Hobson Physics: Concepts & Connections 4e

Physics: Concepts and Connections, 4e (Hobson) Chapter 3 How Things Move 1) According to Aristotle, which of these is a "natural" or "unforced" motion? A) A stone falling straight downward. B) A book coming to rest as it slides along the floor. C) Both of the above. D) Neither of the above. Answer: C Page Ref: Sec. 3.1 & 3.2 2) According to Galileo, which of these is a "natural" or "unforced" motion? A) A stone falling straight downward. B) A book coming to rest as it slides along the floor. C) Both of the above. D) Neither of the above. Answer: D Page Ref: Sec. 3.1 & 3.2 3) A book is given a brief shove along a table top and released so that it slides a short distance and comes to rest. According to Aristotle, it stopped because A) its natural motion is to come to rest. B) of its inertia. C) of gravity. D) of friction. E) the ether slows it down to a stop. Answer: A Page Ref: Sec. 3.1 & 3.2 4) A book is given a brief shove along a table top and released so that it slides a short distance and comes to rest. Galileo would say that the book stopped because A) its natural motion is to come to rest. B) of its inertia. C) of gravity. D) of friction. E) the ether slows it down to a stop. Answer: D Page Ref: Sec. 3.1 & 3.2 5) A stone is lifted and released so that it falls to the ground. According to Aristotle, it fell because A) its natural motion is to fall. B) of its inertia. C) of gravity. D) of friction. E) of electrical attraction. Answer: A Page Ref: Sec. 3.1 & 3.2 6) A stone is lifted and released so that it falls to the ground. According to Galileo, it fell because A) its natural motion is to fall. B) of its inertia. C) of gravity. D) of friction. E) of electrical attraction. Answer: C Page Ref: Sec. 3.1 & 3.2 7) According to Aristotle, which of these is a "natural" or "unforced" form of motion? A) A stone falling straight downward. B) A book coming to rest as it slides along the floor. C) Both a stone falling straight downward and a sliding book coming to rest are natural motions. D) Neither a stone falling straight downward nor a sliding book coming to rest are natural motions. Answer: C Page Ref: Sec. 3.1 & 3.2 8) According to Galileo, which of these is a "natural" or "unforced" form of motion? A) A stone falling straight downward. B) A book coming to rest as it slides along the floor. C) Both a stone falling straight downward and a sliding book coming to rest are natural motions. D) Neither a stone falling straight downward nor a sliding book coming to rest are natural motions. Answer: D Page Ref: Sec. 3.1 & 3.2 9) You give your physics book a quick push so that it slides along a table top. It soon slides to a stop. How would Aristotle and Galileo interpret this? A) Aristotle says this is just the natural motion of the book, but Galileo says the force of friction slows it to a stop. B) Aristotle says the force of friction slows it to a stop, but Galileo says this is just the natural motion of the book. C) Both of them say that this is just the natural motion of the book. D) Both of them say the force of friction slows it to a stop. E) They agree that physics books can make you crazy and it's best not to think about them. Answer: A Page Ref: Sec. 3.1 & 3.2 10) According to Aristotelian physics, what outside influence acts on a stone while it falls? A) None. B) Gravity. C) Fire. D) The Olympic gods. E) Acceleration. Answer: A Page Ref: Sec. 3.1 & 3.2 11) What, if any, evidence did Galileo have for the law of inertia? A) Using a telescope, he observed meteors and comets moving at unchanging velocity through outer space. B) A smooth ball slows down when rolling uphill, and speeds up when rolling downhill, so it should maintain an unchanging speed on a level surface. C) Noting that the length of the year does not change, he concluded that Earth must maintain an unchanging speed when moving around the sun. D) All of the above. E) He didn't have direct evidence, but proposed the law of inertia only because of the known failures of Aristotelian physics. Answer: B Page Ref: Sec. 3.1 & 3.2 12) In what kind of path would the planets move if no force acted on