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- Question : 1DC - How many correct experiments do we need to disprove a theory? How many do we need to prove a theory? Explain.
- Question : 2DC - Suppose you are asked to compute the tangent of 5.00 meters. Is this possible? Why or why not?
- Question : 3DC - What is your height in centimeters? What is your weight in newtons?
- Question : 4DC - The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms are gaining mass at an average rate of about 1 mg>y (y = year) when compared every 10 years or so to the standard international kilogram. Does this apparent increase have any importance? Explain.
- Question : 5DC - What physical phenomena (other than a pendulum or cesium clock) could you use to define a time standard?
- Question : 6DC - Describe how you could measure the thickness of a sheet of paper with an ordinary ruler
- Question : 7DC - If a statement is considered to be true based solely on logic but without any demonstration, it is said to be an axiom. What is the difference between an axiom and a theory?
- Question : 8DC - What are the units of volume? Suppose another student tells you that a cylinder of radius r and height h has volume given by pr3h. Explain why this cannot be right
- Question : 9DC - Three archers each fire four arrows at a target. Joe
- Question : 10DC - Is the vector 1nd + ne + kn2 a unit vector? Is the vector 13.0nd ? 2.0ne2 a unit vector? Justify your answers.
- Question : 11DC - If pressure is force per unit area, show that a 60-kg man with a 3-cm heel size exerts approximately 20 times more pressure on the floor than a 600-kg elephant with a 1-ft heel size.
- Question : 12DC - Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum of zero? Explain.
- Question : 13DC - Estimate the time taken by light to travel the Earth
- Question : 14DC - Air traffic controllers give instructions called
- Question : 15DC - Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.
- Question : 16DC - (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)?
- Question : 17DC - If C S = A S + B S , what must be true about the directions and magnitudes of A S and B S if C = A + B? What must be true about the directions and magnitudes of A S and B S if C = 0?
- Question : 18DC - If A S and B S are nonzero vectors, is it possible for both SA ~ B S and A S : B S to be zero? Explain
- Question : 19DC - d A S : B S to be zero? Explain. Q1.19 The
- Question : 20DC - Let A S represent any nonzero vector. Why is A S >A a unit vector, and what is its direction? If u is the angle that A S makes with the +x-axis, explain why 1A S >A2 ~ nd is called the direction cosine for that axis.
- Question : 21DC - Figure 1.7 shows the result of an unacceptable error in the stopping position of a train. If a train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10.0 m, what is the percent error in the total distance covered? Is it correct to write the total distance covered by the train as 890,010 m? Explain
- Question : 22DC - Which of the following are legitimate mathematical operations: (a) A S ~ 1B S ? C S 2; (b) 1A S ? B S 2 : C S ; (c) A S ~ 1B S : C S 2; (d) A S : 1B S : C S 2; (e) A S : 1B S ~ C S 2? In each case, give the reason for your answer.
- Question : 23DC - Consider the vector products A S : 1B S : C S 2 and 1A S : B S 2 : C S . Give an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors A S , B S , and C S such that these two vector products are equal? If so, give an example
- Question : 24DC - Show that, no matter what A S and B S are, A S ~ 1A S : B S 2 = 0. (Hint: Do not look for an elaborate mathematical proof. Consider the definition of the direction of the cross product.)
- Question : 25DC - (a) If A S ~ B S = 0, does it necessarily follow that A = 0 or B = 0? Explain. (b) If A S : B S = 0, does it necessarily follow that A = 0 or B = 0? Explain
- Question : 26DC - If A S = 0 for a vector in the xy-plane, does it follow that A x = -Ay? What can you say about Ax and Ay?
- Question : 1E - Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.60 mile and (b) feet in 1.90 km.
- Question : 2E - According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm, express this volume in cubic inches
- Question : 3E - How many nanoseconds does it take light to travel 5.50 ft in vacuum? (This result is a useful quantity to remember.)
- Question : 4E - The density of mercury is 13.5 g>cm3. What is this value in kilograms per cubic meter?
- Question : 5E - 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.
- Question : 6E - A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft2. If a lot has an area of 17.0 acres, what is its area in hectares?
- Question : 7E - How many years older will you be 1.10 billion seconds from now? (Assume a 365-day year.)
