Download Chapter 7: Work and Energy

Chapter 7 Lecture
Chapter 7:
Work and
Energy
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Goals for Chapter 7
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Overview energy.
Study work as defined in physics.
Relate work to kinetic energy.
Consider work done by a variable force.
Study potential energy.
Understand energy conservation.
Include time and the relationship of work to
power.
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Introduction
•  In previous chapters, we studied motion.
•  We used Newton's three laws to understand the
motion of an object and the forces acting on it.
•  Sometimes this can be hard.
•  We introduce energy as the next step.
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An Overview of Energy
•  Energy is conserved.
•  Kinetic energy describes motion and relates to the mass
of the object and its speed squared.
•  Energy on earth originates from the sun.
•  Energy on earth is stored thermally and
chemically.
•  Chemical energy is released by
metabolism.
•  Energy is stored as potential energy in
object height and mass and also through
elastic deformation.
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A Study of Energy Transformation –
Figure 7.4
•  This transformation begins as
elastic potential energy in the
elastomer. It then becomes
kinetic energy as the projectile
flies upward. During the upward
flight, kinetic energy becomes
potential until at the top of the
flight, all the energy is potential.
Finally, the stored potential
energy changes back to kinetic
energy as the projectile falls.
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Internal Energy Can be "Lost" as Heat
•  Atoms and molecules of a solid can be thought of as
particles vibration randomly on spring like bonds. This
vibration is an an example of internal energy.
•  Energy can be dissipated by heat (motion transferred at
the molecular level). This is referred to as dissipation.
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What is "Work" as Defined in Physics?
•  Formally, work is the product of a constant force
F through a parallel displacement s.
•  Work is the product of the component of the
force in the direction of displacement and the
magnitude s of the displacement.
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Consider Only Parallel F and S – Figure 7.9
•  Forces applied at angles must be resolved into
components.
•  W is a scalar quantity that can be positive, zero,
or negative.
•  If W > 0 (W < 0), energy is added to (taken from)
the system.
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Applications of Force and Resultant Work –
Figure 7.10
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Sliding on a Ramp – Example 7.2
•  Please refer to the worked example at the
bottom of page 186.
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Work Done By Several Forces – Example 7.3
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Work and Kinetic Energy
•  Unbalanced work causes kinematics.
•  Work-energy theorem:
•  The kinetic energy K of a particle with mass m moving
with speed is
During any displacement of
the particle, the work done by the net external force on
it is equal to its change in kinetic energy.
•  Although Ks are always positive, Wtotal may be positive,
negative, or zero (energy added to, taken away, or left the
same).
•  If Wtotal = 0, then the kinetic energy does not change and
the speed of the particle remains constant.
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Work and Energy Related – Example 7.4
•  Using work and energy to calculate speed.
•  Returning to the tractor pulling a sled problem of
Example 7.3:
•  If you know the initial speed,
and the total work done, you
can determine the final speed
after displacement s.
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A Pile Driver Application – Example 7.5
•  Refer to the worked example on pages 191–192.
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Work Done By a Varying Force
•  In Section 7.2, we defined
work done by a constant
force.
•  Work by a changing force is
sometimes considered.
•  On a graph of force as a
function of position, the total
work done by the force is
represented by the area
under the curve between the
initial and final positions.
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Work Done By a Varying Force
•  In Section 5.4, we learned that
force due to elongation/
compression of a spring
followed Hooke's
law:
•  As seen, this is a prime example of
a varying force. The work done by
a stretching/compressing
a spring is equal to the area of
the shaded triangle, or
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Work Done on a Spring Scale – Example 7.6
•  Energy may be stored in compressed springs on
a bathroom scale.
•  Refer to the worked example on page 194.
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Potential Energy
In cases of conservative
forces (gravity or elastic
forces), there can be "stored"
energy due to the spatial
arrangement of a system, or
potential
energy.
• 
Gravitational potential energy
(Ugrav), near the surface of the
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Potential Energy
•  The change in the potential energy due to
conservative forces is related to the work done
by the net force:
•  If only conservative forces act, then by the
work-energy theorem we can define the total
mechanical energy:
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A Solved Baseball Problem – Example 7.7
•  When the ball, with initial
When the ball, with initial
speed i is thrown straight
upward, it slows down on the
way up as the kinetic energy
is converted to potential
energy
(mgy>0).
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At the top, the kinetic energy
is zero and potential energy is
maximum.
• 
On the way back down, the
potential energy is converted
back to kinetic energy, and
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Conservation of total
Conservation
mechanical energy
of total
Energy Stored in Spring Displacement –
Energy
Stored in Spring Displacement –
Figure 7.25
•  Elastic stored energy stored
•  in a spring can be related to
position.
• 
(Hooke's
Elastic stored
law), the
energy
elastic
stored
in a spring can be related to
position.
• 
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Potential Energy on an Air Track with Mass
and Spring
energy, we use this to
find the final state at any
position.
• 
Using conservation of
total mechanical energy:
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Conversion and Conservation – Figures
7.27 and 7.28
•  As kinetic and potential energy are interconverted,
dynamics of the system may be solved.
Refer to the worked examples on page 202–203.
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Conservative and Nonconservative Forces
•  In the previous section, we discussed that if we
had
In only
the previous
conservative
section,
forces
we acting,
discussed
thenthat
we if we
had only conservative forces acting, then we
energy.
•  If we have nonconservative forces which do
work, we have to add this to the total energy:
•  Wother is the work done by nonconservative
forces (e.g. friction).
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Problems With Nonconservative Forces –
Example 7.12
• Problems With Nonconservative Forces –
now we also include the work done an external, a
This is the same problem as Example 7.8, but
now we also include
nonconservative
force
the
F.work done an external, a
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In addition to the
spring force, there is
a constant force F
Wf = ( K f + U f ) − ( K i + U i )
Wf =
(
1
2
) (
mυ f2 + 12 kxf2 −
1
2
mυ i2 + 12 kxi2
where Wf = Fx > 0
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)
Conservative Forces II – Figure 7.35
The work done by a conservative force is
independent of the path taken.
•  When the starting and ending points are the
same, the total work is zero.
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•  When a quantity of work ΔW is done during a time interval
•  When a quantity of work ΔW is done during a time interval
or work
per unit
is: [J/s]
•  Units of watt [W], or P
1 avwatt
= 1 joule
per time
second
•  The rate at which work is done is not always constant.
•  Units of watt [W], or 1 watt = 1 joule per second [J/s]
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Power – Considers Work and Time to do It
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•  Example 7.16: A marathon stair climb
Example 7.16: A marathon stair climb
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If the runner is initially at
rest and ends at rest, the
work done by the runner is
equal toonthe
gravity
thework
runner.
done by
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