Chapter 6 Energy and Oscillations

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Chapter 6Energy and Oscillations
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Energy and Oscillations
A swinging pendant always returns to the same
point (almost) after each swing. What is
conserved in this motion?
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Simple Machines

• A simple machine multiplies the effect of an
  applied force.
• For example, a lever , and a pulley.

The mechanical advantage of a simple machine is
the ratio of the output force to the input force.
The price to pay is to move through a larger
distance.
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Work

• Work is equal to the force applied times the
  distance moved (only force in the parallel
  direction of motion).
• Work Force x Distance W F d
• units 1 joule (J) 1 Nm
• In Simple Machine, Work output Work input

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Work and Power

• Only forces parallel to the motion do work.

• Power is the rate of doing work
• Power Work divided by Time
• P W / t units 1 watt (W) 1 J / s

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Example (Box 6.1)
A crate is pulled a distance of 4 m across the
floor under the influence of a 50N force applied
by a rope to the crate. What is the work done on
the crate by the 50N force if a) the rope is
horizontal, parallel to the floor? b) the rope
pulls at an angle to the floor, so that the
horizontal component of the 50N force is 30N?
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A string is used to pull a wooden block across
the floor without accelerating the block. The
string makes an angle to the horizontal. Does
the force applied via the string do work on the
block?
Example
If there is a frictional force opposing the
motion of the block, does this frictional force
do work on the block?
What is the work done by the vertical component
of the force?
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A force of 50 N is used to drag a crate 4 m
across a floor. The force is directed at an
angle upward from the crate as shown. What is
the work done by the horizontal component of the
force?
Example
What is the work done by the vertical component
of the force? What is the total work done by the
50-N force?
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Kinetic Energy

• Kinetic energy is the energy associated with an
  objects motion.
• Doing work on an object can increase its kinetic
  energy. Work Done Increase of Energy

Starting from rest on a frictionless floor, you
move a 100-kg crate by applying a net force of
50N for a time 4s. Find a) what is the
acceleration of the crate? b) what is the final
speed of the crate? c) how far will the crate go
in this time? d) the work done on the crate. e)
the final kinetic energy of the crate.
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Negative Work

• Negative work is the work done by a force acting
  in a direction opposite to the objects motion.
• For example, a car skidding to a stop. What force
  is acting to slow the car? Does the force do any
  work on the car?

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Potential Energy

• Potential energy is the energy that an object
  has by virtue of its position or its status
  related to the motion of the object . It
  represents stored energy that can be released
  later.
• gravitational potential energy
• The work done to raise the object is equal to the
  gravitational potential energy that the object
  gains.

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Potential Energy

• The term potential energy implies storing energy
  to be released later.
• For example, the gravitational potential energy
  of the crate can be converted to kinetic energy.

• There are other types of potential energy, such
  as the elastic potential energy (energy stored in
  springs) and chemical potential energy, etc.

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Work is done on a large crate to tilt the crate
so that it is balanced on one edge, rather than
sitting squarely on the floor as it was at first.
Has the potential energy of the crate increased?
Example
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• Conservative forces Forces such as gravity and
  elastic force. The work done against conservative
  forces will increase the systems potential
  energy that can be completely recovered later.
• Gravity and elastic forces are conservative.
• Friction is not conservative.

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Energy Conversion

• Energy can change from one form to another.
• Examples
• Kinetic energy to gravitational potential
  energy
• Gravitational energy to kinetic energy
• Kinetic energy to elastic energy (example pole
  vaulter)
• Kinetic energy to heat

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Conservation of Energy

• Conservation of energy In energy conversion, the
  total energy of all forms (the kinetic plus
  potential energies) of a system remains constant
  if no work is done to the system.

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Example
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Example

• E. 12. At the low point in its swing, a pendulum
  bob with a mass of 2.0kg has a velocity of 5m/s.
• a. What is its kinetic energy at the low point?
• b. Ignore air resistance, how high will the bob
  swing above the low point before reversing
  direction?

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Example

• Work done in pulling a sled up a hill produces an
  increase in potential energy of the sled and
  rider.
• This initial energy is converted to kinetic
  energy as they slide down the hill.
• In any of the point, the total energy (PEKE if
  other energy is ignored) is a constant.

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Example

• E. 14. A sled and rider with a combined mass of
  50kg are at the top of a hill a height of 15 m
  above the level ground below. The sled is given a
  push providing an initial kinetic energy at the
  top of the hill of 1600J.
•  Choosing a reference level at the bottom of the
  hill, what is the potential energy of the sled
  and the rider at the top of the hill?
• After the push, what is the total mechanical
  energy of the sled and the rider at the top of
  the hill?
• If the friction can be ignored, what will be the
  kinetic energy of the sled and rider at the
  bottom of the hill?

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• Any work done by frictional forces is negative.
• That work removes mechanical energy from the
  system.

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A sled and rider with a total mass of 40 kg are
perched at the top of the hill shown. Suppose
that 2000 J of work is done against friction as
the sled travels from the top (at 40 m) to the
second hump (at 30 m). Will the sled make it to
the top of the second hump if no kinetic energy
is given to the sled at the start of its motion?
Example
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Springs and Simple Harmonic Motion

• Simple harmonic motion occurs when the energy of
  a system repeatedly changes from potential energy
  to kinetic energy and vise versa.

Energy added by doing work to stretch the spring
is transformed back and forth between potential
energy and kinetic energy.
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The horizontal position x of the mass on the
spring is plotted against time as the mass moves
back and forth.

• The period T is the time taken for one complete
  cycle.
• The frequency f is the number of cycles per unit
  time.
• The amplitude is the maximum distance from
  equilibrium.

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• A restoring force is a force that exerts a push
  or a pull back towards equilibrium.
• A restoring force that increases in direct
  proportion to the distance from equilibrium
  results in simple harmonic motion.

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U.S. Energy and Future
US Energy Flow Trend (2002) 
 
Unit Quadrillion BTUs (quads)
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Renewable Energy and Energy Efficiency

• Fossil Fuels
• Oil, coal, natural gas
• Renewable Energy Sources
• Solar energy, wind