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Transcript

Final Revision sheet with answers at the end Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. What is the speed of an object at rest? a. 0.0 m/s b. 1.0 m/s c. 9.8 m/s d. 9.81 m/s 2. Which of the following is the equation for average velocity? a. c. v = xt b. d. ____ 3. Suppose you are given a position versus time graph. The slope of a line drawn tangent to a point on the curve of this graph describes what quantity? a. acceleration c. instantaneous velocity b. displacement d. position ____ 4. According to the graph above, during which interval is the cat at rest? a. 0.0–5.0 s c. 10.0–15.0 s b. 5.0–10.0 s d. 15.0–20.0 s ____ 5. According to the graph above, the cat has the fastest speed during which interval? a. 0.0–5.0 s c. 10.0–15.0 s b. 5.0–10.0 s d. 15.0–20.0 s ____ 6. According to the graph above, during which interval does the cat have the greatest positive velocity? a. 0.0–5.0 s c. 10.0–15.0 s b. 5.0–10.0 s d. 15.0–20.0 s ____ 7. Which of the following line segments on a position versus time graph is physically impossible? a. a horizontal line b. a straight line that slopes to the left ____ ____ 8. Acceleration is defined as a. a rate of displacement. b. the rate of change of displacement. c. a straight line that slopes to the right d. a vertical line c. the change in velocity. d. the rate of change of velocity. 9. Which of the following is the equation for acceleration? a. c. a = vt b. ____ 10. What is the SI unit of acceleration? a. m/s b. m /s d. c. m/s d. ms ____ 11. If you know the acceleration of a car, its initial velocity, and the time interval, which of the following can you predict? a. the direction of the car’s final velocity b. the magnitude of the car’s final velocity c. the displacement of the car d. all of the above ____ 12. When a car’s velocity is positive and its acceleration is negative, what is happening to the car’s motion? a. The car slows down. c. The car travels at constant speed. b. The car speeds up. d. The car remains at rest. ____ 13. When a car’s velocity is negative and its acceleration is negative, what is happening to the car’s motion? a. The car slows down. c. The car travels at constant speed. b. The car speeds up. d. The car remains at rest. ____ 14. The graph above describes the motion of a cyclist. During the interval shown, the cyclist is a. slowing down. c. traveling at the same speed. b. speeding up. d. at rest. ____ 15. In the graph above, how does the acceleration at A compare with the acceleration at B? a. The acceleration at A is positive and less than the acceleration at B. b. The acceleration at B is positive and less than the acceleration at A. c. The accelerations at A and B are each zero. d. The accelerations at A and B cannot be determined. ____ 16. Which of the following line segments on a velocity versus time graph is physically impossible? a. horizontal line c. straight line with negative slope b. straight line with positive slope d. vertical line ____ 17. The graph above describes the motion of a ball. At what point does the ball have an instantaneous velocity of zero? a. A c. C b. B d. D ____ 18. The graph above describes the motion of a ball. At what point is the velocity of the ball equal to its velocity at B? a. A c. D b. C d. none of the above ____ 19. The motion of a ball on an inclined plane is described by the equation quantities must have a value of zero? a. x c. v b. x d. t ____ 20. Acceleration due to gravity is also called a. negative velocity. b. displacement. . Which of the following c. free-fall acceleration. d. instantaneous acceleration. ____ 21. Which of the following statements applies to the motion of a ball rising and then falling in free fall? I. The ball has constant acceleration as it moves upward. II. The ball has constant acceleration at the top of its path. III. The ball has constant acceleration as it moves downward. a. I only b. III only c. I and III d. I, II, and III ____ 22. A baseball catcher throws a ball vertically upward and catches it in the same spot as it returns to the mitt. At what point in the ball’s path does it experience zero velocity and nonzero acceleration at the same time? a. midway on the way up b. at the top of its path c. the instant it leaves the catcher’s hand d. the instant before it arrives in the catcher’s mitt ____ 23. When there is no air resistance, objects of different masses dropped from rest a. fall with equal accelerations and with equal displacements. b. fall with different accelerations and with different displacements. c. fall with equal accelerations and with different displacements. d. fall with different accelerations and with equal displacements. ____ 24. Objects that are falling toward Earth in free fall move a. faster and faster. c. at a constant velocity. b. slower and slower. d. slower then faster. ____ 25. Which would fall with greater acceleration in a vacuum—a leaf or a stone? a. the leaf b. the stone c. They would accelerate at the same rate. d. It is difficult to determine without more information. ____ 26. Two