Work & Energy
"There is nothing new to be discovered in physics now,
All that remains is more and more precise
measurement.”
-Lord Kelvin
“Time is nature’s way of making certain that everything
doesn't happen all at once.”
-Woody Allen
Importance of
Numbers
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Debt: 9.2 x 1012 $
Work & Energy
A force is required to accelerate a body.
The exertion of a force over a distance is called work.
This requires energy.
W=Fxd
Work = Force x distance
Work
Cheryl Haworth lifts 297.6* lbs
a distance of 2 meters.
How much work does she do?
W=Fxd
d = 2m
F = m* x a = m x g = 135 kg x 9.8 m/s2
W = Fxd=mxgxd
= 135 kg x 9.8 m/s2 x 2 m
= 2657 Joules
= 2657 Joules  (1 Cal/4186 J)
= 0.635 Calories
*A mass of 135 kg causes a gravitational force
of 297.6 lbs on the surface of Earth
Energy
• Energy is required to do work.
• The energy added to the object equals the work done.
• Energy required to move something a distance against gravity
is called gravitational potential energy
Gravitational Potential Energy:
E=W=Fxd
= (m x g) x h
h = height
g = * 9.82 m/s2
m = mass
e.g. E = 1000 m * 70 kg * 9.82 m/s2
= 6.87x105 Newton meter
* On Earth’s surface
Energy & Work Units
Energy is measured in different units. The most common are:
Joules (J)
= Newton-meter (F x d)
*Calories (Cal)
= 4186 J
Foot-pounds (ft-lbs)
= 1.356 J
British Thermal Units (BTU)
= 1055 J
Kiloton of TNT
= 4.184x1012 J
• Calories with a small “c”, cal = Cal/1000.
• All foods are listed as big C calories or kilocalories (in Europe)
Potential Energy
Cheryl Haworth lifts 297.6* lbs
a distance of 2 meters.
How much energy did the bar gain?
E=W=Fxd
E = Fxd=mxgxd
= 135 kg x 9.8 m/s2 x 2 m
= 2657 Joules
= 2657 Joules  (1 Cal/4186 J)
= 0.635 Calories
*A mass of 135 kg causes a gravitational force
of 297.6 lbs on the surface of Earth
Some Kinds of Energy

Kinetic Energy – the energy of moving objects. This energy is:
E = (1/2) m v2

Heat, or thermal energy – of warm bodies.

Chemical Energy – of chemical reactions (involving electrons)

Gravitational Potential Energy – of a gravitational field. E = m g h

Electromagnetic Energy – energy associated with electric &
magnetic forces.

