Regents Physics

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Regents Physics

• Work and Energy

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Energy and Work

• Energy is the ability to Work
• Work is the transfer of energy to an object when
  the object moves due to an application of a force
• W Fd unit is Joules (J)
• Energy is also measured in Joules

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When is Work Done?

• Work is only done when the direction of motion is
  in the direction of the force
• So we can rewrite the equation to
• W Fcos ? d

F
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The F is important!

• F Fg force due to gravity on an object
• In this case, you are doing work against or with
  the force of gravity
• F applied force pushing or pulling something
• F force of friction ? doing work against
  friction

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The direction is important

• The force must be in the direction of motion
• For example A person holds a book and walks 2 m
  across the room. Is work being done against the
  force of gravity? No!

Force on book
Forces are at 90 degrees. No work is done!
Your motion
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Power ? The Rate at Which Work is Done

• Work is done when a force moves an object in the
  direction of the force
• Work Force x distance
• Power is the rate at which work is done
• Power work (J) / time (s)
• Unit of Power is a Watt (W) J/s
• P Work / time Fd/t Fv

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Forms of Energy

• Energy has many different forms. Here we discuss
  the various forms of energy!
• Forms of Energy
• Stored Energy and Energy of Motion

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Forms of Energy

• Energy has many forms, including
• Thermal Energy heat, is the total kinetic
  energy possessed by the individual particles of
  an object
• Internal Energy is the total of the potential
  and kinetic energies of an object
• Nuclear Energy is the energy released by
  nuclear fission or fusion
• Electromagnetic Energy is the energy associated
  with electric or magnetic fields

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Stored Energy - Potential Energy

• The energy possessed by an object due to its
  position or condition
• If there is no energy loss due to friction, the
  work done to bring an object from its original
  position is equal to the objects change in
  potential energy
• We can see this in observing changes in
  gravitational potential energy

?PE mg?h
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Gravitational Potential Energy

• Objects gravitational potential energy as they
  are lifted to a distance above the Earths
  surface
• Work is done against gravity to lift the object
• As long as there is no loss due to friction, the
  change in potential energy is due only to change
  in height!

?PE mg?h
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Work and Energy Relationship

• If there is no friction, all the work done in
  lifting an object to a new height is equal to the
  objects increase in potential energy
• The change in potential energy depends only on
  the height, not on the path taken
• For example

Work also 98 J
W 98 J
10 Kg
Vs.
10 Kg
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Conservative Forces

• When work done against a force is independent of
  the path taken, the force is said to be a
  conservative force
• Gravitation is an example of this type of a force
• Notice no friction is involved

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Nonconservative Forces

• Air resistance and friction are examples of
  nonconservative forces
• The work done against a nonconservative force is
  dependent upon the path taken
• Path A requires more work than Path B

1.0m
10 Kg
A
B
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Nonconservative example
Wf Ffd Ff ukFN FN gets larger as the
angle gets smaller, soA requires more work
against friction than B
W 98 J Just to lift it
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Energy of Motion - Kinetic Energy

• Energy associated with motion
• Kinetic energy is gained as potential energy is
  lost

KE 1/2mv2
M mass in kilograms V velocity in m/s KE
energy in joules
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Conservation of Energy

• Just like momentum, energy is also conserved
• Energy cannot be created or destroyed, it can
  only be transferred!
• The sum of the changes in a closed system must be
  equal to zero
• We must consider energy conservation under
  perfect and reality like situations

KE gained potential energy lost!
Click picture for demo!
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Ideal Mechanical Systems

• The sum of the kinetic and potential energies in
  a system is called the total mechanical energy
• Ideal Mechanical System is a closed system in
  which no friction or other nonconservative force
  acts
• The sum of the kinetic and potential energy
  changes is equal to zero
• Example the pendulum

Click above for demo!
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Nonideal Mechanical Systems

• When a system is acted upon by a nonconservative
  force, such as friction, it is called a nonideal
  mechanical system
• The friction opposes the motion of two objects in
  contact with each other and moving relative to
  each other
• The frictional energy is converted into internal
  energy..an increase in temperature

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Ideal vs. Nonideal
NonIdeal
Ideal
?KE -?PE
ET PE KE Q
1/2mv2 mgh
ET mgh 1/2mv2 Q
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Regents Physics

• Springs!!

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Elastic Potential Energy

• Energy is stored in a spring when work is done
  stretching or compressing it
• This energy is called elastic potential energy

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Compression / Elongation

• The compression or elongation of a spring is the
  change in spring length from its equilibrium
  position when a force is applied to it
• The compression (elongation) of the spring is
  directly proportional to the applied
  forceprovided the elastic limit of the spring is
  not exceeded
• This gives us an equation!

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Hookes Law
Fs kx
The applied force on a spring is proportional to
the distance the spring is displaced (x) and the
spring constant (k)
k is the spring constant and is the constant of
proportionality between the applied force and
the compression/elongation of the spring Unit is
the Newton - meter
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Springs Store Energy

• Work done to compress/stretch a spring is equal
  to the stored potential energy..just like in
  gravitation!
• Thus

W Fsx ½ kx x ½ kx2 PEs ½ kx2
Click for demo
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End Ask Mr. O for the HW
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Use the following diagram to answer questions 5
- 7. Neglect the effect of friction and air
resistance. 5. As the object moves from point A
to point D across the frictionless surface, the
sum of its gravitational potential and kinetic
energies a. decreases, only. b. decreases and
then increases. c. increases and then
decreases. d. remains the same.
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6. The object will have a minimum gravitational
potential energy at point a. A. b. B. c.
C. d. D. e. E.
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7. The object's kinetic energy at point C is less
than its kinetic energy at point a. A only. b.
A, D, and E. c. B only. d. D and E.