them? A) They would continue in their present orbits, since they already have no force on them. B) Larger elliptical orbits. C) Parabolas, like a thrown rock. D) Straight line with an acceleration of 10 m/sec2. E) Straight line with no acceleration. Answer: E Page Ref: Section 3.3 13) According to Newtonian physics, an object with no forces acting on it must A) fall. B) eventually come to rest. C) be at rest. D) either be at rest or have constant velocity. E) be accelerated, with an unchanging acceleration. Answer: D Page Ref: Section 3.3 14) Meteors in outer space keep moving, rather than slowing down and stopping. This behavior is predicted by A) the law of inertia. B) Newton's law of motion. C) Aristotle's principle of natural motion. D) Galileo's law of falling. E) the law of force pairs. Answer: A Page Ref: Section 3.3 15) In what way did Galileo improve on the physics of Aristotle? A) Galileo understood that energy is always conserved in every physical process. B) Galileo understood that the gravitational force acts between every pair of objects in the universe. C) Galileo understood that no force is needed to keep an object moving in a circle at constant speed. D) Galileo understood that a force is needed to keep an object moving at constant velocity. E) Galileo understood that "natural" (or unforced) motion occurs at constant velocity. Answer: E Page Ref: Section 3.3 16) What keeps the moon moving, i.e. why doesn't the moon slow down and stop? A) Earth's gravity keeps it moving. B) The sun's gravity keeps it moving. C) It actually is slowing down, and will come to rest in a few thousand more years. D) Nuclear processes operating in the central core of the moon. E) It is the natural motion of every object to keep moving by itself. Answer: E Page Ref: Section 3.3 17) In the "space" [or in "outer space"] between Earth and the moon there is A) no air and no force [or pull] due to gravity. B) both air and a force due to gravity. C) air, but no force due to gravity. D) no air, but there is a force due to gravity. E) a big cloud made of chocolate fudge. Answer: D Page Ref: Section 3.3 18) In the figure, the moon is moving clockwise in a circular orbit around Earth. Imagine that gravity was suddenly shut off, throughout the solar system, at the instant when the moon is in the position shown in the figure. How would the moon move, after gravity was shut off? A) In the direction of arrow A, in a straight line. B) In the direction of arrow B, in a straight line. C) In the direction of arrow C, in a straight line. D) It would continue moving in the same circular path. E) Initially in the direction of arrow A, but then curving around toward the direction of arrow B. Answer: B Page Ref: Section 3.3 19) The figure shows a ball tied to a string and swung in a circle, clockwise. If the string suddenly breaks when the ball is in the position shown, which arrow best represents the initial direction of motion of the ball just after the string breaks? A) Arrow A. B) Arrow B. C) Arrow C. D) Arrow D. E) Arrow E. Answer: A Page Ref: Section 3.3 20) Most meteoroids--rocks moving through outer space--have been moving for billions of years. What, if anything, keeps them moving and why? A) According to Newton's law of gravity, the force of gravity keeps them moving. B) According to the law of inertia, nothing is needed to keep them moving. C) According to Newton's law of gravity, nothing is needed to keep them moving. D) According to current theories about the creation of the universe, the big bang keeps them moving. E) According to Newton's law of motion, their own acceleration keeps them moving. Answer: B Page Ref: Section 3.3 21) A ball is moving at 20 m/s. If no forces act on it, then 5 seconds later the ball's speed will be A) zero. B) more than 20 m/s, but the precise answer cannot be found without further information. C) less than 20 m/s, but the precise answer cannot be found without further information. D) 20 m/s. E) None of the above. Answer: D Page Ref: Section 3.3 22) What keeps Earth moving? A) Actually, it isn't moving. B) Its inertia. C) Gravity. D) Solar energy. E) The energy of space. Answer: B Page Ref: Section 3.3 23) Jack and Jill are both traveling straight north. Jack is walking at 4 mph, while Jill is riding a bicycle at 12 mph. Regarding their speeds and velocities: A) they both have the same speed and the same velocity B) they both have the same speed but different velocities. C) they have different speeds, but the same velocities. D) they have different speeds and different velocities. E) None of the above. Answer: D Page Ref: Section 3.4 24) While a rock is falling straight down it has A) an unchanging speed and an unchanging velocity. B) a changing speed and a constant velocity. C) an unchanging speed and a changing velocity. D) a changing speed and a changing velocity. Answer: D Page Ref: Section 3.4 25) Jack rides a bicycle northward at 12 mph. Jill rides southward on the same road at 12 mph. As they pass each other A) their speeds are identical and their velocities are identical. B) their speeds are different and their velocities are different. C) their speeds are different but their velocities are identical. D) their speeds are identical but their velocities are different. E) theoretical physics predicts, surprisingly enough, that they will turn into giant frogs. Answer: D Page Ref: Section 3.4 26) Which of the following describes an object that is moving with an unchanging speed but a changing velocity? A) A car moving along a straight horizontal (level) line at a steady 80 km/hr. B) A car slowing down while moving along a straight line. C) A car rounding a curve at a steady 80 km/hr. D) A car moving up a straight hill [a hill whose "slope" is unchanging] at a steady 80 km/hr, when the car is midway up the hill. E) Both answers "C" and "D" are correct. Answer: C Page Ref: Section 3.4 27) You ride a motor scooter 8 km in 15 minutes. Your [average] speed is A) 32 km/hr. B) 2 km/hr. C) 16 km/hr. D) 4 km/hr. E) 48 km/hr. Answer: A Page Ref: Section 3.4 28) Which of the following situations represents a car whose speed is increasing? A) A car takes longer and longer times to cover equal distances. B) A car covers equal distances in equal times. C) In equal times, a car covers shorter and shorter distances. D) A car covers equal distances in shorter and shorter times. E) None of the above. Answer: D Page Ref: Section 3.4 29) You ride a motor scooter 8 km in 10 minutes. Your speed is A) 32 km/hr. B) 24 km/hr. C) 16 km/hr. D) 40 km/hr. E) None of the above. Answer: E Page Ref: Section 3.4 30) Mary passes Mike from behind while bicycling. As she passes him, A) the two have the same speeds but different velocities. B) the two have different speeds but the same velocities. C) the two have different speeds and different velocities. D) the two have the same speeds and the same velocities. E) Mike turns into a hippopotamus. Answer: C Page Ref: Section 3.4 31) The figure represents a multiple-flash photo of two balls moving to the right, and shows both balls at several numbered times. The time between flashes is 0.20 s, and the large divisions on the measuring rod are centimeters. The speed of the lower ball is A) 0.4 cm/s. B) 0.8 cm/s. C) 1.2 cm/s. D) 4.8 cm/s. E) 6 cm/s. Answer: E Page Ref: Section 3.4 32) It is 6 km to Centerville, and you bicycle there in 20 minutes. Your speed is A) 12 km/hr. B) 9 km/hr. C) 2 km/hr. D) 24 km/hr. E) 18 km/hr. Answer: E Page Ref: Section 3.4 33) An artificial satellite moves at a steady 25,000 km/hr in a circular orbit around Earth. Is it accelerated? A) Yes, because its speed is changing. B) Yes, because its direction of motion is changing. C) No, because its speed is unchanging. D) No, because its direction of motion is unchanging. E) No, for both reasons "C" and "D". Answer: B Page Ref: Section 3.5 34) A bicyclist moves around a circular track at a constant [or unchanging] speed. The bicyclist has A) zero velocity and zero acceleration (in other words, no acceleration). B) zero velocity but non-zero acceleration. C) non-zero velocity but zero acceleration. D) non-zero velocity and non-zero acceleration. E) the heebie-jeebies. Answer: D Page Ref: Section 3.5 35) An auto is moving at a steady 50 mph up a long straight [constant "slope"] incline. While it is on