- Question : 8E - While driving in an exotic foreign land, you see a speed limit sign that reads 185,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1 8 mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)
- Question : 9E - A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If you are driving this car in Europe and want to compare its mileage with that of other European cars, express this mileage in km>L 1L = liter2. Use the conversion factors in Appendix E. (b) If this car
- Question : 10E - 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
- Question : 11E - Neptunium. In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain reaction. Neptunium-237 has a density of 19.5 g>cm3. What would be the radius of a sphere of this material that has a critical mass?
- Question : 12E - (a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg>day for males. Express this quantity in mg>day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 77-kg adult receive? (c) A typical multivitamin tablet can contain 2.0 mg of vitamin B2 (riboflavin), and the RDA is 0.0030 g>day. How many such tablets should a person take each day to get the proper amount of this vitamin, if he gets none from other sources? (d) The RDA for the trace element selenium is 0.000070 g>day. Express this dose in mg>day.
- Question : 13E - Bacteria. Bacteria vary in size, but a diameter of 2.0 mm is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size? (Consult Appendix B for relevant formulas.)
- Question : 14E - With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 16 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle
- Question : 15E - A useful and easy-to-remember approximate value for the number of seconds in a year is p * 107. Determine the percent error in this approximate value. (There are 365.24 days in one year.)
- Question : 16E - Express each approximation of p to six significant figures: (a) 22>7 and (b) 355>113. (c) Are these approximations accurate to that precision?
- Question : 17E - A rather ordinary middle-aged man is in the hospital for a routine checkup. The nurse writes
- Question : 18E - height in millimeters; (e) age in months. 1.18 . How many kernels of corn does it take to fill a 4-L soft drink bottle? (Take that about four kernels fill 1 cm3.)
- Question : 19E - (Take that about four kernels fill 1 cm3.) 1.19 . bio How many times does a typical person blink her eyes in a lifetime?
- Question : 20E - Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? (b) What would the diameter (in meters) of the space station have to be to contain all this air?
- Question : 21E - In Wagner
- Question : 22E - How many times does a human heart beat during a person
- Question : 23E - You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle? (Hint: Start by estimating the diameter of a drop of water.)
- Question : 24E - For the vectors A S and SB in Fig. E1.24, use a scale drawing to find the magnitude and direction of (a) the vector sum A S + B S and (b) the vector difference A S ? B S . Use your answers to find the magnitude and direction of (c) ?A S ? B S and (d) B S ? A S . (See also Exercise 1.31 for a different approach.)
- Question : 25E - A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.)
- Question : 26E - A spelunker is surveying a cave. She follows a passage 170 m straight west, then 250 m in a direction 45
- Question : 27E - Compute the x- and y-components of the vectors A S , B S , C S , and D S in Fig. E1.24
- Question : 28E - Let u be the angle that the vector A S makes with the +x-axis, measured counterclockwise from that axis. Find angle u for a vector that has these components: (a) Ax = 4.00 m, A y = -1.90 m; (b) Ax = 3.70 m, Ay = 1.40 m; (c) Ax = -1.50 m, A y = 2.40 m; (d) Ax = -4.80 m, Ay = -5.00 m.
- Question : 29E - Vector A S has y-component Ay = +13.0 m. A S makes an angle of 32.0
- Question : 30E - Vector A S is in the direction 40.0
- Question : 31E - For the vectors A S and B S in Fig. E1.24, use the method of components to find the magnitude and direction of (a) the vector sum A S + B S ; (b) the vector sum B S + A S ; (c) the vector difference SA ? B S ; (d) the vector difference B S ? A S .
- Question : 32E - A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.
- Question : 33E - A disoriented physics professor drives 3.30 km north, then 3.90 km west, and then 1.35 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.
- Question : 34E - Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = -8.60 cm, A y = 5.20 cm; (b) Ax = -9.70 m, Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.
- Question : 35E - Vector A S is 2.80 cm long and is 60.0
- Question : 36E - In each case, find the x- and y-components of vector A S : (a) A S = 3.20nd ? 6.50ne; (b) AS = 18.2ne ? 7.91nd; (c) AS = -12.0nd + 21.2ne ; (d) AS = 5.0BS, where BS = 8nd ? 4ne
- Question : 37E - Write each vector in Fig. E1.24 in terms of the unit vectors nd and ne
- Question : 38E - Given two vectors A S = 4.00nd + 7.00ne and BS = 5.00nd ? 2.00ne, (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference A S ? B S ; and (c) find the magnitude and direction of the vector difference A S ? B S . (d) In a vector diagram show A S , B S , and A S ? B S , and show that your diagram agrees qualitatively with your answer to part (c).
