The only force, then, acting on the
mg
coaster at the top is ____. This force is the centripetal force.
____________
2
v
Fc mg m v gR vtop,minimum gR
2
R
PEi KEi PE f KE f (f = top
of loop)
mgh mghtop 1 mv2 top,min
2
Substitute in the expression we derived for the minimum
velocity at the top AND the height at the top (the
2R
diameteror ____:
________
gh g 2R 1
2
gR
h 2.5R
Collisions: A couple definitions…
Elastic Collision - A collision in which
momentum kinetic energy
__________ AND ________________
are conserved. This never happens in
our everyday, macroscopic world… only
in atomic-level interactions!
Inelastic Collision – A collision in which
momentum
___________ is still conserved, but
kinetic energy
_______________ is NOT (lost to heat).
The maximum kinetic energy loss occurs
when the objects “stick” together
______________.
Collisions between hard steel balls, such
as in the device known as “Newton’s
Cradle”, are very nearly elastic, so both
momentum AND kinetic energy are
essentially conserved….
When one ball is pulled back and
released, one ball comes out on the
other side…
When two balls are pulled back and
released, two balls come out on the
other side…
When one ball is pulled back and
released, why don’t two balls come out
on the other side with half the speed?…
kinetic energy
…. Because in that case, _____________
would NOT be conserved.
If clay were placed between the balls,
so that the balls stick together, is kinetic
energy still conserved?
1 ball in with speed, v ¼v
4 balls out with speed, _____
m 1
mv 4m v
v 4
2
1
KE f 4m v
1 2 1
KEi mv
2 2 4
1 2
Clearly, KE is KE f mv
8
____________! 75
NOT conserved ___% of the KE was “lost”.
Example: A 50 gram bullet is fired into a heavy, 10 kg,
block of wood. After the collision, the block (with the
bullet imbedded in it) slides across the floor a distance of
1.2 m. The coefficient of sliding friction, , is 0.2.
(a) Calculate the initial velocity of the bullet.
Before Collision Just After Collision After Stopping
vi vf V=0
d = 1.2 m
momentum
Before we can use __________ conservation
energy
to find vi, we must first find vf using ________.
The kinetic energy after the collision must
equal the heat loss (Wfriction) during the sliding
____________________________.
d N d
1
mv f F f
2
2
mv f mg d
1 2
2
v f 0.2 9.8m / s 1.2m
1 2
2
2
v f 2.2m / s
Now, we can use momentum to find the other velocity…
m v=m v
0.05kgvi 10.05kg2.2m / s
vi 442m / s
(b) Calculate the kinetic energy before and just
after the collision. Was KE conserved?
KEbefore 0.05kg 442m / s 4880 J
1 2
2
KE after 10.05kg 2.2m / s 24 J
1 2
2
During the collision, there was a huge heat loss!
_________________