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Chapter 1: Q5DQ (page 389)
You have probably noticed that the lower the tire pressure, the larger the contact area between the tire and the road. Why?
The pressure is inversely related to the contact area.
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A cargo ship travels from the Atlantic Ocean (salt water) to Lake Ontario (freshwater) via the St. Lawrence River. The ship rides several centimeters lower in the water in Lake Ontario than it did in the ocean. Explain
The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s2. Use 1 ft = 30.48 cm to express this acceleration in units of m/s2. (c) The density of water is 1.0 g/cm3. Convert this density to units of kg/m3.
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?
For the hydraulic lift shown in Fig. 12.7, what must be the ratio of the diameter of the vessel at the car to the diameter of the vessel where the force F1 is applied so that a 1520-kg car can be lifted with a force F1 of just 125 N?
The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm.
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