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Chapter 1: Q12DQ (page 356)
12. In pioneer days, when a Conestoga wagon was stuck in the mud, people would grasp the wheel spokes and try to turn the wheels, rather than simply pushing the wagon. Why?
Creating torque on the wheel helps to push the wagon forward.
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If andare nonzero vectors, is it possible for both andto bezero? Explain.
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?
In hot-air ballooning, a large balloon is filled with air heated by a gas burner at the bottom. Why must the air be heated? How does the balloonist control ascent and descent?
You are given two vectors and . Let counter- clockwise angles be positive. (a) What angle does make with the +x-axis? (b) What angle doeslocalid="1662185215101" make with the +x-axis? (c) Vectorlocalid="1662185222673" is the sum of localid="1662185243350" andlocalid="1662185251585" , so localid="1662185235469" What angle does localid="1662185258976" make with the +x-axis?
According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm, express this volume in cubic inches.
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