HW 1,2,3 Solutions Phys270

Significant Figures 2.4. Rewrite the following equations in their clearest and most appropriate forms: (a) x= 3.323 ± 1.4 mm (b) t =1,234,567 ± 54,321 s (c) A= 5.33 X 10^-7 ± 3.21 X 10^-9 m (d) r =0.000,000,538 ± 0.000,000,03 mm

Comparison of Measured and Accepted Values 2.8. Two groups of students measure the charge of the electron and report their results as follows: Group A: e = (1.75 ± 0.04) X 1O^-19 C And Group B: e = (1.62 ± 0.04) X 10^-19 C What should each group report for the discrepancy between its value and the accepted value, e = 1.60 X 10^-19 C (with negligible uncertainty)? Draw an illustration similar to that in Figure 2.2 to show these results and the accepted value. Which of the results would you say is satisfactory?

2.16. You have learned (or will learn) in optics that certain lenses (namely, thin spherical lenses) can be characterized by a parameter called the focal length / and that if an object is placed at a distance p from the lens, the lens forms an image at a distance q, satisfying the lens equation, 11/ = (lip) + (l/q), where / always has the same value for a given lens. To check if these ideas apply to a certain lens, a student places a small light bulb at various distances p from the lens and measures the location q of the corresponding images. She then calculates the corresponding values of l from the lens equation and obtains the results shown in Table 2.9. Make a plot of l against p, with appropriate error bars, and decide if it is true that this particular lens has a unique focal length f Table 2.9. Object distances p (in cm) and corresponding focal lengths

f (I cm); for

Problem) 2.16. Object distance p (negligible uncertainty)

Focal length f

45 55

28

65 75

33

85

(all ± 2) 34 37 40

2.18 If a stone is thrown vertically upward with speed v, it should rise to a height h given by v2 = 2gh. In particular, v2 should be proportional to h. To test this proportionality, a student measures v2 and h for seven different throws and gets the results shown in Table 2.11. (a) Make a plot of v2 against h, including vertical and horizontal error bars. (As usual, use squared paper, label your axes, and choose your scale sensibly.) Is your plot consistent with the prediction that v2