Mass Energy – all objects have energy by virtue of their mass, the
energy released in nuclear explosions, involving nuclei.
Why discuss Energy?
It is transferable and conserved.
Kinetic Energy
E = 1/2 mv2
E = energy (Joules)
m = mass (kilograms)
v = speed (meters/sec.)
Example:
Griffith-Joyner runs 100 m in 10.61 seconds.
What is her Kinetic Energy?
Her mass was 60 kg and height 5’ 6’’
Florence Griffith-Joyner (born Delorez Griffith)
sprints to the finish line
1 Joule = 1 kg meter2/second2
Kinetic Energy
E = 1/2 mv2
E = energy (Joules)
m = mass (kilograms)
v = speed (meters/sec.)
Example:
Griffith-Joyner runs 100 m in 10.61 seconds.
What is her Kinetic Energy?
Her mass was 60 kg and height 5’ 6’’
Florence Griffith-Joyner (born Delorez Griffith)
sprints to the finish line
1 Joule = 1 kg meter2/second2
v = d/t = 100/10.61 = 33.93 m/s
E = 0.5 * 60 kg * (33.93 m/s)2
E = 0.5 * 60 kg * (33.93 m/s)2
= 34,500 Joules = 3.4 x 104 Joules
Another Kinetic Energy Example
A ball with mass of 0.5 kg is dropped from a distance of 10
meters. What is its kinetic energy when it hits the floor?
We know that the ball falls towards the Earth with a constant
acceleration of 9.8 meters/sec2. Last class we showed that the
velocity gained after traveling a distance d is given by
v  2ad  2  9.810  14meters/sec
The kinetic energy is then
1
E  mv 2  0.5  0.5  14 2  49 Joules
2
Potential Energy Example
A NATS102 professor lifts a ball with mass 0.5
kg a height of 10 meters. How much potential
energy does the ball gain?
W = mah = 0.5  9.8  10 = 49 Joules
But this is the same as the kinetic energy the ball
gained by falling 10 meters.
What’s going on???
Kinetic Energy Examples
1.
A ball with mass of 0.01 kg traveling at 100 km/hour.
What is its Kinetic Energy?
First convert v=100 km/hour to unit of meter/sec: Note
100 km = 100x1000 m = 100,000 m
Note 1 hr = 3600 seconds
Thus:
v=100,000 m/hour x 1hour/3600 sec=28 meters/sec
And:
E = 0.5 x 0.01 x (28)2 Joules
E = 3.9 Joules
A more interesting example
2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000
kg/m3, traveling at 30 km/sec. What is its Kinetic Energy?
First: what is the asteroid’s mass?
mass = density x volume
mass = density x (4/3)  R3
where R = radius = (1/2) diameter
Compare your answer to the energy of that of 15
kilotons of TNT, which is the energy of the atomic
bomb dropped on Hiroshima.
Mass and Energy
One of Einstein’s many contributions was the
recognition that mass is simply another form of
energy. Mass and other forms of energy can be
interchanged, as can kinetic energy, potential energy,
heat, etc. The amount of energy contained in an
object with mass m is given by the famous equation
E = mc2
where c is the speed of light. The speed of light is
equal to c = 3108 meters/second.
The energy of a NATS102 Student
A NATS102 student has a mass of 80 kg (weight of 170 lbs). According to
Einstein’s equation, he/she has an energy of
E = mc2 = 80 kg (3108 m/s)2 Joules
E = 7.21018 Joules
convert to kilotons of TNT
E = 7.21018 J x (1 kton/4.1841012 J) =1.71018 kilotons
This is enormous. The tremendous amount of energy contained in matter is
the reason for the power of nuclear bombs, reactors, stars, supernovae, etc.
Conservation of Energy

Energy is neither created nor destroyed but only transformed
from one form to another.

In a closed system, the total amount of energy is conserved. If
we add up the amount of energy in a closed system including
all of the different forms, the sum will not change with time.

The total amount of energy never changes, it only moves from
place to place and from one form to another.

Conservation of Energy applies not just to kinetic and potential
energy, as in the example, but to all kinds of energy (heat,
chemical, …)
Conservation Laws in Physics



Conservation laws are powerful tools
Most fundamental quantities (mass, energy, &
momentum) satisfy conservation laws.
Conservation laws are easy – no vectors
Conservation of Energy
m = 50.9 kg
Power
The rate of doing work or
expending energy
P = Energy/Time
Rock climbers
gain a lot of
potential energy
but do so slowly,
at low power
Power
Training
Cyclists do work more
quickly than rock
climbers. They
expend more power.
Lance Armstrong
expends about
10,000 Calories in
a 2 hour race. This
corresponds to a
power of roughly 6
kilowatts.
Racing: Tour de France
Lance training in Arizona
Niagara Falls
570,000 kg of water descend every second.
The falls height is 55 meters.
Thus the potential energy of 1 kg of water is
E=mha=19.855 J = 539 J.
The total power is then
P=570,000539 Joules/sec=3.1108 Watts
or 310 Megawatts.
Climbing out of the Grand
Canyon
How big a lunch is needed?
Energy from lunch =
Work to be done
W=
=
=
=
mgh
(62 kg)(9.82m/s2)(1500 m)
9.1x105 Joules
218 Calories
That is,
1 peach & a glass of milk
That’s it?
Nope – we’re inefficient
Humans work at roughly 15%
efficiency. The rest of the
energy goes into heat and
non-work productive
movement.
So, to climb the Grand Canyon,
we need 1450 Cal !
Two club sandwiches, one egg, 1
fruit and 1 glass of milk.
A more interesting example
2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000
kg/m3, traveling at 30 km/sec. What is its Kinetic Energy?
First: what is the asteroid’s mass?
mass = density x volume
mass = density x (4/3)  R3
v=30 km/sec = 30,000 meters/sec
E = 0.5 x 1x1013 x (30,000)2 Joules
E = 4.5x1021 Joules
Convert to kilotons of TNT
E = 4.5x1021 Joules x (1 kiloton/4.184x1012 Joules)
E = 2.2x108 kilotons of TNT
The atomic bomb dropped on Hiroshima released and energy of 15
kilotons