Physics 2211: Lecture 14 Todays Agenda WORK

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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...
• 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 (Emc2), 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
?
Fr
displacement
Dot Product
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Definition of Work

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

?
F cos ?
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Aside Dot Product (or Scalar Product)
Definition Some properties (a
is a scalar) ( is a vector) The
dot product of perpendicular vectors is 0 !!
ba
?
?
ab
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Aside Examples of dot products
y
x
z
Suppose
Then
1x4 2x(-5) 3x6 12
1x1 2x2 3x3 14 4x4
(-5)x(-5) 6x6 77
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Aside Properties of dot products

• Magnitude
• Pythagorean Theorem!!

ay
ax
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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
?
Fr
displacement
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Lecture 14, Act 1Work 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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Work 1-D Example (constant force)

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

Work done by on box (since
is parallel to ) WF (10 N) x (5
m) 50 Joules (J)
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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 F 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.

v1
v2
F
m
?x
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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

v1
v2
F
a
m
?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)

v1
v2
F
m
a
?x
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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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Lecture 14, Act 2Work 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
m1
m2
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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