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

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 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 intervals

5.2: Definite integral Precise calculation of total distance traveled x tot 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

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 (  =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 F g on the drop? (b) How many excess electrons does it have?