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Chapter 1: Q13E (page 28)
Bacteria vary in size, but a diameter ofis not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size? (Consult Appendix B for relevant formulas.)
Given
Bacteria Diameter =
Radius
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Express each approximation of 蟺 to six significant figures: (a) 22/7 and (b) 355/113. (c) Are these approximations accurate to that precision?
In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 km away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin at the nest and extend the +x-axis to the release point, what was the bird鈥檚 average velocity in (a) for the return flight and (b) for the whole episode, from leaving the nest to returning?
Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 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?
A hammer with mass m is dropped from rest from a height h above the earth鈥檚 surface. This height is not necessarily small compared with the radiusof the earth. Ignoring air resistance, derive an expression for the speed v of the hammer when it reaches the earth鈥檚 surface. Your expression should involve h,, and(the earth鈥檚 mass).
You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of in the rope. If Sneezy hangs from a similar rope while delivering presents at the earth鈥檚 equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.) Consult Appendix F and start with a free-body diagram of Sneezy at the equator.
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