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Chapter 1: Q8E (page 195)
A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force to the cart as it undergoes a displacement . How much work does the force you apply do on the grocery cart?
The total work applied by constant force to the grocery cart is -150 J.
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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 describing the size of a large ship, one uses such expressions as 鈥渋t displaces 20,000 tons.鈥� What does this mean? Can the weight of the ship be obtained from this information?
Question-. (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is the negative of another? Why? Does your answer here contradict what you said in part (a)?
You normally drive on the freeway between San Diego and Los Angeles at an average speed of 105 km/h (65 mi/h), and the trip takes 1 h and 50 min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average speed of only 70 km/h (43 mi/h). How much longer does the trip take?
(a) Write each vector in Fig. E1.39 in terms of the unit vectors and . (b) Use unit vectors to express vector , where (c) Find the magnitude and direction .
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