students are standing on a fire escape, one twice as high as the other. Simultaneously, each drops a ball. If the first ball strikes the ground at time t , when will the second ball strike the ground? (Disregard air resistance. Assume a = g = 9.81 m/s .) a. t = 4t b. t = 2t c. t = d. t = t t ____ 27. Which of the following is a physical quantity that has a magnitude but no direction? a. vector c. resultant b. scalar d. frame of reference ____ 28. Which of the following is a physical quantity that has both magnitude and direction? a. vector c. resultant b. scalar d. frame of reference ____ 29. Which of the following is an example of a vector quantity? a. velocity c. volume b. temperature d. mass ____ 30. Identify the following quantities as scalar or vector: the mass of an object, the number of leaves on a tree, wind velocity. a. vector, scalar, scalar c. scalar, vector, scalar b. scalar, scalar, vector d. vector, scalar, vector ____ 31. Identify the following quantities as scalar or vector: the speed of a snail, the time it takes to run a mile, the free-fall acceleration. a. vector, scalar, scalar c. vector, scalar, vector b. scalar, scalar, vector d. scalar, vector, vector ____ 32. For the winter, a duck flies 10.0 m/s due south against a gust of wind with a speed of 2.5 m/s. What is the resultant velocity of the duck? a. 12.5 m/s south c. 7.5 m/s south b. –12.5 m/s south d. –7.5 m/s south ____ 33. Multiplying or dividing vectors by scalars results in a. vectors. b. scalars. c. vectors if multiplied or scalars if divided. d. scalars if multiplied or vectors if divided. ____ 34. A car travels down a road at a certain velocity, vcar. The driver slows down so that the car is traveling only half as fast as before. Which of the following is the correct expression for the resulting velocity? a. 2vcar c. – vcar b. vcar d. –2vcar ____ 35. A football player runs in one direction to catch a pass, then turns and runs twice as fast in the opposite direction toward the goal line. Which of the following is a correct expression for the original velocity and the resulting velocity? a. –vplayer, –2vplayer c. vplayer, –2vplayer b. vplayer, 2vplayer d. 2vplayer, –vplayer ____ 36. A student walks from the door of the house to the end of the driveway and realizes that he missed the bus. The student runs back to the house, traveling three times as fast. Which of the following is the correct expression for the return velocity if the initial velocity is vstudent? a. 3vstudent c. vstudent b. vstudent d. –3vstudent ____ 37. Which of the following is the best coordinate system to analyze a painter climbing a ladder at an angle of 60° to the ground? a. x-axis: horizontal along the ground; y-axis: along the ladder b. x-axis: along the ladder; y-axis: horizontal along the ground c. x-axis: horizontal along the ground; y-axis: up and down d. x-axis: along the ladder; y-axis: up and down ____ 38. An ant on a picnic table travels 3.0 10 cm eastward, then 25 cm northward, and finally 15 cm westward. What is the magnitude of the ant’s displacement relative to its original position? a. 70 cm c. 52 cm b. 57 cm d. 29 cm ____ 39. In a coordinate system, a vector is oriented at angle with respect to the x-axis. The x component of the vector equals the vector’s magnitude multiplied by which trigonometric function? a. cos c. sin b. cot d. tan ____ 40. In a coordinate system, a vector is oriented at angle with respect to the x-axis. The y component of the vector equals the vector’s magnitude multiplied by which trigonometric function? a. cos c. sin b. cot d. tan ____ 41. How many displacement vectors shown in the figure above have horizontal components? a. 2 c. 4 b. 3 d. 5 ____ 42. In a coordinate system, the magnitude of the x component of a vector and , the angle between the vector and x-axis, are known. The magnitude of the vector equals the x component a. divided by the cosine of c. multiplied by the cosine of b. divided by the sine of d. multiplied by the sine of ____ 43. Find the resultant of these two vectors: 2.00 10 units due east and 4.00 10 units 30.0 north of west. a. 300 units, 29.8 north of west c. 546 units, 59.3 north of west b. 581 units, 20.1 north of east d. 248 units, 53.9 north of west ____ 44. Which of the following is the motion of objects moving in two dimensions under the influence of gravity? a. horizontal velocity c. vertical velocity b. directrix d. projectile motion ____ 45. Which of the following is an example of projectile motion? a. a jet lifting off a runway b. a thrown baseball c. an aluminum can dropped straight down into the recycling bin d. a space shuttle being launched ____ 46. Which of the following is not an example of projectile motion? a. a volleyball served over a net c. a hot-air balloon drifting toward Earth b. a baseball hit by a bat d. a long jumper in action ____ 47. What is the path of a projectile (in the absence of friction)? a. a wavy line b. a parabola c. a hyperbola d. Projectiles do not follow a predictable path. ____ 48. Which of the following exhibits parabolic motion? a. a stone thrown into a