Tuesday, Feb 5, 2008

Collected HW on scientific notation and algebra

Handed back Graphing Labs
Discussed some problem areas
With a straight line graph, you get a relationship between variables given by the slope. The equation for a straight line through the origin is y = m*x, or in the case of this lab with the circumference plotted on the y-axis, C = slope * diameter. By finding the slope, you have determined the value of pi.

Used the method of max and min slope to determine the uncertainty in the slope.

Lectured on uncertainties:
1. If you have multiple measurements:
Find the average by: (M1 + M2 + ... + Mn)/n
Find the uncertainty by: (abs(M1-avg) + abs(M2-avg) + ... + abs(Mn-avg))/n

2. If you have one measurement of each quantity:
2a. Max Min method
Example of area of a rectangle
Max area = (L + uncL)*(W + uncW)
Min area = (L - uncL)*(W - uncW)
Avg area = (Max area + Min area)/ 2
Unc Area = (Max area - Min area)/ 2

2b. Method of Relative Uncertainty
This method cannot be used if the terms are added or subtracted but otherwise is powerful and easy to use
Used example of area of a rectangle
Area = L * W
Unc Area = A * (uncL/L + uncW/W)

If you have a complicated expression like: Z = (A^1/2) * (B^3)/(C^5)
you can use this method taking the absolute values of the exponents as coefficients in the relative uncertainty equation: uncZ = Z*((1/2)*uncA/A + 3*uncB/B + 5*uncC/C)

Handed out practice sheet on uncertainties with summary of class notes - will post answers in answer folder.

Showed Cosmos video of Eratosthenes finding circumference of Earth (including Beethoven's 7th symphony).

Handed out RA Chapter 1, due Wednesday.