Winter wk 1 Thus.6.Jan.05

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Winter wk 1 Thus.6.Jan.05

• Calculus Ch.5 Integration
• 5.1 How do we measure distance traveled?
• 5.2 The definite integral
• If we have time, Physics Ch.22 from yesterday
  Electric fields
• Seminar in CAL tonight come at 530

Energy Systems, EJZ
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Calculus Ch.5 Integration

• 5-1 How do we measure distance traveled?
• Thought experiment how far does a car go?
• Estimate distance traveled in each time interval
• Making distance estimates precise
• Take smaller and smaller time intervals
• Conceptests
• Practice problems 1, 2, 4, 5, 6, 10, 14

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5-1 Estimating distance traveled

• Speed distance/time, so Distance ________
• Plot speed vs time
• Estimate distance for each interval
• Area of (speedtime) segments
• Fig.5.1 LH sum underestimate,
• RH sum overestimate
• Practice problems 2, 4, 10

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Calc Ch.5-1 Conceptest 1
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Calc Ch.5-1 Conceptest 1 soln
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Calc Ch.5-1 Conceptest 2
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5.1 2
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5.1 4
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5.1 10
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Calculus Ch.5.2 Definite integral

• Sums using Sigma notation
• Taking the limit to get the definite integral
• Definite integral as an Area
• Riemann sums
• Conceptests
• Practice problems 1, 2, 4, 16, 20, 22, 28

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5.2 Sums using sigma notation

• Time interval total time/number of steps
• Dt (b-a) / n
• Speed at a given time f(t)
• Area of speedtime interval distance f(t)Dt
• Total distance traveled sum over all intervals

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5.2 Definite integral

• Precise calculation of total distance traveled
  xtot needs infinitesimally small time intervals,
• so take the limit as Dt ?0, that is,
• an infinite number of tiny intervals n ? ?
• Practice problems 1, 2, 4, 16

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Calc Ch.5-2 Conceptest 1
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Calc Ch.5-2 Conceptest 1 soln
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Calc Ch.5-2 Conceptest 2
(Just consider A1)
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Ch.5-2 1
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Ch.5-2 4
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Physics Ch.22 Electric Field

• 22-3 Electric field E maps the direction and
  strength of the force F (Q1, 1, 2)
• 22-4 Field due to a point charge (Q2, 5, 4, 11,
  )
• 22-8 Point charge can be accelerated by an
  electric field (Q8, 38, 39, 49)
• Compare to gravity 75, 85 (42)

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E field maps electric force

• 22-3 Electric field E maps the direction and
  strength of the force F (Q1, 1, 2)

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Field due to a point charge

• 22-4 Field due to a point charge (Q2, 5, 4, 11,
  )
• If the Earths electric field is 150 N/C near the
  surface, what is the charge Q on the Earth?
• What is the charge density (sQ/area)?

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22-8 E field can accelerate charges

• Q8, 38, 39, 49
• Compare E to gravity 75, 85 (42) A spherical
  water droplet is suspended in a cloud with E462
  N/C (a) What is Fg on the drop?
• (b) How many excess electrons does it have?