Work, Energy, and Power
“It is important to realize that in physics today, we have
no knowledge of what energy is.” - R.P. Feynman
Work and Energy
Work and Energy concepts (and also
momentum, later) provide an alternative,
easier approach to mechanics!
WORK
• Causes transfer of energy
(between masses) or transforms
energy (from one type to another).
• work is the amount of energy
transferred by forces.
ENERGY
• Measures a change in the condition
of matter (change can be in velocity,
position, mass, etc.)
• There is no such thing as pure energy.
Energy is the measure of a change
(and force is the agent of the change).
Energy Example: Driving a Car
SPEED UP
SLOW DOWN
‘ROUND A CORNER
F
d
d
F
F
F and d
are parallel
F and d
are opposite
car gains
kinetic energy
car loses
kinetic energy
d
F and d
are perpendicular
car maintains
kinetic energy
Energy Example: The Launch of a Rocket
LIFTOFF!
d
SPEED!
Fa
ORBIT!
d
d
Fg
Fa
F and d
are parallel
F and d
are parallel
F and d
are perpendicular
rocket gains
potential energy
rocket gains
kinetic energy
rocket has constant
energy (circular orbit)
Work
Work depends on three things:
• force on an object
W  Fd cos
• displacement of an object
• angle between the force and displacement
(force must cause the displacement)
Units (metric or SI)
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applet
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applet
1 joule  1 newton  1 meter  1 N  m
• work is a scalar quantity, but can be
positive, negative, or zero because it
represents the amount of energy change.
work is positive when 0˚≤ θ < 90˚
work is negative when 90˚< θ ≤ 180˚
work is zero when θ = 90˚
Fk
Fn
Fa
PHYSICS
Fg
d
Which force does positive work?
Which does negative work?
Which does zero work?
Kinetic Energy
Kinetic energy is the energy of motion of matter
(translational) Kinetic Energy - depends on the motion of
macroscopic objects (e.g. a car in motion) moving linearly
Wnet  Fd
F  ma
Wnet  mad
v f 2  vi 2  2ad
Wnet  m 12 (v f 2  vi 2 )
work, dynamics, kinematics!
KE  12 mv 2
Wnet  KE
in joules mass velocity
WORK-ENERGY
THEOREM
Thermal Energy - depends on the motion of microscopic objects
(e.g. atomic vibrations). Technically not the same as heat.
in joules
TE  Fk d
friction
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applet
distance
Potential Energy
Potential energy is the energy of position of matter
Gravitational Potential - depends on the
position of mass in a gravitational field
g field
in joules
GPE  mgh
mass
height
Elastic Potential - depends on the
position of mass on an atomic scale
in joules
EPE  12 kx 2
spring position
constant
Power
Power is the rate at which work is done (or energy is used)
W
P
t
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web page
Units (metric or SI)
1 watt 
1 joule
J
1
1 second
s
Power can also be expressed in
terms of force and velocity
W Fd cos 
P

 Fv
t
t
Conservation of Mechanical Energy
Mechanical energy is
the sum of kinetic and
potential energy.
ME  KE  PE
Conservative forces
(gravity, spring force)
keep mechanical energy
constant.
Potential and kinetic
energy may change, but
the total mechanical
energy does not change.
KEi  PEi  KE f  PE f
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animation
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applet
Conservation of Mechanical Energy
Example
A spring with constant 800 N/m is
compressed 10 cm. It is released
against a cart with mass of 0.25 kg that
moves along a track without friction.
What is the cart’s speed when it
leaves the spring?
EPEi  KE f
1
2

1
2
kxi 2  12 mv f 2
(800)(0.10)2  12 (0.25)v f 2
v f  5.66 m/s
At what height above the original release
point does the cart come to rest?
What is the cart’s speed when it
reaches the top of a 0.75 m high hill?
KEi  KE f  GPE f
1
2
mvi 2  12 mv f 2  mgh
1
2
(0.25)(5.66)2  12 (0.25)v f 2  (0.25)(9.8)(0.75)
or
1
2
mvi 2  mgh f
1
2
(0.25)(5.66)2  (0.25)(9.8)h f
h f  1.63 m
1
2
mvi 2  mghi  mgh f where hi  0.75 m
vi  4.16 m/s
kxi  mv f  mgh
2
1
2
or
v f  4.16 m/s
1
2
KEi  GPE f
2
or
1
2
kxi 2  mgh f
Law of Conservation of Energy
Non-conservative forces (friction, applied, normal, tension)
change the mechanical energy, but total energy remains constant.
W  KEi  PEi  KE f  PE f  TE
result of applied or
normal or tension
result of gravity
or spring force
result of
friction
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animation
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animation
Law of Conservation of Energy
Examples (Assume there is zero air friction in these problems)
A 75-kg Olympic ski jumper starts
h  d sin   100 sin 30Þ 50 m
from rest and glides down a 30˚
GPEi  KE f  TE
incline 100-meter long. The track has
surface friction. If the jumper leaves
mghi  12 mv f 2  Fk d
the track with a velocity of 28 m/s,
(75)(9.8)(50)  12 (75)(28 2 )  Fk (100)
what is the average force of kinetic
friction on the skies from the track?
Fk  73.5 N
In frustration, a physics student
shoves a 1.2-kg textbook with a force
of 14 newtons across a 0.5 meter wide
desk that has no surface friction. If
the book lands on the ground with a
velocity of 5.2 m/s, how high is the
desk above the ground?
Honors: A 400-g wood block is
attached to a spring. The block can
slide along a table with coefficient of
friction 0.25. A force of 20 N
compresses the spring 20 cm and the
block is released. How far beyond
the equilibrium position will the
spring stretch?
W  GPEi  KE f
Fd cos  mghi  12 mv f 2
(14)(0.5)cos 0Þ(1.2)(9.8)(hi )  12 (1.2)(5.2 2 )
hi  0.784 m
k  Fsp / xi  20 / 0.2  100 N/m
EPEi  EPE f  TE
1
2
kxi 2  12 kx f 2  Fk (xi  x f )
Fk   k mg  (0.25)(0.4)(9.8)  0.98 N
1
2
(100)(0.2 2 )  12 (100)(x f 2 )  (0.98)(0.2  x f )
x f  0.18 m