1. Why should your log slopes have equaled one half? 2. Suppose you had consiste

Question

1. Why should your log slopes have equaled one half?

2. Suppose you had consistently measured the length l wrong so that your value was 1 cm greater than the actual value. How would the slope and intercept have been affected? Explain your reasoning.

3. Suppose that your rings had thick rims so that the difference between Ri and Ro was considerable. Let %u2206R = Ro - Ri . Then

Ro =R+%u2206R 2

and

Ri = R - %u2206R . 2

Complete the algebra and show that the period for a thick ring would be

d (%u2206R)2 T=2%u03C0 g+ 4Rg .

4. Which of the five rings in this experiment was most likely to have a big difference between its theoretical and actual period? How would this difference have affected your calculations for g? Explain your reasoning. (Big Hint: Look at the answer to question 3.)

Explanation / Answer

1) It sometimes happens that the power value in an equation is known or assumed; the purpose of the graphical analysis is to find some other parameter of the equation. It is then justifiable to impose a straight line of the known slope onto the data points. It is easiest to construct lines of slope corresponding to integer powers or reciprocals of integers. Suppose you wanted a slope for power 2 Mark the point (n2,n) and connect it to the point (1,1) with a straight line. The number n can be any convenient value. Suppose we take n = 2.

2)

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