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| 55403 | The distance from the Sun to the nearest star is about 4 x 1016 m. The Milky Way galaxy is roughly a disk of diameter ~1021 m and thickness ~1019. Find the order of magnitude of the number of stars in the Milky Way. Assume the distance between the Sun and our nearest neighbor is typical. |
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| 55404 | The consumption of natural gas by a company satisfies the empirical equation V = 1.50t + 0.008 00t 2, where V is the volume in millions of cubic feet and t the time in months. Express this equation in units of cubic feet and seconds. Assign proper units to the coefficients. Assume a month is equal to 30.0 days. |
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| 55405 | The basic function of the carburetor of an automobile is to “atomize” the gasoline and mix it with air to promote rapid combustion. As an example, assume that 30.0 cm3 of gasoline is atomized into N spherical droplets, each with a radius of 2.00 X10-5 m. What is the total surface area of these N spherical droplets? |
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| 55406 | Soft drinks are commonly sold in aluminum containers. To an order of magnitude, how many such containers are thrown away or recycled each year by U.S. consumers? |
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| 55407 | Approximately how many raindrops fall on a one-acre lot during a one-inch rainfall? Explain your reasoning. |
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| 55408 | One cubic centimeter of water has a mass of 1.00 x 10-3 kg. (a) Determine the mass of 1.00 m3 of water. (b) Biological substances are 98% water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of 1.0 µm, a human kidney, and a fly. Model the kidney as a sphere with a radius of 4.0 cm and the fly as a cylinder 4.0 mm long and 2.0 mm in diameter |
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| 55409 | In physics it is important to use mathematical approximations. Demonstrate that for small angles (<20°) tan a ≈ sin a ≈ a = πa` /180° Where, is in radians and a` is in degrees. Use a calculator to find the largest angle for which tan, may be approximated by sin, if the error is to be less than 10.0%. |
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| 55410 | Assume there are 100 million passenger cars in the United States and that the average fuel consumption is 20 mi/gal of Gasoline. If the average distance traveled by each car is 10 000 mi/yr, how much gasoline would be saved per year if average fuel consumption could be increased to 25 mi/gal? |
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| 55411 | How many significant figures are in the following numbers? (a) 78.9 ± 0.2 (d) 0.005 3. (c) 2.46 X 10-6 (b) 3.788 X 109 |
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| 55412 | To an order of magnitude, how many piano tuners are in New York City? The physicist Enrico Fermi was famous for asking questions like this on oral Ph.D. qualifying examinations. His own facility in making order-of-magnitude calculations is exemplified in Problem 45.48. |
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| 55413 | Grass grows densely everywhere on a quarter-acre plot of land. What is the order of magnitude of the number of blades of grass on this plot? Explain your reasoning. Note that 1 acre = 43 560 ft2. |
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| 55414 | The pyramid described in Problem 32 contains approximately 2 million stone blocks that average 2.50 tons each. Find the weight of this pyramid in pounds. |
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| 55415 | A pyramid has a height of 481 ft and its base covers an area of 13.0 acres (Fig. P1.32). If the volume of a pyramid is given by the expression V = ⅓ Bh, where B is the area of the base and h is the height, find the volume of this pyramid in cubic meters. (1 acre = 43 560 ft2) |
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| 55416 | One cubic meter (1.00 m3) of aluminum has a mass of 2.70 x 103 kg, and 1.00 m3 of iron has a mass of 7.86 x 103 kg. Find the radius of a solid aluminum sphere that will balance a solid iron sphere of radius 2.00 cm on an equal-arm balance. |
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| 55417 | There are nearly π X 107 s in one year. Find the percentage error in this approximation, where “percentage error’’ is defined as Percentage error = | assumed value – true value | x 100 % True value |
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| 55418 | The tropical year, the time from vernal equinox to the next vernal equinox, is the basis for our calendar. It contains 365.242199 days. Find the number of seconds in a tropical year. |
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| 55419 | Estimate the number of Ping-Pong balls that would fit into a typical-size room (without being crushed). In your solution state the quantities you measure or estimate and the values you take for them. |
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| 55420 | Assuming that 70% of the Earth’s surface is covered with water at an average depth of 2.3 mi, estimate the mass of the water on the Earth in kilograms. |
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| 55421 | The diameter of our disk-shaped galaxy, the Milky Way, is about 1.0 x 105 light-years (Ly). The distance to Messier 31, which is Andromeda, the spiral galaxy nearest to the Milky Way, is about 2.0 million Ly. If a scale model represents the Milky Way and Andromeda galaxies as dinner plates 25 cm in diameter, determine the distance between the two plates. |
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| 55422 | The radius of a solid sphere is measured to be (6.50 ± 0.20) cm, and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density. |
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