this incline, A) its velocity and acceleration are both zero. B) its velocity is zero but its acceleration is not zero [i.e. it does have an acceleration]. C) its acceleration is zero but its velocity is not zero. D) neither its velocity nor its acceleration are zero. E) it has the heebie-jeebies. Answer: C Page Ref: Section 3.5 36) Which of these is not accelerating? A) a car while it is rounding a corner at constant [or steady] speed B) a car starting up from rest C) a car going over the crest of a rounded hill at a constant speed D) a car while it is moving at unchanging speed up a straight [or steady] incline E) actually all of these cars are accelerating Answer: D Page Ref: Section 3.5 37) An object is not accelerated if A) its speed changes while its direction of motion remains unchanged. B) its speed remains unchanged while its direction of motion changes. C) it is acted upon by an external influence. D) its speed and its direction of motion are both unchanging. E) both answers "B" and "D" are correct. Answer: D Page Ref: Section 3.5 38) While a rock is falling straight down it has A) zero velocity. B) an unchanging velocity. C) an increasing velocity. D) a decreasing velocity. E) None of the above. Answer: C Page Ref: Section 3.5 39) While a rock is falling straight down it has A) zero acceleration. B) a constant [or unchanging] acceleration. C) an increasing acceleration. D) a decreasing acceleration. E) none of the above. Answer: B Page Ref: Section 3.5 40) A satellite orbits the earth at an unchanging speed of 18,000 mph. This satellite A) is accelerated. B) has a changing velocity. C) Both of the above. D) None of the above. Answer: C Page Ref: Section 3.5 41) In which of the following cases does the automobile have an acceleration? A) An auto moving along a straight (or steady) upward incline at constant speed. B) An auto rounding a curve at constant speed. C) Both of the above. D) None of the above. Answer: B Page Ref: Section 3.5 42) Which of the following describes an object that is accelerated? A) A car rounding a curve at a steady 80 km/hr B) A car slowing down while moving along a straight line C) Both of the above. D) A car moving up a straight hill [a hill whose "slope" is unchanging] at a steady 80 km/hr, when the car is midway up the hill E) All of the above. Answer: C Page Ref: Section 3.5 43) A car is rounding the top, or crest, of a hill while moving at a steady 50 km/hr. What can you say about this car's acceleration, and why? A) The car is accelerated, because its speed is changing. B) The car is accelerated, because its direction of motion is changing. C) The car is not accelerated, because its direction of motion is not changing. D) The car is not accelerated, because its speed is not changing. E) The car is not accelerated, because neither its direction of motion nor its speed are changing. Answer: B Page Ref: Section 3.5 44) Is it possible for the driver of a car to accelerate the car without pressing on the accelerator? A) Yes, by pressing on the brake. B) Yes, by turning the steering wheel. C) Yes, by both of the above methods. D) No, because the only way to speed up is to press on the accelerator. E) No, because of the way that we define the word "acceleration" in physics. Answer: C Page Ref: Section 3.5 45) The figure represents a multiple-flash photo of two balls moving to the right, and shows both balls at several numbered times. In the figure, A) both balls are accelerated, and the upper ball is moving fastest. B) neither ball is accelerated, and the upper ball is moving fastest. C) both balls are accelerated, and the lower ball is moving fastest. D) the lower ball is accelerated, but the upper ball is not accelerated. E) neither ball is accelerated, and the lower ball is moving fastest. Answer: E Page Ref: Section 3.5 46) The figure represents a multiple-flash photo of two balls moving to the right, and shows both balls at several numbered times. In the figure, A) neither ball passes the other ball during their motion. B) the upper ball, which has a larger acceleration, passes the lower ball. C) the lower ball, which has a larger acceleration, passes the upper