Physics 218 Lecture 15

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Physics 218Lecture 15

• Dr. David Toback

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Notes

• Exam Next Tuesday
• Here. Usual class time Covering
• Exam 1 material
• Chapter 3(9)
• Chapter 4(1-8)
• Chapter 5(1-3)
• Chapter 6(1-8)
• Chapter 7(1-4)
• Calculus 2
• Today Rest of Chapter 8 NOT ON EXAM

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Overview of Chapter 8

• Chapter 8 is a mish-mash of topics
• The basic idea is to learn about energy so you
  can do a new set of problems that you cant do
  using previous ideas. This means understanding
• Potential Energy, Mechanical Energy and when
  there is Conservation of Mechanical Energy
  (conservative forces)

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Today

• Topics
• Potential Energy, Mechanical Energy and when
  there is Conservation of Mechanical Energy
  (conservative forces).
• Conservation of Energy
• Conservative and non-Conservative Forces
• How to back and forth between types of problems
• In many ways this is a review for the exam

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Potential Energy

• Amount of energy that could be released
• Gravitation potential energy
• If you lift up a ball it has the potential to do
  damage.
• Raise it a height h gt U mgh
• Compress a spring
• Spring potential energy U ½kx2
• Doing External Work can change the potential
  energy

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Forces Potential Energy

• Another definition

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Mechanical Energy Conservative Systems

• If there is net work on an object, it changes the
  kinetic energy of the object (Gravity forces a
  ball falling from height h to speed up. Work
  done.)
• Wnet DK
• If there is a change in the potential energy,
  there is net work done on an object (ball
  falling from height h speeds up. Work done, loss
  of potential energy)
• DUTotal -Wnet

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Conservation of Mechanical Energy

• DK DU 0
• K2U2 K1U1
• E K U
• ½mv2 (mgy ½kx2)

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Conservative Forces

• If there are only conservative forces in the
  problem, then there is conservation of mechanical
  energy
• Conservative Can go back and forth along any
  path and the potential energy and kinetic energy
  keep turning into one another
• Gravity
• Springs
• Others
• Non-Conservative As you move along a path, the
  potential energy or kinetic energy is turned into
  heat, light, sound etc.
• Friction
• Others

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Old Problems

• Lets do some old problems in some new ways

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Example with Gravity

• A rock is held at height h and dropped.
• What is the speed when it hits the ground?
• A rock, at any height y relative to the ground,
  has potential energy of Umgy.
• What must be the force on the rock?

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Law of Conservation of Energy

• Even if there is friction, Energy is conserved
• Friction turns the energy into heat
• Total Energy Kinetic Energy Potential Energy
  Heat Others
• This is what is conserved
• Can use lost mechanical energy to estimate
  things about friction

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Spherical Roller Coaster

• A roller coaster of mass m starts at rest at
  height y1 and falls down the path, then back up
  until it hits height y2 (y1 gt y2). An odometer
  tells us that the total scalar distance traveled
  is d.
• Assuming we dont know anything about the
  friction or the path, how much work is done by
  friction on this path?
• Assuming a constant force of friction, F, between
  the car and the track is constant, find F.

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Friction and Springs
A block of mass m is traveling on a rough
surface. It reaches a spring (spring constant k)
with speed vo and compresses it by an amount X.
Determine m
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Gravitational Potential Energy

• If I move to outer space, does is it still true
  that Umgh?
• What is U in outer space?

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Escape Velocity

• What happens if I throw a ball up in the air?
  Will it fall down?
• What if I throw it up really fast?
• What if I throw it up REALLY fast?
• Can I throw it up so fast that it will never come
  down? How fast would that be?

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Package Dropped from a Rocket

• Drop a package with speed V at a height r0 so far
  above the earths surface, the mgh approximation
  doesnt work. Eventually, the package falls to
  the surface of the earth.
• What is the final speed of the package?
• Why doesnt the answer depend on the direction of
  the initial velocity?

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Exam

• Tuesday, here at the regular time
• 4 Problems
• Problems similar to those in the
  book/homework/lecture
• No numbers

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Next Thursday

• Reading Conservation of Linear Momentum

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Advice 1

• How to prepare
• Do all the homework problems and keep doing them
  until they are easy!
• How do you know when you are ready to take the
  exam?
• Pick the hardest problems from the lecture,
  examples and HW.
• You are ready when you can do any of those
  problems without looking at ANY
  notes/books/examples etc.
• My Advice 2 ?

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My Advice II Dont come underprepared
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Conservative Forces

• Conservative Work doesnt depend on the path
  taken
• A force is conservative if the net work done by
  the force on an object moving around any closed
  path is zero
• Friction is an example of a non-conservative Force

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Law of Conservation of Energy

• Even if there is friction, Energy is conserved
• Friction turns the energy into heat
• Total Energy Kinetic Energy Potential Energy
  Heat Others
• This is what is conserved

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Power Potential Energy

• Definition Power is the rate at which work is
  done.
• P dw/dt
• Pavg Dw/Dt
• Name the unit after James Watt
• 1 Watt 1Joule/sec
• Definition

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Gravitational Potential Energy

• What is the change in potential energy as you
  move from one point in space to another?
• What is a useful coordinate axis to define the
  gravitational potential energy?
• What is the potential energy in that reference
  point?