Topic 1 Measurements and Errors (Practice)

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Roderick Reeves
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These rings were produced as a result of interference of monochromatic light.

1 Topic 1 Measurements and Errors (Practice) Name: 1. Data analysis question. The photograph below shows a magnified image of a dark central disc surrounded by concentric dark rings. These rings were produced as a result of interference of monochromatic light. The graph below shows how the ring diameter D varies with the ring number n. The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the photograph. Error bars for the diameter D are shown.

2 (a) State one piece of evidence that shows that D is not proportional to n. (b) On the graph opposite, draw the line of best-fit for the data points. (2) (c) It is suggested that the relationship between D and n is of the form D = cn p where c and p are constants. Explain what graph you would plot in order to determine the value of p. (3) IB Questionbank Physics 2

3 (d) Theory suggests that p = 2 1 and so D 2 = kn (where k = c 2 ). A graph of D 2 against n is shown below. Error bars are shown for the first and last data points only. (i) Using the first graph, calculate the percentage uncertainty in D 2, of the ring n = 7. (2) (ii) Based on the second graph, state one piece of evidence that supports the relationship D 2 = kn. IB Questionbank Physics 3

4 (iii) Use the second graph to determine the value of the constant k, as well as its uncertainty. (4) (iv) State the unit for the constant k. (Total 14 marks) IB Questionbank Physics 4

5 2. Data analysis question. Gillian carried out an experiment to investigate the craters formed when steel balls are dropped into sand. To try and find the relationship between the diameter of the crater and the energy of impact of steel balls of the same diameter, she dropped a steel ball from different heights h into sand and measured the resulting diameter d of the crater. The data are shown plotted below. (a) The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to be shown. Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10). (2) (b) Draw a best-fit line for the data points. (2) (c) The original hypothesis, made by Gillian, was that the diameter of the crater is directly proportional to the energy of impact of the steel balls. Explain why the data does not support this hypothesis. (3) IB Questionbank Physics 5

(d) Since Gillian s data did not support her hypothesis, she researched to find alternative hypotheses. She found that there are two theories used to predict a relationship between d and h.

6 (d) Since Gillian s data did not support her hypothesis, she researched to find alternative hypotheses. She found that there are two theories used to predict a relationship between d and h. 1 Theory 1 predicts that d = const (h) 3 and theory 2 predicts that d = const (h) 4. In order to test which theory her data supports, she plotted a graph of lg(d) against lg(h). The plot produced a straight line that could be drawn through all the error bars. 1 The graph includes the lines of maximum and minimum gradients based on the first error bar for the first non-zero data point and the last error bar. The last error bar is too small to be shown. State and explain if the original data support theory 1 or theory 2. (4) (Total 11 marks) IB Questionbank Physics 6

7 3. This question is about liquid flow. The diagram shows a storage container for liquids. The container is filled from above. The distance between the base of the container and the ground is h 0. The container, which is initially empty, is then filled at a constant rate. The height h of the liquid surface above the ground is measured as a function of time t. The results of the measurements are shown plotted below. IB Questionbank Physics 7

8 (a) Draw a best-fit line for the data. (b) It is hypothesized that h is directly proportional to t. State and explain whether this hypothesis is correct for the periods (i) t = 0 to t = 120 s. (ii) t > 120 s. (c) Use data from the graph to determine the value of h 0. (2) (d) The area of the base of the container is 1.8 m 2. Deduce that the volume of liquid entering the storage container each second is approximately 0.02 m 3 s 1. (3) IB Questionbank Physics 8

9 (f) The empty container is now filled at half the rate in (d). Using the axes, sketch a graph to show the variation of h with t in the range t = 0 to t = 900 s. (2) (Total 11 marks) IB Questionbank Physics 9

10 4. The volume V of a cylinder of height h and radius r is given by the expression V = r 2 h. In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below. V 7 h 3 The approximate uncertainty in r is A. 10. B. 5. C. 4. D. 2. (Total 1 mark) 5. A volume is measured to be 52 mm 3. This volume in m 3 is A m 3. B m 3. C m 3. D m 3. (Total 1 mark) IB Questionbank Physics 10

11 6. Two cars, X and Y, are travelling towards a junction. The velocity of car X is V X and car Y is V Y. Which of the following vectors represent the velocity of Y relative to X? (Total 1 mark) 7. The time taken for a stone dropped from rest to fall vertically through 16 m is 2.0 s. Based on these measurements, what is the best estimate for the acceleration of free fall? A. 4.0 m s 2 B. 8.0 m s 2 C. 9.8 m s 2 D. 10 m s 2 (Total 1 mark) IB Questionbank Physics 11

12 8. Two lengths, a and b, are measured to be 51±1 cm and 49±1 cm respectively. In which of the following quantities is the percentage uncertainty the largest? A. a + b B. a b C. a b D. a b (Total 1 mark) 9. In an experiment to measure the acceleration of free fall at the surface of the Earth the following results were obtained. The results are A. accurate and precise. B. inaccurate but precise. C. accurate but imprecise. Acceleration of free fall / m s D. inaccurate and imprecise. (Total 1 mark) IB Questionbank Physics 12

CHAPTER 1, TEST REVIEW

CHAPTER 1, TEST REVIEW IB PHYSICS Name: Period: Date: # Marks: XX Raw Score: IB Curve: DEVIL PHYSICS BADDEST CLASS ON CAMPUS 1. Which of the following is equivalent to the joule? A. N m 2 B. N m 2 C. kg m s 2 D. kg m 2 s 2 CHAPTER