Chapter 1: Problems (1.57 - 1.61)

1.57 An acre, a unit of land measurement still in wide use, has a length of one furlong (1/8 mi) and a width one-tenth of its length. a) How many acres are in a square mile? b) How many square feet are in an acre? See Appendix E. c) An acre-foot is the volume of water that would cover one acre of flat land to a depth of one foot. How many gallons are in an acre-foot?

1.58 An estate on the California coast was offered for sale for $4,950,000. The total area of the estate was 102 acres (see problem 1.57). a) Considering the price of the estate to be proportional to its area, what was the cost of one square meter of the estate? b) What would be the price of a portion of the estate the size of a postage stamp (7/8 in. by 1.0 in.)?

1.59 The Hydrogen Maser.  You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. For the following questions, use only three significant figures. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.). a) What is the time for one cycle of the radio wave?  b) How many cycles occur in 1 h? c) How many cycles would have occurred during the age of the earth, which is estimated to be $4.6 \times 10^ 9$ years? d) By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the Earth?

1.60 Estimate the number of atoms in your body. (Hint: Based on what you know about biology and chemistry, what are the most common types of atom in your body?  What is the mass of each type of atom? Appendix D gives the atomic masses for different elements, measure in atomic mass units; you can find the value of an atomic mass unit, or 1 u, in Appendix F.)

1.61 Biological tissues are typically made up of 98% water. Given that the density of water is $1.0 \times 10^3 kg/m^3$, estimate the mass of a) the heart of an adult human; b) a cell with a diameter of 0.5 $\mu$m; c) a honey bee.