ball. D) the upper ball, which has a larger speed, passes the lower ball. E) the lower ball, which has a larger speed, passes the upper ball. Answer: E Page Ref: Section 3.5 47) Is it possible for an object to accelerate but without changing its speed? A) Yes, for example when a car is halfway up a straight hill [a hill whose slope, or angle with the horizontal, does not change] and moving a an unchanging speed. B) Yes, for example when a car turns a corner while maintaining an unchanging speed. C) Both of the above. D) No, because the word "acceleration" means "speeding up." E) No, because the word "acceleration" means "a change in speed." Answer: B Page Ref: Section 3.5 48) A simple "do it yourself" experiment, performed in class, showing that objects accelerate as they fall is A) dropping an object from several meters high, and measuring its position at the end of each second. B) using a flash camera to photograph the position of a ball at several equally-spaced times as the ball falls. C) dropping an object to the floor from various heights, and observing the sound of the object hitting the floor. D) dropping an object to the floor from various heights, and measuring the time of fall. E) throwing an object horizontally from some distance above the ground, and measuring the time for it to hit the ground as compared with an object that is simply dropped from the same distance above the ground. Answer: C Page Ref: Section 3.6 49) While a stone is falling [neglecting air resistance], A) the direction of its velocity is downward. B) its speed is changing. C) it is accelerated. D) All of the above. E) None of the above. Answer: D Page Ref: Section 3.6 50) In our study of falling objects, we noted that the total distance fallen was approximately 5 m in 1 s, 20 m in 2 s, 45 m in 3 s, and 80 m in 4 s. Which of the following best describes the pattern in this data? A) Distance is proportional to the square of the time. B) Distance is inversely proportional to the square of the time. C) Distance is proportional to the time. D) The path followed by the motion is elliptical. E) The path followed by the motion is parabolic. Answer: A Page Ref: Section 3.6 51) Which statement is the most accurate for falling objects on Earth? A) Heavy objects fall significantly faster than light objects. B) Neglecting the effects of air resistance, heavy objects fall faster than light objects. C) Neglecting the effects of air resistance, light objects fall faster than heavy objects. D) All objects fall at roughly the same speed. E) Neglecting the effects of air resistance, all objects fall at roughly the same speed. Answer: E Page Ref: Section 3.6 52) Edgar Jones, angry at having purchased a tasteless pizza, drops his pizza off the Brooklyn bridge. As it falls, Edgar's pizza has a constant [or unchanging] (NOTE: neglect air resistance.) A) speed. B) acceleration. C) velocity. D) position. E) All of the above. Answer: B Page Ref: Section 3.6 53) An object is dropped from rest on the planet Jupiter. At the end of 1 second, it has fallen 8 m and is moving at 16 m/s. What was its average speed during the entire first second [i.e. from t=0 until =1 sec]? A) 4 m/s B) 8 m/s C) 12 m/s D) 16 m/s E) None of the above. Answer: B Page Ref: Section 3.6 54) Continuing the previous question, the total distance fallen after [i.e. at the end of] two seconds will be A) 16 m. B) 24 m. C) 32 m. D) 64 m. E) None of the above. Answer: C Page Ref: Section 3.6 55) Continuing the previous question, at the end of two seconds the object's speed will be A) 16 m/s. B) 32 m/s. C) 48 m/s. D) 64 m/s. E) None of the above. Answer: B Page Ref: Section 3.6 56) Suppose you are on the moon and you drop a rock and a feather at the same time. You will find that A) the two fall at the same speed, but this speed is slower than a rock would fall on Earth. B) the two fall at the same speed, and this speed is the same as the speed of a rock falling on Earth. C) the rock falls faster than the feather, although both of them fall slower than they would on Earth. D) the rock falls faster than the feather, and both speeds are the same as they would be on Earth. E) they don't