- Question : 39E - (a) Write each vector in Fig. E1.39 in terms of the unit vectors nd and ne. (b) Use unit vectors to express vector C S , where SC = 3.00 A S ? 4.00 B S . (c) Find the magnitude and direction of C S .
- Question : 40E - You are given two vectors A S = -3.00nd + 6.00ne and SB = 7.00nd + 2.00ne. Let counterclockwise angles be positive. (a) What angle does A S make with the +x@axis? (b) What angle does SB make with the +x@axis? (c) Vector C S is the sum of A S and B S , so C S = A S + B S . What angle does C S make with the +x@axis?
- Question : 41E - Given two vectors A S = -2.00nd + 3.00ne + 4.00kn and SB = 3.00nd + 1.00ne ? 3.00kn, (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference A S ? B S ; and (c) find the magnitude of the vector difference SA ? B S . Is this the same as the magnitude of B S ? A S ? Explain.
- Question : 42E - (a) Find the scalar product of the vectors A S and B S given in Exercise 1.38. (b) Find the angle between these two vectors. 1.43 . For the vectors A S , B S , and C S in Fig. E1.24, find the scalar products (a) A S ~ B S ; (b) B S ~ C S ; (c) A S ~ C
- Question : 43E - For the vectors A S , B S , and C S in Fig. E1.24, find the scalar products (a) A S ~ B S ; (b) B S ~ C S ; (c) A S ~ C S . 1.44 .. Find the vector product A S : B
- Question : 44E - Find the vector product A S : B S (expressed in unit vectors) of the two vectors given in Exercise 1.38. What is the magnitude of the vector product?
- Question : 45E - he vector product? 1.45 .. Find the angle between each of these pairs of vectors: (a) A S = -2.00nd + 6.00ne and BS = 2.00nd ? 3.00ne (b) A S = 3.00nd + 5.00ne and BS = 10.00nd + 6.00ne (c) A S = -4.00nd + 2.00ne and BS = 7.00nd + 14.00ne
- Question : 46E - For the two vectors in Fig. E1.35, find the magnitude and direction of (a) the vector product A S : B S ; (b) the vector product SB : A
- Question : 47E - For the two vectors A S and D S in Fig. E1.24, find the magnitude and direction of (a) the vector product A S : D S ; (b) the vector product D S : A
- Question : 48E - For the two vectors A S and B S in Fig. E1.39, find (a) the scalar product A S ~ B S ; (b) the magnitude and direction of the vector product A S : B
- Question : 49P - White Dwarfs and Neutron Stars. Recall that density is mass divided by volume, and consult Appendix B as needed. (a) Calculate the average density of the earth in g>cm3, assuming our planet is a perfect sphere. (b) In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf that has about the same mass as it does now but is reduced to about 15,000 km in diameter. What will be its density at that stage? (c) A neutron star is the remnant of certain supernovae (explosions of giant stars). Typically, neutron stars are about 20 km in diameter and have about the same mass as our sun. What is a typical neutron star density in g>cm3?
- Question : 50P - An acre has a length of one furlong 11 8 mi2 and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat land to a depth of 1 foot. How many gallons are in 1 acre-foot?
- Question : 51P - An Earthlike Planet. In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth
- Question : 52P - The Hydrogen Maser. A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. For the following questions, use only three significant figures. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.) (a) What is the time for one cycle of the radio wave? (b) How many cycles occur in 1 h? (c) How many cycles would have occurred during the age of the earth, which is estimated to be 4.6 * 109 years? (d) By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth?
- Question : 53P - Breathing Oxygen. The density of air under standard laboratory conditions is 1.29 kg>m3, and about 20% of that air consists of oxygen. Typically, people breathe about 1 2 L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is stored uncompressed in a cubical tank, how long is each side of the tank?
