Phys1111

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Phys1111

• Chapter 6
• Energy and Work

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Energy
Energy is defined as the capacity to do
mechanical work

• Forms of energy
• Kinetic Energy (KE) energy of motion
• A moving car
• Rotating shaft
• Potential Energy (PE) stored energy or energy
  of position
• Gravitational potential energy
• A ball positioned above the ground
• Elastic potential energy
• Two objects connected by a spring
• Kinetic and Potential energies are both forms of
  Mechanical Energy

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Energy

• Other Forms of Energy
• Chemical energy
• Fossil fuels, food
• Nuclear energy
• The energy found in the atomic nucleus
• Thermal energy
• Hot object
• Light (or radiant ) energy
• Solar energy
• Electrical energy
• Batteries
• Electric generators

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Energy

• Energy transfer or conversion
• Energy is a conserved quantity, that is, the
  total amount of energy in the universe is a
  constant.
• Energy is not created or destroyed but can be
• Transferred from one object (or system) to
  another
• (a bat transfers energy to a ball, Sun transfers
  energy to Earth, etc.)
• Converted (transformed) from one form to the
  other
• (electrical to mechanical, chemical to
  electrical, mechanical to heat, etc.)

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Work

• work is
• the mechanical transfer of energy to or from a
  system by external forces.
• expressed as the product of a force and the
  distance through which it moves a body in the
  direction of that force

SYSTEM Motion energy kinetic energy
KE Stored energy potential energy
PE Mechanical energy Emechan KE PE
Energy transfer
Environment
Work W
System boundary
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Work
Component of the force in the direction of motion
?
?s
Work
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Work

• The SI unit of work is called joule (J)
• 1joule 1 Newton X 1 meter
• 1J 1Nm 1kg.m2/s2
• Work is a scalar quantity.

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Work
In one dimension
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Work
In General
Positive Work
?
?
Negative Work
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Work

• Example 1
• The figure below shows three forces applied to a
  block on a frictionless surface
• that moves to the right by 3m.
• What is the work done by each force?
• What is the net work done by the three forces?

F2 9.0N
60o
F1 5.0N
F3 3.0N
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Kinetic Energy
m
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Kinetic Energy
A bodies kinetic energy is defined to be half its
mass times the square of its speed v.
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Kinetic Energy

• Example 2
• Find the kinetic energy of
• a bullet of mass 5.0g moving at a speed of
  300m/s.
• a bullet of mass 5.0g moving at a speed of
  600m/s.
• a bullet of mass 2.5g moving at a speed of
  300m/s.
• a bullet of mass 5.0g moving at a speed of 300m/s
  to the left.

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Gravitational Potential Energy
y
B
?s yB - yA
yB
A
yA
0
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Gravitational Potential Energy

• Where
• m is the mass of the object
• g is the acceleration due to gravity
  (approximately 9.8 m/s2 at the earth's surface)
• y is the height to which the object is raised,
  relative to a given reference level (such as the
  earth's surface).
• choice of the reference level (coordinate
  frame) is arbitrary.
• gravitational potential energy will have
  different values depending on the choice of the
  reference level.
• The SI unit of work is also joule (J).

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Energy of a falling object
y
1
y1
?s y1 y2
2
y2
0
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Energy of a falling object
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Energy of a falling object
Thus
or
When gravity is the only force doing work on a
body the total mechanical energy is conserved.
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Energy of a falling object
Energy conversion for an object thrown vertically
upward
Kinetic Energy
KE
Total Energy
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Potential Energy
PE
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6
7
3
8
2
9
1
1
9
2
3
4
8
5
6
7
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Energy of a falling object

• Example 3
• A ball of mass 0.200kg is thrown vertically
  upward from the ground with an initial
• velocity of 10.0m/s. Neglect air resistance. Find
• the total mechanical energy of the ball,
• Its maximum height,
• Its speed as it returns to original level.