fall--they remain suspended above the surface of the moon. Answer: A Page Ref: Section 3.6 57) On the planet Venus, a Venusian picks up a stone and drops it into a deep hole. If it falls 3 m in 1 second, how far will it fall in 2 seconds? You can neglect Venusian air resistance. A) 6 m B) 9 m C) 12 m D) 15 m E) 20 m Answer: C Page Ref: Section 3.6 58) Falling objects [dropped near the earth's surface, neglecting air resistance] all fall at A) the same constant (or unchanging) speed. B) the same constant [or unchanging] velocity. C) an acceleration that is larger for more massive objects. D) the same constant [or unchanging] acceleration. E) zero acceleration. Answer: D Page Ref: Section 3.6 59) Galileo's principle of falling is limited by the condition that A) air resistance must be negligible. B) the two objects must have the same weight. C) Both of the above. D) the two objects must have the same size. E) actually, this principle has no limitations. Answer: A Page Ref: Section 3.6 60) In twice the time, an object will fall A) twice as far. B) four times as far. C) eight times as far. D) 12 times as far. E) 16 times as far. Answer: B Page Ref: Section 3.6 61) In twice the time, an object will attain a speed that is A) twice as fast. B) four times as fast. C) eight times as fast. D) 12 times as fast. E) 16 times as fast. Answer: A Page Ref: Section 3.6 62) A rock is dropped from rest off of a high cliff on another planet, planet X. There is no atmosphere, and thus no air resistance, on planet X. At the end of 1 second, the rock is moving at a speed of 6 m/s. At the end of 2 seconds, it is moving at 12 m/s. How fast will the rock be moving at 4 seconds after being dropped? A) 18 m/s B) 20 m/s C) 24 m/s D) 36 m/s E) 40 m/s Answer: C Page Ref: Section 3.6 63) Continuing the previous question, what is the rock's average speed during the entire first second [from t=0 until t=1 sec]? A) 0 B) 3 m/s C) 5 m/s D) 6 m/s E) 10 m/s Answer: B Page Ref: Section 3.6 64) The acceleration due to gravity is 10 m/sec2. If an object falls from rest, its instantaneous speed at the end of the fifth second is A) 10 m/sec. B) 50 m/sec. C) 100 m/sec. D) 5 m/sec. E) impossible to determine from the given information. NOTE: neglect air resistance. Answer: B Page Ref: Section 3.6 65) An astronaut drops a rock on the moon. It falls 1 meter in 1 second. In 4 seconds, it falls a total distance of A) 4 meters. B) 8 meters. C) 9 meters. D) 12 meters. E) 16 meters. Answer: E Page Ref: Section 3.6 66) If a helium-filled balloon is released on Earth, it rises. How would a helium-filled balloon move if it were released a few feet above the surface of the moon? A) it would rise B) it would remain suspended at the point of release C) it would fall at the same rate a rock falls when dropped on the moon D) it would fall, but much more slowly than a rock dropped on the moon E) it would turn into a giant pumpkin Answer: C Page Ref: Section 3.6 67) On Mars, the acceleration due to gravity is 8 m/s/s. If an object is dropped over the surface of Mars, how fast will it be moving at the end of 3 seconds of fall? A) 8 m/s B) 16 m/s C) 24 m/s D) 32 m/s E) 72 m/s Answer: C Page Ref: Section 3.6 68) On the moon, an object dropped from rest falls a distance of 1 m in 1 second. How far will it have fallen during 3 seconds? A) 3 m B) 6 m C) 9 m D) 12 m E) 18 m Answer: C Page Ref: Section 3.6 69) On the planet Jupiter, a dropped object picks up a speed of 20 m/sec in one second. How fast will it be going at the end of 3 seconds of fall, neglecting "air" resistance on Jupiter? A) 20 m/sec B) 40 m/sec C) 60 m/sec D) 80 m/sec E) 180 m/sec Answer: C Page Ref: Section 3.6 70) On Mars, an object dropped from rest falls a distance of 4 m in 1 second. How far will it fall in 2 second, neglecting "air" resistance on Mars? A) 8 m B) 12 m C) 16 m D) 24 m E) 32 m Answer: C Page Ref: Section 3.6 71) While a rock is falling straight down with negligible air resistance, it has A) zero speed. B) an unchanging speed. C) a decreasing speed. D) an increasing speed. E) None of the above. Answer: D Page Ref: Section 3.6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1