lake c. a leaf falling from a tree b. a space shuttle orbiting Earth d. a train moving along a flat track ____ 49. Which of the following does not exhibit parabolic motion? a. a frog jumping from land into water b. a basketball thrown to a hoop c. a flat piece of paper released from a window d. a baseball thrown to home plate The figure above shows the path of a ball tossed from a building. Air resistance is ignored. ____ 50. In the figure above, the magnitude of the ball’s velocity is least at location a. A. c. C. b. B. d. D. ____ 51. In the figure above, the magnitude of the ball’s velocity is greatest at location a. A. c. C. b. B. d. D. ____ 52. In the figure above, the horizontal component of the ball’s velocity at A is a. zero. b. equal to the vertical component of the ball’s velocity at C. c. equal in magnitude but opposite in direction to the horizontal component of the ball’s velocity at D. d. equal to the horizontal component of its initial velocity. ____ 53. In the figure above, at which point is the ball’s speed about equal to the speed at which it was tossed? a. A c. C b. B d. D ____ 54. A track star in the long jump goes into the jump at 12 m/s and launches herself at 20.0° above the horizontal. What is the magnitude of her horizontal displacement? (Assume no air resistance and that a = –g = –9.81 m/s .) a. 4.6 m b. 9.2 m c. 13 m d. 15 m ____ 55. A passenger on a bus moving east sees a man standing on a curb. From the passenger’s perspective, the man appears to a. stand still. b. move west at a speed that is less than the bus’s speed. c. move west at a speed that is equal to the bus’s speed. d. move east at a speed that is equal to the bus’s speed. ____ 56. A piece of chalk is dropped by a teacher walking at a speed of 1.5 m/s. From the teacher’s perspective, the chalk appears to fall a. straight down. c. straight down and forward. b. straight down and backward. d. straight backward. ____ 57. A jet moving at 500.0 km/h due east is in a region where the wind is moving at 120.0 km/h in a direction 30.00 north of east. What is the speed of the aircraft relative to the ground? a. 620.2 km/h c. 588.7 km/h b. 606.9 km/h d. 511.3 km/h ____ 58. Which of the following is the cause of an acceleration? a. speed c. force b. inertia d. velocity ____ 59. Which of the following statements does not describe force? a. Force causes objects at rest to remain stationary. b. Force causes objects to start moving. c. Force causes objects to stop moving. d. Force causes objects to change direction. ____ 60. What causes a moving object to change direction? a. acceleration c. inertia b. velocity d. force ____ 61. Which of the following forces arises from direct physical contact between two objects? a. gravitational force c. contact force b. fundamental force d. field force ____ 62. A newton is equivalent to which of the following quantities? a. kg c. kgm/s b. kgm/s d. kg(m/s) ____ 63. The length of a force vector represents the a. cause of the force. b. direction of the force. c. magnitude of the force. d. type of force. ____ 64. A free-body diagram represents all of the following except a. the object. c. forces exerted by the object. b. forces as vectors. d. forces exerted on the object. ____ 65. The free-body diagram shown above represents a car being pulled by a towing cable. In the diagram, the 5800 N force is a. the gravitational force acting on the car. b. the backward force the road exerts on the car. c. the upward force the road exerts on the car. d. the force exerted by the towing cable on the car. ____ 66. A free-body diagram of a ball falling in the presence of air resistance would show a. only a downward arrow to represent the force of air resistance. b. only a downward arrow to represent the force due to gravity. c. a downward arrow to represent the force due to gravity and an upward arrow to represent the force of air resistance. d. an upward arrow to represent the force due to gravity and a downward arrow to represent the force of air resistance. ____ 67. Which of the following is the tendency of an object to maintain its state of motion? a. acceleration c. force b. inertia d. velocity ____ 68. A crate is released on a frictionless plank inclined at angle with respect to the horizontal. Which of the following relationships is true? (Assume that the x-axis is parallel to the surface of the incline.) a. F = F c. F = F b. F = 0 d. none of the above ____ 69. A car goes forward along a level road at constant velocity. The additional force needed to bring the car into equilibrium is a. greater than the normal force times the coefficient of static friction. b. equal to the normal force times the coefficient of static friction. c. the normal force times the coefficient of kinetic friction. d. zero. ____ 70. A single force acts on an object. The components of this force act along the +x-axis and the –y-axis. The single force that will bring the object into equilibrium has components that act along the a. +x-axis and +y-axis. c. x-axis and +y-axis. b. +x-axis and y-axis. d. x-axis and y-axis. ____ 71. As an object falls