Chapter 11: Work

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Chapter 11 Work

• How many kinds of energy are there?
• Under what conditions is energy conserved
• How does a system gain or lose energy?

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Stop to think 11.1 P304Stop to think
11.2 P306Stop to think 11.3 P310Stop to think
11.4 P312Stop to think 11.7 P327

• Example 11.1 P307
• Example 11.6 P311
• Example 11.8 P313

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Work and kinetic energy
Force F does work as the particle moves from Si
to Sf
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The work-kinetic energy teorem

• We integrate both sides

Question 1 Kg ball free fall from 5m high place
to the ground, how much work is Done by the
gravitational force?
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Calculating work

• Constant Force
• T is the angle between force and displacement.

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Calculating the work of a constant force.
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The work done by a force depends on the angle ?
between the force and displacement, not on the
direction the particle is moving. The work done
on all four particles in the figure is the same,
despite the face that they are moving in four
different direction.
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The dot product of two vectors

• Dot product
• It is scalar
• We also can do dot product using components

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The work done by a variable force

• From the definition of work
• (1) Do integral
• (2) Find the area under the force-vs position
  graph
• Ex. The spring force is a variable force F -kx
• ( we chose equilibrium position x(e) as origin
  )

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Work and potential energy

• Conservative force A force for which the work
  done on a particle as it moves from an initial to
  final position is independent of the path
• For example
• Gravitational force is conservative force, If it
  does positive
• work, always make potential energy decrease.
• Gravitation force and spring force are
  conservative force.

Independent of path
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Nonconservative force

• A force for which the work is not independent of
  the path is called a nonconservative force.
• For example, friction.
• If there are only conservative forces
• because Wc ?K -?U? ?K ?U 0
• ( total mechanical energy is conserved)
• If there is nonconservative force
• ?K ?U Wnc or

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Problem 11.49

• Use work and energy to solve the problem.
• (a) the table is frictionless, W(fric)0
• Ei m2 gh m1 gy1
• Ef 1/2 (m1m2)V2 m1 g y1
• From Ei Ef, you can find V
• (b) if there is a friction force between
• m1 and table. f(k) µ(m1g)
• Ei f(k)h Ef
• m2 gh -µ(m1g)h ½(m1m2)V2

m1
m2
y1
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P11.56 The spring shown in Fig. is compressed
50cm and used to launch a 100 Kg students. The
track is frictionless until it stars up the
incline. The students coefficient of kinetic
friction on the 30o incline is 0.15

• The system is compressed spring, student and the
  ground.
• Just before and after student is losing the
  contact with the spring, the energy conservation
  equation is
• How far up the incline does the student go?

V20
h1
h2
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How far up the incline does the student go?

• The total energy at top of 10 m should equal the
  total energy
• at bottom. After that student goes to incline
  with friction.
• We can apply the energy and work equation.
• With h2 s sin(30o) and friction
• F(k) µ mg cos(30o)
• Get

h1
h2
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Finding force from potential energy

• The work done by conservative force is

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Power

• Power rate of transfer of energy
• is defined as
• unit of power is Watt.
• When work as the source of energy trasfer