Chapter 1: Exercises (1.11 - 1.15)

1.11 Neptunium. In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a chain reaction. This element has a density of 19.5 g/cm³. What would be the radius of a sphere of this material that has a critical mass?

1.12 A useful and easy-to-remember approximate value for the number f seconds in a year is $\pi\times 10^7$. Determine the percent error in this approximate value. (There are 365.24 days in one year.)

1.13 Figure 1.5 shows the result of unacceptable error in the stopping position of a train. a) If a train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10 m, what is percentage error in the total distance covered? b) Would it be correct to write the total distance covered by the train as 890,010 m? Explain.

1.14 With a wooden ruler you measure te length o a rectangular piece of sheet metal to be 12 mm. You use micrometer calipers to measure the width of the rectangle and obtain the value of 5.98 mm. Give your answers o the following questions to the correct number of significant figures. a) What is the area of the rectangle? b) What is the ratio of the rectangle's width to its length? c) What is the perimeter of the rectangle? d) What is the difference between the length and the width? e) What is the ratio of the length to the width?

1.15 Estimate the percent error in measuring a) a distance of about 75 cm with a meter stick; b) a mas of about 12 g with a chemical balance; c) a time interval of about 6 min with a stopwatch.