toward Earth, a. the object does not exert a force on Earth. b. the object exerts a downward force on Earth. c. Newton’s third law does not apply. d. the upward acceleration of Earth is negligible because of its large mass. ____ 72. A sculpture is suspended in equilibrium by two cables, one from a wall and the other from the ceiling of a museum gallery. Cable 1 applies a horizontal force to the right of the sculpture and has a tension, F . Cable 2 applies a force upward and to the left at an angle of 37.0 to the negative x-axis and has a tension, F . The gravitational force on the sculpture is 5.00 10 N. What is F ? a. 4440 N c. 8310 N b. 6640 N d. 3340 N ____ 73. If a nonzero net force is acting on an object, then the object is definitely a. at rest. c. being accelerated. b. moving with a constant velocity. d. losing mass. ____ 74. Which statement about the acceleration of an object is correct? a. The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object. b. The acceleration of an object is directly proportional to the net external force acting on the object and directly proportional to the mass of the object. c. The acceleration of an object is inversely proportional to the net external force acting on the object and inversely proportional to the mass of the object. d. The acceleration of an object is inversely proportional to the net external force acting on the object and directly proportional to the mass of the object. ____ 75. According to Newton’s second law, when the same force is applied to two objects of different masses, a. the object with greater mass will experience a great acceleration, and the object with less mass will experience an even greater acceleration. b. the object with greater mass will experience a smaller acceleration, and the object with less mass will experience a greater acceleration. c. the object with greater mass will experience a greater acceleration, and the object with less mass will experience a smaller acceleration. d. the object with greater mass will experience a small acceleration, and the object with less mass will experience an even smaller acceleration. ____ 76. A sled traveling at a speed of 3.0 m/s slows to a stop 4.0 m from the point where its passenger rolled off. What is the magnitude of the horizontal net force that slows the 110 N sled? (Assume ag = 9.81 m/s .) a. 130 N c. 37 N b. 34 N d. 13 N ____ 77. Two perpendicular forces, one of 45.0 N directed upward and the other of 60.0 N directed to the right, act simultaneously on an object with a mass of 35.0 kg. What is the magnitude of the resultant acceleration of the object? a. 2.14 m/s c. 5.25 m/s b. 3.00 m/s d. 1.41 m/s ____ 78. Which are simultaneous equal but opposite forces resulting from the interaction of two objects? a. net external forces c. gravitational forces b. field forces d. action-reaction pairs ____ 79. Newton’s third law of motion involves the interactions of a. one object and one force. c. two object and one force. b. one object and two forces. d. two objects and two forces. ____ 80. A hammer drives a nail into a piece of wood. Identify an action-reaction pair in this situation. a. The nail exerts a force on the hammer; the hammer exerts a force on the wood. b. The hammer exerts a force on the nail; the wood exerts a force on the nail. c. The hammer exerts a force on the nail; the nail exerts a force on the hammer. d. The hammer exerts a force on the nail; the hammer exerts a force on the wood. ____ 81. A ball is dropped from a person’s hand and falls to Earth. Identify an action-reaction pair in this situation. a. The hand exerts a force on the ball; Earth exerts a force on the hand. b. Earth exerts a force on the ball; the hand exerts a force on Earth. c. Earth exerts a force on the hand; the hand exerts a force on the ball. d. Earth exerts a force on the ball; the ball exerts a force on Earth. ____ 82. The magnitude of the gravitational force acting on an object is a. frictional force. c. inertia. b. weight. d. mass. ____ 83. A measure of the quantity of matter is a. density. b. weight. c. force. d. mass. ____ 84. A book with a mass of 2.0 kg is held in equilibrium on a board with a slope of 60.0 by a horizontal force. What is the normal force exerted on the book? a. 39 N c. 15 N b. 61 N d. 34 N ____ 85. What are the units of the coefficient of friction? a. N c. N b. 1/N d. The coefficient of friction has no units. ____ 86. There are six books in a stack, and each book weighs 5 N. The coefficient of static friction between the books is 0.2. With what horizontal force must one push to start sliding the top five books off the bottom one? a. 1 N c. 3 N b. 5 N d. 7 N ____ 87. A crate is carried in a pickup truck traveling horizontally at 15.0 m/s. The truck applies the brakes for a distance of 28.7 m while stopping with uniform acceleration. What is the coefficient of static friction between the crate and the truck bed if the crate does not slide? a. 0.400 c. 0.892 b. 0.365 d. 0.656 ____ 88. An ice skater moving at 10.0 m/s coasts to a halt in 1.0 10 m on a smooth ice surface. What is the coefficient of friction between the ice and the skates? a. 0.025 c. 0.102 b. 0.051 d. 0.205 Short Answer 89. Distinguish between the displacement of a traveler who takes a train from New York to Boston and the displacement of a traveler who flies from Boston to New York. 90. If a cat moves from a negative position to a positive position, is the cat’s displacement negative or positive? Explain. 