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- Question : 1P - (a) Use information on the endpapers of this book to calculate the average density of the Earth. (b) Where does the value fit among those listed in Table 14.1 in Chapter 14? Look up the density of a typical surface rock like granite in another source and compare it with the density of the Earth.
- Question : 2P - A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 3 10227 kg. (a) Determine the density of the proton. (b) State how your answer to part (a) compares with the density of osmium, given in Table 14.1 in Chapter 14.
- Question : 3P - Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.
- Question : 4P - What mass of a material with density r is required to make a hollow spherical shell having inner radius r1 and outer radius r2?
- Question : 5P - You have been hired by the defense attorney as an expert witness in a lawsuit. The plaintiff is someone who just returned from being a passenger on the first orbital space tourist flight. Based on a travel brochure offered by the space travel company, the plaintiff expected to be able to see the Great Wall of China from his orbital height of 200 km above the Earth
- Question : 6P - A surveyor measures the distance across a straight river by the following method (Fig. P1.6). Starting directly across from a tree on the opposite bank, she walks d 5 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is u 5 35.08. How wide is the river?
- Question : 7P - A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Fig- ure P1.7a. The atoms reside at the corners of cubes of side L 5 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as shown in Figure P1.7b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.
- Question : 8P - The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position as x 5 kamt n, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m 5 1 and n 5 2. Can this analysis give the value of k?
- Question : 9P - Which of the following equations are dimensionally correct? (a) vf 5 vi 1 ax (b) y 5 (2 m) cos (kx), where k 5 2 m21
- Question : 10P - (a) Assume the equation x 5 At 3 1 Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt 5 3At2 1 B.
- Question : 11P - A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kilograms per cubic meter).
- Question : 12P - Why is the following situation impossible? A student
- Question : 13P - One cubic meter (1.00 m3) of aluminum has a mass of 2.70 3 103 kg, and the same volume of iron has a mass of 7.86 3 103 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.
- Question : 14P - Let rAl represent the density of aluminum and rFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rFe on an equal-arm balance.
- Question : 15P - One gallon of paint (volume 5 3.78 3 1023 m3) covers an area of 25.0 m2. What is the thickness of the fresh paint on the wall?
- Question : 16P - An auditorium measures 40.0 m 3 20.0 m 3 12.0 m. The density of air is 1.20 kg/m3. What are (a) the volume of the room in cubic feet and (b) the weight of air in the room in pounds?
- Question : 17P - (a) Compute the order of magnitude of the mass of a bathtub half full of water. (b) Compute the order of magnitude of the mass of a bathtub half full of copper coins.
- Question : 18P - To an order of magnitude, how many piano tuners reside in New York City? The physicist Enrico Fermi was famous for asking questions like this one on oral Ph.D. qualifying examinations.
- Question : 19P - Your roommate is playing a video game from the latest Star Wars movie while you are studying physics. Distracted by the noise, you go to see what is on the screen. The game involves trying to fly a spacecraft through a crowded field of asteroids in the asteroid belt around the Sun. You say to him,
- Question : 20P - How many significant figures are in the following numbers? (a) 78.9 6 0.2 (b) 3.788 3 109 (c) 2.46 3 1026 (d) 0.005 3
- Question : 21P - The tropical year, the time interval from one vernal equinox to the next vernal equinox, is the basis for our calendar. It contains 365.242 199 days. Find the number of seconds in a tropical year.
- Question : 22P - Review. The average density of the planet Uranus is 1.27 3 103 kg/m3. The ratio of the mass of Neptune to that of Uranus is 1.19. The ratio of the radius of Neptune to that of Uranus is 0.969. Find the average density of Neptune.
- Question : 23P - Review. In a community college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 94.7%. The difference between the number of cars and the number of SUVs is 18. Find the number of SUVs in the lot.
- Question : 24P - Review. Find every angle u between 0 and 3608 for which the ratio of sin u to cos u is 23.00.
- Question : 25P - Review. The ratio of the number of sparrows visiting a bird feeder to the number of more interesting birds is 2.25. On a morning when altogether 91 birds visit the feeder, what is the number of sparrows?
- Question : 26P - Review. Prove that one solution of the equation 2.00x4 2 3.00x3 1 5.00x 5 70.0 is x 5 22.22.
