Staple Your Homework

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Staple Your Homework We will not accept any
unstapled HWs from now on..
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IIIB. Work and Energy Methods
Work-Energy Equation
Remember when we evaluate work due to gravity, it
always gives the same result
Independent of the path from i to f
The work done by gravity is then always
Potential Energy Energy associated with current
position of a body that can later be converted
into Kinetic Energy of the body
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Potential Energy
Generalize idea arising from gravity
Suppose we can express a force in terms of the
gradient of some scalar function
The work done by this force can then be written as
Work done only depends on the difference in the
potential energy V between points i and f
the Rush Limbaugh Force
the Jerry Falwell Force
the John McCain Force
Gravity
APPLIED FORCES
What would be a non-conservative force?
Barack Obama
FRICTION
Hillary Clinton
Air Resistance/Drag
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Another example Spring force (linear spring)
Force opposes displacement from reference (zero
force) position
k is the spring constant and is a property of
the spring itself
If equilibrium spring length is xo and spring is
stretched to length x then sx-xo
Spring/Elastic Potential Energy is
Independent of the path
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Spring does it have to be an actual coil of wire?
NO. Every solid material acts like a spring when
deformed by a small amount
Bar
Stretch Force / Constant S F / k1
Bar
Deflection Force / Constant S F / k2
Stiffness coefficient k depends on material
properties, shape and size of the bar (round?
Square? Hollow tube? Diameter/width length etc)
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Work-Energy Again
Body starts at si, vi ends at sf , vf .
Various forces acting during the motion along
some path
Divide forces into Conservative,
Non-conservative, Constraint
Plug in to work-energy equation
Work done by Non-Conservative Forces
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If there are no Non-Conservative Forces, then we
have
Conservation of (Mechanical) Energy
Non-conservative forces put energy into or take
energy out of the system so that the total energy
changes (it is not conserved)
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Bowling Ball starts from rest touching my nose
I will release the ball and stand still while it
swings
During motion, gravity acts tension in cord
neglect drag
Tension does no work since it is perpendicular to
motion at all times (neglect stretching)
Therefore, energy is conserved
Height y0 is NOT possible
(Would require negative kinetic energy ?
imaginary velocity)
I can safely stand and wont get hit unless
there is an earthquake that provides extra energy
to the bowling ball
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Work-Energy Applies to Systems of Interacting
Bodies
Total kinetic energy of all particles
Total potential energy of all particles
Total work done by all non-conservative forces
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Force P applied to lift mass m, which starts from
rest at the horizontal position
What is velocity of mass when it reaches the
vertical position?
(Neglect mass, and thus energies, of the
connecting rod)
Work-Energy applies
P is constant and in direction of path of handle
1.5 L
L
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Example Bungee Jumping life or death design
How fast is jumper going when he/she hits the
ground?
Bungee of length L30m initial height 75m mass
70kg
Bungee acts like a spring with k50 N/m
Forces gravity, spring force
h
Energy is conserved until hitting ground
Choose ground as y0
so yih
Lets look at some real data.
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Nick Curtin
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Class Lecture Notes will no longer be posted
on-line
because there is no electronic version
Powerpoint slides were used to help get all
students off to a solid start through the
additional ability to refer to class notes in
precise detail, and to allow the coverage of a
considerable amount of material in a fairly short
time
Tell your friends and classmates who are not
here.