91. Explain how a dog that has moved can have a displacement of zero. 92. Construct a graph of position versus time for the motion of a dog, using the data in the table above. Explain how the graph indicates that the dog is moving at a constant speed. 93. Construct a graph of position versus time for the motion of a dog, using the data in the table above. What is the dog’s average velocity? 94. Construct a graph of position versus time of a jogger, using the data in the table above. What is the average velocity of the jogger? 95. The ratio of the change in an object’s velocity to the time required for the change to occur describes what quantity? 96. A motorized scooter starts from rest and accelerates for 4 s at 2 m/s . It continues at a constant speed for 6 s. Graph the scooter’s velocity versus time. Explain how you could use the graph to show that the scooter’s acceleration is constant during the intervals 1.0–2.0 s and 5.0–6.0 s. 97. What is free fall? 98. What is the magnitude of the acceleration of an object in free fall near Earth’s surface? 99. Why is the direction of free-fall acceleration usually negative? 100. What is a scalar quantity? 101. What is a vector quantity? 102. Which is a vector quantity, distance or displacement? 103. The length of a vector arrow in a diagram is proportional to what property of the vector? 104. What is a resultant? 105. Breaking a vector into two components is given what term? 106. If the magnitude of a vector component is zero, what is the orientation of the vector with respect to that axis? 107. If the magnitude of a vector component equals zero, what is the magnitude of the other vector component? 108. What is the term for the curved, parabolic path that an object follows when thrown, launched, or otherwise projected near the surface of the Earth? 109. Briefly explain why a basketball being thrown toward a hoop is considered projectile motion. The figure above shows the path of a ball tossed from a building. Air resistance is ignored. 110. In the figure above, what would happen to the height of the ball’s path if it were launched with a greater velocity? 111. In the figure above, what would happen to the width of the ball’s path if it were launched with a lesser velocity? 112. The length of the force vector is proportional to what property of a force? 113. Why is force not a scalar quantity? 114. Construct a free-body diagram of a car being towed. 115. What is the natural tendency of an object that is in motion? 116. If two teams playing tug-of-war pull on a rope with equal but opposite forces, what is the net external force on the rope? 117. For an object to be in equilibrium, the net force acting on the object must have what value? 118. A block of wood supported by two concrete blocks is chopped in half by a karate instructor. Identify an action-reaction pair, and compare the forces exerted by each object. 119. How do mass and weight vary with altitude? 120. Distinguish between mass and weight. 121. In what direction does the force of air resistance act? 122. What happens to air resistance when an object accelerates? 123. When a car is moving, what happens to the velocity and acceleration of the car if the air resistance becomes equal to the force acting in the opposite direction? 124. Why is air resistance considered a form of friction? 125. How does the coefficient of static friction for two surfaces in contact compare to the coefficient of kinetic friction for the same two surfaces? 126. In this text, what does the symbol represent? Problem 127. A horse trots past a fencepost located 14 m to the left of a gatepost. It then passes another fencepost located 15 m to the right of the gatepost 14 s later. What is the average velocity of the horse? 128. A biker travels at an average speed of 11.1 m/s along a 8.9 103 m straight segment of a bike path. How much time does the biker take to travel this segment? 129. A hiker travels south along a straight path for 1.2 h with an average speed of 4.1 km/h and then travels north for 1.7 h with an average speed of 4.7 km/h. What is the hiker’s displacement for the total trip? 130. A stroller walks the first half of a straight 1.4 km trail at a steady pace of 1.7 m/s, east. He walks the second half at a constant stride of 0.37 m/s, east. What is his average velocity along the trail? 131. The graph above shows displacement versus time. What is the average velocity for line A? 132. The graph above shows displacement versus time. What is the average velocity for line B? 133. The graph above shows displacement versus time. What is the average velocity for line C? 134. A soccer ball is moving horizontally at a speed of 4.0 m/s. It then undergoes a constant acceleration. After 8.00 s, the ball is moving at 4.8 m/s. What is the ball’s displacement? 