- Question : 54P - A rectangular piece of aluminum is 7.60 { 0.01 cm long and 1.50 { 0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in the area is equal to the sum of the fractional uncertainties in the length and in the width. (This is a general result.)
- Question : 55P - As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 { 0.02 cm and a thickness of 0.0700 { 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio
- Question : 56P - Biological tissues are typically made up of 98% water. Given that the density of water is 1.0 * 103 kg>m3, estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5 mm; (c) a honeybee
- Question : 57P - Estimate the number of atoms in your body. (Hint: Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix D gives the atomic masses of different elements, measured in atomic mass units; you can find the value of an atomic mass unit, or 1 u, in Appendix E.)
- Question : 58P - Two ropes in a vertical plane exert equal-magnitude forces on a hanging weight but pull with an angle of 72.0
- Question : 59P - Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0
- Question : 60P - Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A S , B S , and C S shown in Fig. P1.60. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero
- Question : 61P - As noted in Exercise 1.26, a spelunker is surveying a cave. She follows a passage 177 m straight west, then 215 m in a direction 45
- Question : 62P - Emergency Landing. A plane leaves the airport in Galisteo and flies 145 km at 68.0
- Question : 63P - Dislocated Shoulder. A patient with a dislocated shoulder is put into a traction apparatus as shown in Fig. P1.63. The pulls A S and B S have equal magnitudes and must combine to produce an outward traction force of 5.52 N on the patient
- Question : 64P - A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, next 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point (Fig. P1.64). Find the magnitude and direction of the third leg of the journey. Draw the vector-addition diagram and show that it is in qualitative agreement with your numerical solution.
- Question : 65P - You leave the airport in College Station and fly 23.0 km in a direction 34.0o south of east. You then fly 46.0 km due north. How far and in what direction must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?
- Question : 66P - On a training flight, a student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas
- Question : 67P - As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0
- Question : 68P - An explorer in Antarctica leaves his shelter during a whiteout. He takes 43 steps northeast, next 80 steps at 60
- Question : 69P - You are lost at night in a large, open field. Your GPS tells you that you are 122.0 m from your truck, in a direction 58.0
- Question : 70P - A ship leaves the island of Guam and sails 290 km at 49.0
- Question : 71P - Bones and Muscles. A physical therapy patient has a forearm that weighs 21.5 N and lifts a 114.0-N weight. These two forces are directed vertically downward. The only other significant forces on this forearm come from the biceps muscle (which acts perpendicular to the forearm) and the force at the elbow. If the biceps produces a pull of 232 N when the forearm is raised 43.0
- Question : 72P - You decide to go to your favorite neighborhood restaurant. You leave your apartment, take the elevator 10 flights down (each flight is 3.0 m), and then walk 15 m south to the apartment exit. You then proceed 0.200 km east, turn north, and walk 0.100 km to the entrance of the restaurant. (a) Determine the displacement from your apartment to the restaurant. Use unit vector notation for your answer, clearly indicating your choice of coordinates. (b) How far did you travel along the path you took from your apartment to the restaurant, and what is the magnitude of the displacement you calculated in part (a)?
- Question : 73P - While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 km at 30.0
- Question : 74P - A fence post is 59.0 m from where you are standing, in a direction 38.0
- Question : 75P - A dog in an open field runs 10.0 m east and then 30.0 m in a direction 55.0
- Question : 76P - Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 30.0 m in a direction 60.0
- Question : 77P - You are camping with Joe and Karl. Since all three of you like your privacy, you don
- Question : 78P - Bond Angle in Methane. In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates for which one of the C
- Question : 79P - Vectors A S and B S have scalar product -7.00, and their vector product has magnitude +9.00. What is the angle between these two vectors?
- Question : 80P - A cube is placed so that one corner is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (Fig. P1.80). Use vectors to compute (a) the angle be tween the edge along the z-axis (line ab) and the diagonal from the origin to the opposite corner (line ad), and (b) the angle be tween line ac (the diagonal of a face) and line ad.
- Question : 81P - Vector A S has magnitude 12.0 m, and vector B S has magnitude 12.0 m. The scalar product A S ~ B S is 76.0 m2. What is the magnitude of the vector product between these two vectors?
