winter wk 1 – thus.6.jan.05 calculus ch.5: integration –5.1: how do we measure distance...
TRANSCRIPT
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?– 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
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
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
5.2: Sums using sigma notation
Time interval = total time/number of steps
t = (b-a) / n
Speed at a given time = f(t)
Area of speed*time interval = distance = f(t)*t
Total distance traveled = sum over all intervalsn
tot 1 2 n ii=0
x f(t ) t + f(t ) t +...+ f(t ) t = f(t ) t
5.2: Definite integral
Precise calculation of total distance traveled xtot
needs infinitesimally small time intervals,
so take the limit as t 0, that is,
an infinite number of tiny intervals: n
Practice problems #1, 2, 4, 16
n
tot ini=0
x = lim f(t ) t ( )b
a
f t dt
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 (=Q/area)?