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Chapter 1: Q5 E (page 1)
A machine part is undergoing SHM with a frequency of and amplitude . How long does it take the part to go from to ?
The machine part takes to go from to .
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Given two vectors and , (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference ; and (c) find the magnitude and direction of the vector difference . (d) In a vector diagram show and , and show that your diagram agrees qualitatively with your answer to part (c).
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?
Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.
A particle of mass 3m is located from a particle of mass m.
(a) Where should you put a third mass M so that the net gravitational force on M due to the two masses is precisely zero?
(b) Is the equilibrium of M at this point stable or unstable (i) for points along the line connecting m and 3m, and (ii) for points along the line passing through M and perpendicular to the line connecting m and 3m?
If ,what must be true about the directions and magnitudes of and if ? What must be true about the directions and magnitudes of role="math" localid="1647990633202" and if ?
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