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Chapter 1: Q10DQ (page 294)
To maximize the moment of inertia of a flywheel while minimizing its weight, what shape and distribution of mass should it have? Explain.
A thin-walled hollow cylinder is used to maximize the moment of inertia of a flywheel while minimizing its weight.
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The black dots at the top of Fig. represent a series of high-speed photographs of an insect flying in a straight line from left to right (in the positive x-direction). Which of the graphs in Fig. most plausibly depicts this insect鈥檚 motion?
In Wagner鈥檚 opera Das Rheingold,the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of gold is 19.3 g/cm3, and take its value to be about $10 per gram.
As planets with a wide variety of properties are being discovered
outside our solar system, astrobiologists are considering whether and how life
could evolve on planets that might be very different from earth. One recently
discovered extrasolar planet, or exoplanet, orbits a star whose mass is 0.70
times the mass of our sun. This planet has been found to have 2.3 times the
earth鈥檚 diameter and 7.9 times the earth鈥檚 mass. For planets in this size range,
computer models indicate a relationship between the planet鈥檚 density and
composition:
Based on these data, what is the most likely composition of this planet? (a)
Mostly iron; (b) iron and rock; (c) iron and rock with some lighter elements; (d)
hydrogen and helium gases.
How many times does a human heart beat during a person鈥檚 lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm3 of blood with each beat.)
A shaft is drilled from the surface to the center of the earth (see Fig. 13.25). As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With this approximation, the gravitational force on an object with mass m, that is inside the earth at a distance r from the center, has magnitude (as shown in Example 13.10) and points toward the center of the earth. (a) Derive an expression for the gravitational potential energyof the object鈥揺arth system as a function of the object鈥檚 distance from the center of the earth. Take the potential energy to be zero when the object is at the center of the earth. (b) If an object is released in the shaft at the earth鈥檚 surface, what speed will it have when it reaches the center of the earth?
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