Physics 2211, Spring 2002

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Physics 2211 Lecture 14Todays AgendaWORK
ENERGY

• Work Energy
• Discussion
• Definition
• Dot Product
• Work of a constant force
• Work/kinetic energy theorem

Work Energy are covered in Chapters 6 and 7 in
Tipler. (Read both chapters together.)
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Work Energy

• One of the most important concepts in physics
• Alternative approach to mechanics
• Many applications beyond mechanics
• Thermodynamics (movement of heat)
• Quantum mechanics, etc.
• Very useful tools
• You will learn new (sometimes much easier) ways
  to solve problems

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Forms of Energy

• Kinetic Energy of motion.
• A car on the highway has kinetic energy.

• We have to remove this energy to stop it.
• The breaks of a car get HOT !
• This is an example of turning one form of energy
  into another (thermal energy).
• Thermal, Potential, Nuclear (E mc2), etc.

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Mass Energy (but not in Physics 2211)

• Particle Physics

E 1010 eV
(a)
(b)
E mc2
M
( poof ! )
(c)
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Energy Conservation

• Energy cannot be destroyed or created.
• Just changed from one form to another.
• We say energy is conserved!
• True for any isolated system.
• i.e., when we put on the brakes, the kinetic
  energy of the car is turned into heat using
  friction in the brakes. The total energy of the
  car-breaks-road-atmosphere system is the same.
• The energy of the car alone is not conserved...
• It is reduced by the braking.
• Doing work on an isolated system will change
  its energy.

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Definition of Work
Ingredients Force ( ), displacement (
) Work, W, of a constant force acting through a
displacement is
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Definition of Work

• Only the component of along the displacement
  is doing work.
• Example Train on a track.

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Aside Dot Product (or Scalar Product)
Definition
Some properties
The dot product of perpendicular vectors is 0 !!
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Aside Examples of dot products
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Aside Properties of dot products

• Magnitude

• Pythagorean Theorem!!

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Aside Properties of dot products

• Components

• Derivatives

• Apply to velocity

• So if v is constant
• (like for Uniform Circular Motion)

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Back to the definition of Work
Ingredients Force ( ), displacement (
) Work, W, of a constant force acting through a
displacement is
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ExampleWork Energy

• A box is pulled up a rough (mk gt 0) incline by a
  rope-pulley-weight arrangement as shown below.
• How many forces are doing work on the box?

(a) 2 (b) 3 (c) 4
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Example Solution

• Draw FBD of box

• Any force not perpendicularto the motion will do
  work

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Work 1-D Example (constant force)

• A force of 10 N pushes a box across a
  frictionlessfloor for a distance ?x 5 m.

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Units

• Force x Distance Work

Newton x ML / T2
Meter Joule L ML2 / T2
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Work Kinetic Energy

• A force 10 N pushes a box across a
  frictionlessfloor for a distance ?x 5 m. The
  speed of the box is v1 before the push and v2
  after the push.

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Work Kinetic Energy

• Since the force F is constant, acceleration a
  will be constant. We have shown that for
  constant a
• v22 - v12 2a(x2-x1) 2a?x.
• multiply by 1/2m 1/2mv22 - 1/2mv12 ma?x
• But F ma 1/2mv22 - 1/2mv12 F?x

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Work Kinetic Energy

• So we find that
• 1/2mv22 - 1/2mv12 F?x WF
• Define Kinetic Energy, K K 1/2mv2
• K2 - K1 WF
• WF ?K (Work / Kinetic Energy Theorem)

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Work / Kinetic Energy Theorem

• Net (or Total) Work done on object
• change in kinetic energy of object

• Well prove this for a variable force later.

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ExampleWork Energy

• Two blocks have masses m1 and m2, where m1 gt m2.
  They are sliding on a frictionless floor and have
  the same kinetic energy when they encounter a
  long rough stretch (i.e., mk gt 0) which slows
  them down to a stop. Which one will go farther
  before stopping?

(a) m1 (b) m2 (c) they will go the same
distance
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Example Solution

• The work-energy theorem says that for any object
  WNET DK.
• In this example the only force that does work is
  friction (since both N and mg are perpendicular
  to the blocks motion).

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Example Solution

• The work-energy theorem says that for any object
  WNET DK
• In this example the only force that does work is
  friction (since both N and mg are perpendicular
  to the blocks motion).

• The net work done to stop the box is -f D
  -mkmgD.

• This work removes the kinetic energy that the
  box had
• WNET K2 - K1 0 - K1

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Example Solution

• The net work done to stop a box is -f D
  -mkmgD.
• This work removes the kinetic energy that the
  box had
• WNET K2 - K1 0 - K1
• This is the same for both boxes (same starting
  kinetic energy).

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Recap of todays lecture

• Work Energy
• Discussion
• Definition
• Dot Product
• Work of a constant force
• Work/kinetic energy theorem
• Read Tipler 6.2 and 6.3