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Chapter 1: Q10 DQ (page 389)
Which has a greater buoyant force on it: apiece of wood floating with part of its volume above water or a piece of submerged iron? Or, must you know their masses before you can answer? Explain.
The iron piece will have the greater buoyant force.
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The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (a) Compute the acceleration due to gravity on the surface of Venus from these data. (b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?
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?
At what distance above the surface of the earth is the acceleration due to the earth鈥檚 gravity 0.980 m/s2 if the acceleration due to gravity at the surface has magnitude 9.8 m/s2?
Hot Jupiters. In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star (hence the term 鈥渉ot Jupiter鈥�). The orbit was just the distance of Mercury from our sun, and it takes the planet onlydays to make one orbit (assumed to be circular). (a) What is the mass of the star? Express your answer in kilograms and as a multiple of our sun鈥檚 mass. (b) How fast (in km>s) is this planet moving?
In each case, find the x- and y-components of vector: (a); (b); (c); (d), where.
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