135. A rock is thrown downward from the top of a cliff with an initial speed of 13 m/s. If the rock hits the ground after 2.7 s, what is the height of the cliff? (Disregard air resistance. a = g = 9.81 m/s .) 136. A rock is thrown straight upward with an initial velocity of 25.4 m/s where the acceleration due to gravity has a magnitude of 9.81 m/s . What is the rock’s displacement after 2.65 s? 137. A coin released at rest from the top of a tower hits the ground after falling 5.7 s. What is the speed of the coin as it hits the ground? (Disregard air resistance. a = g = 9.81 m/s .) 138. A rock is thrown straight upward with an initial velocity of 6.4 m/s in a location where the acceleration due to gravity has a magnitude of 9.81 m/s . To what height does it rise? 139. A pair of glasses are dropped from the top of a 36.0 m high stadium. A pen is dropped from the same position 2.22 s later. How high above the ground is the pen when the glasses hit the ground? (Disregard air resistance. a = g = 9.81 m/s .) 140. A dog walks 17 steps north and then walks 51 steps west to bury a bone. If the dog walks back to the starting point in a straight line, how many steps will the dog take? Use the graphical method to find the magnitude of the net displacement. 141. What is the magnitude of the resultant displacement of a dog looking for its bone in the yard if the dog first heads 57.0 north of west for 10.3 m and then turns and heads west for 4.00 m? 142. A stone is thrown at an angle of 30.0 above the horizontal from the top edge of a cliff with an initial speed of 15 m/s. A stopwatch measures the stone’s trajectory time from the top of the cliff to the bottom at 6.30 s. What is the height of the cliff? (Assume no air resistance and that a = g = 9.81 m/s .) 143. A firefighter 74.0 m away from a burning building directs a stream of water from a fire hose at an angle of 36.0 above the horizontal. If the velocity of the stream is 55.0 m/s, at what height will the stream of water strike the building? (a = g = 9.81 m/s ) 144. A boat moves at 12.00 m/s relative to the water. If the boat is in a river where the current is 9.00 m/s, how long does it take the boat to make a complete round trip of 1400.0 m upstream followed by 1400.0 m downstream? 145. In a game of tug-of-war, a rope is pulled by a force of 182 N to the right and by a force of 108 N to the left. What is the magnitude and direction of the net horizontal force on the rope? 146. A package of meteorological instruments is held aloft by a balloon that exerts an upward force of 511 N on the package. The gravitational force acting on the package is 312 N. What is the magnitude and direction of the force that a scientist must exert on a rope attached to the package to keep it from rising? 147. A sled is pulled at a constant velocity across a horizontal snow surface. If a force of 4.0 10 N is being applied to the sled rope at an angle of 11 to the ground, what is the magnitude of the force of friction of the snow acting on the sled? 148. A trapeze artist on a rope is momentarily held to one side by a partner on a platform The rope makes an angle of 26.0 with the vertical. Insuch a condition of static equilibrium, what is the magnitude of the horizontal force being applied by the partner? The weight of the artist is 7.61 10 N. 149. A wagon having a mass of 91 kg is accelerated across a level road at 0.97 m/s . What net force acts on the wagon horizontally? 150. A farmhand attaches a 27 kg bale of hay to one end of a rope passing over a frictionless pulley connected to a beam in the hay barn. Another farmhand then pulls down on the opposite end of the rope with a force of 397 N. Ignoring the mass of the rope, what will be the magnitude and direction of the bale’s acceleration if the gravitational force acting on it is 265 N? 151. A sailboat with a mass of kg experiences an ocean current force of N directed to the east and a wind force against its sails with a magnitude of N directed toward the northwest (45.0 N of W). What is the magnitude of the resultant acceleration of the boat? 152. A rope attached to an engine pulls a 240 N crate up an 14.7° ramp at constant speed. The coefficient of kinetic friction for the surfaces of the crate and ramp is 0.32. What is the magnitude of the force that the rope exerts on the crate parallel to the ramp? (g = 9.81 m/s ) 153. A couch with a mass of 1.00 10 kg is placed on an adjustable ramp connected to a truck. As one end of the ramp is raised, the couch begins to move downward. If the couch slides down the ramp with an acceleration of 0.79 m/s when the ramp angle is 12.0, what is the coefficient of kinetic friction between the ramp and the couch? (g = 9.81 m/s ) 154. An Olympic skier moving at 19.0 m/s down a 26.0 slope encounters a region of wet snow and slides 136 m before coming to a halt. What is the coefficient of friction between the skis and the snow? (g = 9.81 m/s2) 155. A fox sees a piece of carrion being thrown from a hawk’s nest and