Physics 2211a Kulp Class 27: What is energy

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Physics 2211a (Kulp)Class 27 What is energy?
No class meeting on Friday, 27 Oct Notes posted
on class website

• W. D. Kulp
• william.kulp at physics.gatech.edu
• Office W501b
• Office Hours MF 11-12 AM, Tu 9-10 AM, by appt.
• www.physics.gatech.edu/academics/Classes/fall200
  6/2211/a/

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Where are we?

• Last week momentum

• Today Class 27
• Analyze the motion of a particle and determine
  its kinetic energy.
• Calculate the gravitational potential energy of
  an object and use this to analyze the motion of
  the object.
• Use conservation of energy to analyze the motion
  of a particle moving without friction along a
  trajectory under the influence of gravity.

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What is energy?

• We do not know.
• It is a number that does not change.
• We can calculate the value of different kinds of
  energy using formulas we have discovered.
• The formulas do not reveal the mechanism of
  energy and we do not know the reasons for the
  formulas.

• We will begin by discussing two kinds of energy
• gravitational potential energy
• kinetic energy

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Gravitational potential energy, Ug

• This is an energy of position.
• Its value is the product of weight x height.
• We are interested in changes in Ug

1 kg

• ?Ug -9.8 kg m2/s2 -9.8 J

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Kinetic energy, K

• This is an energy of motion.
• Its value is half of the product of mass x
  speed2.
• Useful for calculations this is a scalar, not a
  vector!

• For an object in vertical free fall
• This is an example of conservation of energy.

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Transformation of energy

• Energy can be converted from one form to another
  without loss in a system where energy is
  conserved.

K 0
U mg(2h) 3.92 J
2h
K mgh
h
U mgh 1.96 J
K 2mgh
U 0
0

• If m 200 g and h 1 m, what is the impact
  speed of the ball?

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Zero of potential energy

• There is not an absolute reference point for U
  0.

• If m 200 g and h 1 m, what is the impact
  speed of the ball? Choose the zero for potential
  energy at highest point.

K 0
U 0
0
K mgh
-h
U -mgh -1.96 J
K 2mgh
U mg(-2h) -3.92 J
-2h
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The ballistic pendulum

• A 10 g bullet is fired into a 1200 g wood block
  that hangs from a 150-cm-long string. The bullet
  lodges in the block, and the block swings out to
  an angle of 40.
• What was the speed of the bullet?

• Use momentum conservation
• Use energy conservation

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Conservation of Energy

• Consider a general model for a system with only
  kinetic and potential energy.

Energy into system
Readily available energy, K (kinetic) Stored
energy, U (potential) Total energy E K U
Energy out of system

• Under what conditions is energy conserved?
• What happens to the energy when E isnt
  conserved?
• How do you calculate U for forces other than
  gravity?

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Spring things

• Hookes Law
• The restoring force of a spring (the force that
  returns the spring to equilibrium) is
  proportional to the displacement from equilibrium.

• Elastic Potential Energy
• The energy of position for a spring depends on
  the square of the displacement from equilibrium.

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Whats next?

• Friday, 10/27 Class 28 How does a spring work?
• Given the spring constant, displacement from
  equilibrium, or the force applied on an object
  for an ideal spring, use Hooke's Law to analyze
  the motion of an object in contact with the
  spring.
• Calculate the total energy (potential kinetic)
  of an ideal spring.
• Use conservation of energy to analyze the motion
  of an object under the influence of an ideal
  spring.

Extra problems for self-study on MasteringPhysics

• To-do list
• Homework 26 before class on Friday
• Read assignment (10.4 - 10.5)