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 5:30
Energy Systems, EJZ
Calculus Ch.5: Integration
5-1: How do we measure distance traveled?
• Thought experiment: how far does a car go?
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•
Making distance estimates precise
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Estimate distance traveled in each time interval
Take smaller and smaller time intervals
Conceptests
Practice problems #1, 2, 4, 5, 6, 10, 14
5-1: Estimating distance traveled
Speed = distance/time, so Distance = ________
Plot speed vs time
Estimate distance for each interval
Area of (speed*time) segments
Fig.5.1: LH sum = underestimate,
RH sum = overestimate
Practice problems # 2, 4, 10
Calc Ch.5-1 Conceptest 1
Calc Ch.5-1 Conceptest 1 soln
Calc Ch.5-1 Conceptest 2
5.1 #2
5.1 #4
5.1 #10
Calculus Ch.5.2: Definite integral
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•
•
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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
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 speed*time interval = distance = f(t)*Dt
Total distance traveled = sum over all intervals
x tot  f(t1 ) Dt + f(t 2 ) Dt +...+ f(t n ) Dt =
n
 f(t ) Dt
i
i=0
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  
b
n
x tot = lim
n 
 f(t ) Dt   f (t ) dt
i
i=0
Practice problems #1, 2, 4, 16
a
Calc Ch.5-2 Conceptest 1
Calc Ch.5-2 Conceptest 1 soln
Calc Ch.5-2 Conceptest 2
(Just consider A1)
Ch.5-2 #1
Ch.5-2 #4
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)
E field maps electric force
22-3: Electric field E maps the direction and
strength of the force F (Q1, #1, 2)
Field due to a point charge
22-4: Field due to a point charge (Q2, 5, #4, 11, )
If the Earth’s electric field is 150 N/C near the
surface, what is the charge Q on the Earth?
What is the charge density (s=Q/area)?
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 E=462 N/C
(a) What is Fg on the drop?
(b) How many excess electrons does it have?