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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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Question: The purity of gold can be tested by weighing it in air and in water. How? Do you think you could get away with making a fake gold brick by gold-plating some cheaper material?
You have probably noticed that the lower the tire pressure, the larger the contact area between the tire and the road. Why?
For a spherical planet with mass , volume , and radius ,derive an expression for the acceleration due to gravity at the planet鈥檚 surface, , in terms of the average density of the planet, , and the planet鈥檚 diameter, . The table gives the values of and for the eight major planets:
(a) Treat the planets as spheres. Your equation for as a function of
and
shows that if the average density of the planets is constant, a graph of
versus
will be well represented by a straight line. Graph
as a function of
for the eight major planets. What does the graph tell you about the variation in average density? (b) Calculate the average density for each major planet. List the planets in order of decreasing density, and give the calculated average density of each. (c) The earth is not a uniform sphere and has greater density near its center. It is reasonable to assume this might be true for the other planets. Discuss the effect this nonuniformity has on your analysis. (d) If Saturn had the same average density as the earth, what would be the value of
at Saturn鈥檚 surface?
You take an empty glass jar and push it into a tank of water with the open mouth of the jar downward, so that the air inside the jar is trapped and cannot get out. If you push the jar deeper into the water, does the buoyant force on the jar stay the same? If not, does it increase or decrease? Explain.
You are on the roof of the physics building, above the ground (Fig. P2.70). Your physics professor, who istall, is walking alongside the building at a constant speed of. If you wish to drop an egg on your professor鈥檚 head, where should the professor be when you release the egg? Assume that the egg is in free fall.
(Fig. P2.70)
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