rushes to snatch it. The nest is 14.0 m high, and the carrion is thrown with a horizontal velocity of 1.3 m/s. The fox is 8.0 m from the base of the tree. What is the magnitude of the fox’s average velocity if it grabs the carrion in its mouth just as it touches the ground? (Assume no air resistance and that a = g = 9.81 m/s .) final Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: A A C B C A D D B C D A B B C D C D C C D B A A C C Given a = g x = 2x v =v =0 Solution PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: I I I II II II II I I I I II II I II II I II I I I II I I I OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: 2-1.1 2-1.1 2-1.3 2-1.3 2-1.3 2-1.3 2-1.3 2-2.1 2-2.1 2-2.1 2-2.1 2-2.1 2-2.1 2-2.2 2-2.2 2-2.2 2-2.2 2-2.2 2-2.3 2-3.1 2-3.1 2-3.1 2-3.3 2-3.3 2-3.3 27. 28. 29. 30. 31. 32. PTS: 1 ANS: B ANS: A ANS: A ANS: B ANS: B ANS: C Given v = 10.0 m/s south v = 2.5 m/s north DIF: PTS: PTS: PTS: PTS: PTS: IIIC 1 1 1 1 1 OBJ: DIF: DIF: DIF: DIF: DIF: 2-3.3 I I I II II OBJ: OBJ: OBJ: OBJ: OBJ: 3-1.1 3-1.1 3-1.1 3-1.1 3-1.1 DIF: PTS: PTS: PTS: PTS: PTS: IIIA 1 1 1 1 1 OBJ: DIF: DIF: DIF: DIF: DIF: 3-1.2 I II II II I OBJ: OBJ: OBJ: OBJ: OBJ: 3-1.3 3-1.3 3-1.3 3-1.3 3-2.1 DIF: PTS: PTS: PTS: PTS: IIIA 1 1 1 1 OBJ: DIF: DIF: DIF: DIF: 3-2.2 I I I II OBJ: OBJ: OBJ: OBJ: 3-2.3 3-2.3 3-2.3 3-2.3 Solution vR 33. 34. 35. 36. 37. 38. PTS: ANS: ANS: ANS: ANS: ANS: ANS: Given 1 A B C D C D x = 3.0 10 cm y = 25 cm x = –15 cm Solution 39. 40. 41. 42. PTS: ANS: ANS: ANS: ANS: 1 A C C A 43. ANS: D Given d = 2.00 10 units east d = 4.00 10 units 30.0 north of west Solution Measuring direction with respect to x = (east), 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. PTS: 1 DIF: IIIB ANS: D PTS: 1 ANS: B PTS: 1 ANS: C PTS: 1 ANS: B PTS: 1 ANS: A PTS: 1 ANS: C PTS: 1 ANS: B PTS: 1 ANS: D PTS: 1 ANS: D PTS: 1 ANS: C PTS: 1 ANS: B Given vi = 12 m/s at 20.0° above the horizontal Solution OBJ: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: 3-2.4 I I I I I I II II II II OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: 3-3.1 3-3.1 3-3.1 3-3.2 3-3.2 3-3.2 3-3.2 3-3.2 3-3.2 3-3.2 PTS: 1 DIF: IIIC OBJ: 3-3.3 55. ANS: C PTS: 1 DIF: I OBJ: 3-4.1 56. ANS: A PTS: 1 DIF: I OBJ: 3-4.1 57. ANS: B Given vpa = velocity of plane relative to the air = 500.0 km/h east vag = velocity of air relative to the ground = 120.0 km/h 30.00° north of east Solution 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. PTS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: Given 1 C A D C C C C D C B D D C D C DIF: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: IIIB 1 1 1 1 1 1 1 1 1 1 1 1 1 1 OBJ: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: 3-4.2 I I I I I I I II II I I I II II OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: 4-1.1 4-1.1 4-1.1 4-1.1 4-1.1 4-1.2 4-1.2 4-1.2 4-1.2 4-2.1 4-2.2 4-2.3 4-2.3 4-3.3 F = 5.00 10 N = 37.0 Solution 73. 74. 75. 76. PTS: ANS: ANS: ANS: ANS: 1 C A B D DIF: PTS: PTS: PTS: IIIC 1 1 1 OBJ: DIF: DIF: DIF: 4-2.3 I I II Given v = 3.0 m/s x = 4.0 m v = 0.0 m/s Solution , so magnitude of horizontal net force = 13 N PTS: 1 77. ANS: A DIF: IIIB Given F = 45.0 N, upward F = 60.0 N, to the right m = 35.0 kg Solution OBJ: 4-3.2 OBJ: 4-3.1 OBJ: 4-3.1 OBJ: 4-3.1 78. 79. 80. 81. 82. 83. 84. PTS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: 1 D D C D B D A DIF: PTS: PTS: PTS: PTS: PTS: PTS: IIIB 1 1 1 1 1 1 OBJ: DIF: DIF: DIF: DIF: DIF: DIF: 4-3.2 I I II II I I OBJ: OBJ: OBJ: OBJ: OBJ: OBJ: 4-3.3 4-3.3 4-3.3 4-3.3 4-4.1 4-4.1 Given m = 2.0 kg = 60.0 g = 9.81 m/s Solution PTS: 1 85. ANS: D 86. ANS: B Given F =5N = 0.2 Solution DIF: IIIB PTS: 1 OBJ: 4-4.2 DIF: I OBJ: 4-4.4 PTS: 1 87. ANS: A DIF: IIIA OBJ: 4-4.4 DIF: IIIB OBJ: 4-4.4 Given v = 15.0 m/s x = 28.7 m g = 9.81 m/s Solution PTS: 1 88. ANS: B Given v = 10.0 m/s g = 9.81 m/s x = 1.0 10 m Solution PTS: 1 DIF: IIIC OBJ: 4-4.4 SHORT ANSWER 89. ANS: The magnitudes of the displacements are equal, but the displacements are in opposite directions. Therefore, one displacement is positive and one displacement is negative. PTS: 1 DIF: II OBJ: 2-1.1 90. ANS: The displacement is positive because a change of position in the direction of increasing positive position is positive displacement. PTS: 1 DIF: II OBJ: 2-1.1 91. ANS: The dog’s initial position and its final position are the same position. PTS: 1 DIF: II OBJ: 2-1.1 92. ANS: The dog is moving at a constant speed because the position versus time graph is a straight line with a positive slope. PTS: 1 93. ANS: +0.50 m/s DIF: I OBJ: 2-1.3 DIF: I OBJ: 2-1.3 Given x = 0.5 m x = 3.0 m t = 1.0 s t = 6.0 s Solution PTS: 1 94. ANS: +0.40 m/s Given x = 2.8 m x = 5.2 m t = 2.0 s t = 8.0 s Solution PTS: 1 95. ANS: acceleration DIF: IIIA OBJ: 2-1.3 PTS: 1 DIF: I OBJ: 2-2.1 96. ANS: The scooter’s acceleration is constant during both intervals because the velocity versus time graph is a straight line for each of the intervals. 8 4 10 97. ANS: Free fall is the motion of an object falling with a constant acceleration due to gravity in the absence of air resistance. 