Problem 12
(a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in \(\mu\)g/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 75-kg adult receive? (c) A typical multivitamin tablet can contain 2.0 mg of vitamin B\(_2\) (riboflavin), and the RDA is 0.0030 g/day. How many such tablets should a person take each day to get the proper amount of this vitamin, if he gets none from other sources? (d) The RDA for the trace element selenium is 0.000070 g/day. Express this dose in mg/day.
Problem 14
With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle's width to its length; (c) the perimeter of the rectangle; (d) the difference between the length and the width; and (e) the ratio of the length to the width?
Problem 15
A useful and easy-to-remember approximate value for the number of 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.)
Problem 16
Express each approximation of \(\pi\) to six significant figures: (a) 22/7 and (b) 355/113. (c) Are these approximations accurate to that precision?
Problem 17
A rather ordinary middle-aged man is in the hospital for a routine checkup. The nurse writes "200" on the patient's medical chart but forgets to include the units. Which of these quantities could the 200 plausibly represent? The patient's (a) mass in kilograms; (b) height in meters; (c) height in centimeters; (d) height in millimeters; (e) age in months.
Problem 20
Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm\(^3\) of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? (b) What would the diameter (in meters) of the space station have to be to contain all this air?
Problem 26
A spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction \(45^{\circ}\) east of south. and then \(280 \mathrm{~m}\) at \(30^{\circ}\) east of north. After a fourth displacement,she finds herself back where she started. Use a scale drawing to determine the magnitude and direction of the fourth displacement. (See also Problem 1.61 for a different approach.)
Problem 28
Let \(\theta\) be the angle that the vector \(\overrightarrow{A}\) makes with the \(+$$x\)-axis, measured counterclockwise from that axis. Find angle \(\theta\) for a vector that has these components: (a) A\(_x\) = 2.00 m, A\(_y\) = \(-\)1.00 m; (b) A\(_x\) = 2.00 m, A\(_y\) = 1.00 m; (c) A\(_x\) = \(-\)2.00 m, A\(_y\) = 1.00 m; (d) A\(_x\) = -2.00 m, A\(_y\) = -1.00 m.
Problem 29
Vector \(\overrightarrow{A}\) has \(y\)-component A\(_y\) = \(+\)9.60 m. \(\overrightarrow{A}\) makes anangle of 32.0\(^{\circ}\) counterclockwise from the \(+$$y\)-axis. (a) What is the \(x\)-component of \(\overrightarrow{A}\)? (b) What is the magnitude of \(\overrightarrow{A}\)?
Problem 30
Vector \(\overrightarrow{A}\) is in the direction 34.0\(^{\circ}\) clockwise from the \(-$$y\)-axis. The \(x\)-component of \(\overrightarrow{A}\) is A\(_x\) = -16.0 m. (a) What is the \(y\)-component of \(\overrightarrow{A}\)? (b) What is the magnitude of \(\overrightarrow{A}\)?