- Question : 82P - Obtain a unit vector perpendicular to the two vectors given in Exercise 1.41
- Question : 83P - The scalar product of vectors A S and B S is +59.0 m2. Vector A S has magnitude 9.00 m and direction 28.0
- Question : 84P - Two vectors A S and B S have magnitudes A = 3.00 and B = 3.00. Their vector product is A S : B S = -5.00kn + 2.00nd. What is the angle between A S and B S ?
- Question : 85P - You are given vectors A S = 4.9nd ? 6.9ne and BS = -3.6nd + 6.7ne. A third vector, CS, lies in the xy-plane. Vector CS is perpendicular to vector A S , and the scalar product of C S with B S is 10.0. From this information, find the components of vector C S .
- Question : 86P - Later in our study of physics we will encounter quantities represented by 1A S : B S 2 ~ C S . (a) Prove that for any three vectors A S , B S , and C S , A S ~ 1B S : C S 2 = 1A S : B S 2 ~ C S . (b) Calculate 1A S : B S 2 ~ C S for vector A S with magnitude A = 4.98 and angle uA = 26.7
- Question : 87P - You are a team leader at a pharmaceutical company. Several technicians are preparing samples, and you want to compare the densities of the samples (density = mass>volume) by using the mass and volume values they have reported. Unfortunately, you did not specify what units to use. The technicians used a variety of units in reporting their values, as shown in the following table. Sample ID Mass Volume A 8.00 g 1.67 * 10-6 m3 B 6.00 mg 9.38 * 106 mm3 C 8.00 mg 2.50 * 10-3 cm3 D 9.00 * 10-4 kg 2.81 * 103 mm3 E 9.00 * 104 ng 1.41 * 10-2 mm3 F 6.00 * 10-2 mg 1.25 * 108 mm3 List the sample IDs in order of increasing density of the sample
- Question : 88P - You are a mechanical engineer working for a manufacturing company. Two forces, F S 1 and F S 2 , act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between F S 1 and F S 2 from 0o to 90o while the magnitude of each force stays constant. And, you can measure the magnitude of the resultant force they produce (their vector sum), but you cannot directly measure the magnitude of each separate force. You measure the magnitude of the resultant force for four angles u between the directions of the two forces as follows: U Resultant force (N) 0.0
- Question : 89P - Navigating in the Solar System. The Mars Polar Lander spacecraft was launched on January 3, 1999. On December 3, 1999, the day Mars Polar Lander impacted the Martian surface at high velocity and probably disintegrated, the positions of the earth and Mars were given by these coordinates: x y z Earth 0.3182 AU 0.9329 AU 0.0000 AU Mars 1.3087 AU -0.4423 AU -0.0414 AU With these coordinates, the sun is at the origin and the earth
- Question : 90CP - Completed Pass. The football team at Enormous State University (ESU) uses vector displacements to record its plays, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at +1.0nd ? 5.0ne, where the units are yards, nd is to the right, and ne is downfield. Subsequent displacements of the receiver are +9.0nd (he is in motion before the snap), +11.0ne (breaks downfield), -6.0nd + 4.0ne (zigs), and +12.0nd + 18.0ne (zags). Meanwhile, the quarterback has dropped straight back to a position -7.0ne. How far and in which direction must the quarterback throw the ball? (Like the coach, you will be well advised to diagram the situation before solving this numerically.)
- Question : 91CP - Navigating in the Big Dipper. All of the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.91 shows the distances from the earth to each of these stars. The distances are given in light-years (ly), the distance that light travels in one year. One light-year equals 9.461 * 1015 m. (a) Alkaid and Merak are 25.6o apart in the earth
- Question : 92PP - What is total volume of the gas-exchanging region of the lungs? (a) 2000 mm3; (b) 2 m3; (c) 2.0 L; (d) 120 L
- Question : 93PP - If we assume that alveoli are spherical, what is the diameter of a typical alveolus? (a) 0.20 mm; (b) 2 mm; (c) 20 mm; (d) 200 mm.
- Question : 94PP - ndividuals vary considerably in total lung volume size, total lung volume, and number of alveoli per individual? As the total volume of the lungs increases, (a) the number and volume of individual alveoli increase; (b) the number of alveoli increases and the volume of individual alveoli decreases; (c) the volume of the individual alveoli remains constant and the number of alveoli increases; (d) both the number of alveoli and the volume of individual alveoli remain constant

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