98. ANS: 9.81 m/s 99. ANS: Since the usual choice of coordinates uses positive as the direction away from Earth, the direction of free-fall acceleration is negative because the object accelerates toward Earth. 100. ANS: A scalar quantity is a quantity that has only magnitude. 101. ANS: A vector quantity is a quantity that has magnitude and direction. 102. ANS: Displacement is a vector quantity. 103. ANS: The length of the vector arrow is proportional to the magnitude of the vector. 104. ANS: A resultant is a vector that represents the sum of two or more vectors. 105. ANS: resolving the vector 106. ANS: The vector is perpendicular to that axis. 107. ANS: The magnitude of the other component vector is the magnitude of the vector. 108. ANS: projectile motion 109. ANS: Objects sent into the air and subject to gravity exhibit projectile motion. 110. ANS: The height of the ball’s path would increase. 111. ANS: The width of the ball’s path would decrease. 112. ANS: magnitude 113. ANS: A scalar quantity has only magnitude. Force has both magnitude and direction, so it cannot be a scalar quantity. PTS: 1 114. ANS: DIF: II OBJ: 4-1.2 115. ANS: The natural condition for a moving object is to remain in motion once it has been set in motion. 116. ANS: zero 117. ANS: zero 118. ANS: The hand exerts a force on the wood, and the wood exerts an equal force on the hand. Each end of the wood exerts a force on a block, and each block exerts an equal force on the wood. 119. ANS: Mass remains constant, but weight decreases with altitude. 120. ANS: Mass is the amount of matter in an object and is an inherent property of an object. Weight is not an inherent property of an object and is the magnitude of the force due to gravity acting on the object. 121. ANS: Air resistance acts in the direction opposite the direction of an object’s motion. 122. ANS: In most cases, air resistance increases with increasing speed. 123. ANS: The acceleration is then zero, and the car moves at a constant velocity. 124. ANS: Air resistance is a form of friction because it is a retarding force. It acts in the direction opposite an object’s motion. 125. ANS: The coefficient of static friction is larger than the coefficient of kinetic friction for the same two surfaces in contact. 126. ANS: coefficient of kinetic friction PROBLEM 127. ANS: 2.1 m/s, to the right Given x = 14 m x = 15 m t = 14 s Solution 128. ANS: 8.0 102 s Given v = 11.1 m/s x = 8.9 103 m Solution 129. ANS: 3.1 km, north Given v = 4.1 km/h t = 1.2 h v = 4.7 km/h t = 1.7 h Solution x = x + x = v t + v t x = (4.1 km/h)(1.2 h) + (4.7 km/h)(1.7 h) x = –4.9 km/h + 8.0 km/h = +3.1 km = 3.1 km, north 130. ANS: 0.61 m/s, east Given x = x = v = 1.7 m/s v = 0.37 m/s Solution 131. ANS: 3.0 m/s Given x = 0.0 m x = 9.0 m t = 0.0 s t = 3.0 s Solution 132. ANS: 1.0 m/s Given x = 0.0 m x = 3.0 m t = 0.0 s t = 3.0 s Solution 133. ANS: 0.33 m/s Given x = 0.0 m x = 3.0 m t = 0.0 s t = 9.0 s Solution 134. ANS: 35.2 m Given v = 4.0 m/s v = 4.8 m/s t = 8.00 s Solution 135. ANS: 71 m Given a = g = 9.81 m/s t = 2.7 s v = 13 m/s Solution height of cliff = 71 m 136. ANS: 32.9 m Given a = g = 9.81 m/s v = 25.4 m/s t = 2.65 s Solution PTS: 1 137. ANS: 56 m/s DIF: IIIA OBJ: 2-3.2 Given a = g = 9.81 m/s v = 0.0 m/s t = 5.7 s Solution /s speed = 56 m/s PTS: 1 138. ANS: 2.1 m DIF: IIIB OBJ: 2-3.2 DIF: IIIB OBJ: 2-3.2 Given a = g = 9.81 m/s v = 6.4 m/s v = 0.0 m/s Solution PTS: 1 139. ANS: 34.8 m Given a = g = 9.81 m/s v = 0.0 m/s x1 = 36.0 m vi,2 = 0.0 m/s t = 2.22 s Solution h 36.0 m – 1.2 m 34.8 m 140. ANS: 54 steps Solution Students should use graphical techniques. Their answers can be checked using the techniques presented in Section 2. 141. ANS: 12.92 m Given d 10.3 m at 57.0 north of west d 4.00 m west d d 10.3 m 4.00 m 57.0 0.0 Solution 142. ANS: 148 m Given v 15 m/s at 30.0° above the horizontal t 6.30 s g 9.81 m/s Solution 143. ANS: 40.1 m Given v 55.0 m/s 36.0 x 74.0 m Solution 144. ANS: Given vrg velocity of river to ground 9.00 m/s downstream vbr velocity of boat to river 12.00 m/s x 1400.0 m downstream x 1400.0 m downstream Solution downstream upstream 145. ANS: 74 N, to the right Given F 182 N, to the right F 108 N, to the left Solution F =F +F F 74 N, to the right 146. ANS: 199 N, downward Given Fballoon,y 511 N, upward Fg 312 N, downward Solution 147. ANS: 39 N Given F 4.0 10 N 11 Solution 148. ANS: 3.71 10 N Given 7.61 10 N F 26.0 Solution 149. ANS: 88 N Given m 91 kg ax 0.97 m/s Solution 150. ANS: 4.9 m/s , upward Given F F m 397 N 265 N 27 kg Solution a 4.9 m/s , upward 151. ANS: 2.3 m/s Given F 3.45 10 N, east F m 6.53 10 N, 45.0 N of W 2.1 10 kg Solution a = 2.3 m/s 152. ANS: 135 N Given F 240 N 14.7 0.32 Solution PTS: 1 153. ANS: 0.131 Given m 1.00 10 kg a g 0.79 m/s 12.0 9.81 m/s Solution DIF: IIIB OBJ: 4-4.4 154. ANS: 0.337 Given: vx,i 19.0 m/s x 136 m 26.0 g 9.81 m/s2 Solution Choose a coordinate system such that the positive x-direction is down the ski slope. The force of friction will be in the negative x-direction. 155. ANS: 3.4 m/s Given v v 1.3 m/s horizontally y 14.0 m d 8.0 m Solution PTS: 1 DIF: IIIC OBJ: 3-3.3