Additional Examples 6-2, 6-3
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Path independence of Gravitational potential
energy
d
?y
?y
?
The gravitational potential energy gained is the
same in either case it depends only on the
vertical displacement and not on the specific
path that displacement is achieved
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The Law of Conservation of Energy
The total amount of energy in the universe
remains constant Energy can change form but it
can never be created or destroyed
Energy is also conserved for an isolated system.
Isolated system is one that can not exchange
energy with its surrounding
Isolated System Energy Constant
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The Law of Conservation of Energy

• Generally energy is transferred in two ways
• as a heat (Q) because of the temperature
  difference between the two objects.
• as work done (Wext ) by external force.
• Q and Wext may be positive or negative.
• positive Q and positive Wext mean energy is
  transferred into the system.
• negative Q and negative Wext mean energy is
  taken out of the system.

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The Law of Conservation of Energy

• Total energy (E) of a system is

Consider the system below
state 2
state 1
PE2 , KE2, Eint2
PE1, KE1, Eint1
PE1, KE1, Eint1
Q, Wext
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The Law of Conservation of Energy
For a system whose internal energy and
temperature do not change (Q 0 and Eint
constant), we have
This equation is the work energy theorem for
point objects.
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The Law of Conservation of Energy
Example 4 A cave rescue team lifts an injured
spelunker directly upward and out of a
sinkhole by means of motor-driven cable. The lift
is performed in three stages, each requiring a
vertical distance of 10.0m (1) the initially
stationary spelunker is accelerated to a speed
of 5.00m/s (2) he is then lifted at a constant
speed of 5.00m/s. (3) finally he is decelerated
to zero speed. How much work is done on the
80.0kg man by the force lifting him during each
stage?
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Conservative and non-conservative forces

• A force is conservative force if the work done
  by this force is the same along any path
  connecting the same two points or equivalently,
  if the total work done by this force around any
  closed path (one that returns to its starting
  point) is zero.

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Conservative and non-conservative forces

• For an object moving around a closed path

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Conservative and non-conservative forces
The work done by non-conservative force (Fnc )
depends on the path taken.
1
B
2
A
3
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Conservative and non-conservative forces

• Work done by friction force
• Friction force is an example of none
  conservative force.

• The work done by friction force is always negative

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Conservative and non-conservative forces
Friction and hence non-conservative forces
convert mechanical energy into internal Energy.
or in general
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Conservative and non-conservative forces

• For a system in which
• Fnc are internal forces
• there is no heat transfer into or out of the
  system (Q 0)
• The work energy theorem is

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Conservative and non-conservative forces

• Example 5
• A child and sled having a combined weight of 335N
  start from rest and slide
• 25.0m down a 15o slope assuming a constant
  resistance force of 20.0N.
• Find the work done by the resistive force.
• Find the speed of the sled at the bottom of the
  slope.

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Elastic Force
X 0
X
F
Fs
X
F
Fs
Fs force exerted by spring X springs
displacement from the equilibrium position k
spring constant or elastic constant The SI unit
of k is N/m Large k stiff spring Small k soft
spring
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Elastic Potential Energy
X 0
F 0
F
Fs
F
Fs
X
Elastic potential energy
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Elastic Potential Energy

• Whenever we apply the conservation of energy and
  work-energy theorem, the potential energy of the
  system must include all kinds of potential
  energies.

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Elastic Potential Energy

• Example 6
• The figure below shows an 8.00kg stone resting on
  a spring. The spring
• is compressed 10.0cm by the stone.
• What is the spring constant?
• The stone is pushed down an additional 30.0cm and
  released. What is the elastic potential energy of
  the compressed spring just before that release?
• To what maximum height does the stone rise,
  measured from the release point?

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Energy Rates
Power is the rate at which energy is transferred
?E in time ?t
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Energy Rates

• If the energy transfer is accomplished by doing
  work W

When work is done on or by an object due to a
force in the direction of its motion
v is uniform or average speed
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Energy Rates
Example 7 How much work could be performed by a
1hp motor in 1hour?
Example 8 How much mechanical power must be
supplied by a car to pull a boat on a trailer at
a speed of 20.0m/s if the force exerted by the
car on a trailer is 2000N?
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• Exercises
• 6.14, 6.16,6.19, 6.22, 6.27, 6.33,6.40, 6.41,
  6.43, 6.46,6.47,
• 6.61, 6.84