- Question : 27P - Review. From the set of equations p 5 3q pr 5 qs 12 pr 2 1 12 qs 2 5 12 qt2 involving the unknowns p, q, r, s, and t, find the value of the ratio of t to r.
- Question : 28P - Review. Figure P1.28 shows students studying the thermal conduction of energy into cylindrical blocks of ice. As we will see in Chapter 19, this process is described by the equation Q Dt 5 kpd2sTh 2 Tc d 4L For experimental control, in one set of trials all quantities except d and Dt are constant. (a) If d is made three times larger, does the equation predict that Dt will get larger or get smaller? By what factor? (b) What pattern of proportionality of Dt to d does the equation predict? (c) To display this proportionality as a straight line on a graph, what quantities should you plot on the horizontal and vertical axes? (d) What expression represents the theoretical slope of this graph?
- Question : 29P - In a situation in which data are known to three significant digits, we write 6.379 m 5 6.38 m and 6.374 m 5 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m 5 6.38 m. We could equally well write 6.375 m 5 6.37 m,
- Question : 30P - (a) What is the order of magnitude of the number of micro organisms in the human intestinal tract? A typical bacterial length scale is 1026 m. Estimate the intestinal volume and assume 1% of it is occupied by bacteria. (b) Does the number of bacteria suggest whether the bacteria are beneficial, dangerous, or neutral for the human body? What functions could they serve?
- Question : 31P - The distance from the Sun to the nearest star is about 4 3 1016 m. The Milky Way galaxy (Fig. P1.31) is roughly a disk of diameter 1021 m and thickness , 1019 m. 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.
- Question : 32P - Why is the following situation impossible? In an effort to boost interest in a television game show, each weekly winner is offered an additional $1 million bonus prize if he or she can personally count out that exact amount from a supply of one-dollar bills. The winner must do this task under supervision by television show executives and within one 40-hour work week. To the dismay of the show
- Question : 33P - Bacteria and other prokaryotes are found deep underground, in water, and in the air. One micron (1026 m) is a typical length scale associated with these microbes. (a) Estimate the total number of bacteria and other prokaryotes on the Earth. (b) Estimate the total mass of all such microbes.
- Question : 34P - A spherical shell has an outside radius of 2.60 cm and an inside radius of a. The shell wall has uniform thickness andis made of a material with density 4.70 g/cm3. The space inside the shell is filled with a liquid having a density of 1.23 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a. (b) For what value of the variable a does m have its maximum possible value? (c) What is this maximum mass? (d) Explain whether the value from part (c) agrees with the result of a direct calculation of the mass of a solid sphere of uniform density made of the same material as the shell. (e) What If? Would the answer to part (a) change if the inner wall were not concentric with the outer wall?
- Question : 35P - Air is blown into a spherical balloon so that, when its radius is 6.50 cm, its radius is increasing at the rate 0.900 cm/s. (a) Find the rate at which the volume of the balloon is increasing. (b) If this volume flow rate of air entering the balloon is constant, at what rate will the radius be increasing when the radius is 13.0 cm? (c) Explain physically why the answer to part (b) is larger or smaller than 0.9 cm/s, if it is different.
- Question : 36P - In physics, it is important to use mathematical approximations. (a) Demonstrate that for small angles (, 208) tan a < sin a < a 5 pa9 1808 where a is in radians and a9 is in degrees. (b) Use a calculator to find the largest angle for which tan a may be approximated by a with an error less than 10.0%.
- Question : 37P - The consumption of natural gas by a company satisfies the empirical equation V 5 1.50t 1 0.008 00t2, where V is the volume of gas in millions of cubic feet and t is the time in months. Express this equation in units of cubic feet and seconds. Assume a month is 30.0 days.
- Question : 38P - A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 12.08. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.08. (a) Draw a picture of the problem, neglecting the height of the woman
- Question : 39P - A woman stands at a horizontal distance x from a mountain and measures the angle of elevation of the mountaintop above the horizontal as u. After walking a distance d closer to the mountain on level ground, she finds the angle to be f. Find a general equation for the height y of the mountain in terms of d, f, and u, neglecting the height of her eyes above the ground.

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