1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below.

Transcription

1 Name Vectors Practice 1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the object, will establish equilibrium? 16 N toward the right 16 N toward the left 4 N toward the right 4 N toward the left 2. Two 20.-newton forces act concurrently on an object. What angle between these forces will produce a resultant force with the greatest magnitude? 0º 45º 90.º 180.º 3. A motorboat, which has a speed of 5.0 meters per second in still water, is headed east as it crosses a river flowing south at 3.3 meters per second. What is the magnitude of the boat's resultant velocity with respect to the starting point? 5. Which diagram represents a box in equilibrium? 3.3 m/s 5.0 m/s 6.0 m/s 8.3 m/s 4. The diagram below represents two concurrent forces. Which vector represents the force that will produce equilibrium with these two forces? 6. Two forces act concurrently on an object. Their resultant force has the largest magnitude when the angle between the forces is A child walks 5.0 meters north, then 4.0 meters east, and finally 2.0 meters south. What is the magnitude of the resultant displacement of the child after the entire walk? 1.0 m 5.0 m 3.0 m 11.0 m 8. As the angle between two concurrent forces decreases, the magnitude of the force required to produce equilibrium decreases increases remains the same

2 Base your answers to questions 9 and 10on the information below. A stream is 30. meters wide and its current flows southward at 1.5 meters per second. A toy boat is launched with a velocity of 2.0 meters per second eastward from the west bank of the stream. 9. How much time is required for the boat to reach the opposite bank of the stream? 8.6 s 12 s 15 s 60. s 10.What is the magnitude of the boat's resultant velocity as it crosses the stream? 0.5 m/s 2.5 m/s 3.0 m/s 3.5 m/s 11.In the diagram below, a 20.-newton force due north and a 20.-newton force due east act concurrently on an object, as shown in the diagram below. 15. Two 30.-newton forces act concurrently on an object. In which diagram would the forces produce a resultant with a magnitude of 30. newtons? The additional force necessary to bring the object into a state of equilibrium is 20. N, northeast 20. N, southwest 28 N, northeast 28 N, southwest 12. Note that the following question has only three choices. A 6.0-newton force and an 8.0-newton force act concurrently on a point. As the angle between these forces increases from 0 to 90, the magnitude of their resultant decreases increases remains the same 13. A 5.0-newton force and a 7.0-newton force act concurrently on a point. As the angle between the forces is increased from 0 to 180, the magnitude of the resultant of the two forces changes from 0.0 N to 12.0 N 2.0 N to 12.0 N 12.0 N to 2.0 N 12.0 N to 0.0 N 14. The diagram below represents a 5.0-newton force and a 12-newton force acting on point P. The resultant of the two forces has a magnitude of 5.0 N 7.0 N 12 N 13 N 16. A girl leaves a history classroom and walks 10. meters north to a drinking fountain. Then she turns and walks 30. meters south to an art classroom. What is the girl s total displacement from the history classroom to the art classroom? 20. m south 20. m north 40. m south 40. m north 17. Two concurrent forces have a maximum resultant of 45 Newtons and a minimum resultant of 5 Newtons. What is the magnitude of each of these forces? 0 N and 45 N 5 N and 9 N 20. N and 25 N 0 N and 50. N 18. What is the total displacement of a student who walks 3 blocks east, 2 blocks north, 1 block west, and then 2 blocks south? 0 2 blocks east 2 blocks west 8 blocks

3 19. Which vector diagram best represents a cart slowing down as it travels to the right on a horizontal surface? 21. The vector diagram below represents two forces, F1 and F2 simultaneously acting on an object. Which vector best represents the resultant of the two forces? 22. The diagram below shows a resultant vector, R. Which diagram best represents a pair of component vectors, A and B, that would combine to form resultant vector R? 20. Which pair of forces acting concurrently on an object will produce the resultant of greatest magnitude? 23. A 5-newton force directed east and a 5-newton force directed north act concurrently on a point. The resultant of the two forces is 5 N northeast 10 N southwest 7 N northeast 7 N southwest 24. If two 10.-newton concurrent forces have a resultant of zero, than the angle between the forces must be

4 25. Which vector diagram represents the greatest magnitude of displacement for an object? 26. Forces A and B have a resultant R. Force A and resultant R are represented in the diagram below. 29. A force vector was resolved into two perpendicular components, F1 and F2, as shown in the diagram below. Which vector best represents force B? Which vector best represents the original force? 27. Which combination of three concurrent forces acting on a body could not produce equilibrium? 1 N, 3 N, 5 N 2 N, 2 N, 2 N 3 N, 4 N, 5 N 4 N, 4 N, 5 N 28. A plane flies 400. kilometers south and then 300. kilometers east. The magnitude of the displacement is 100. km 500. km 700. km 1,200. km

5 30. The diagram below represents two forces acting concurrently on an object at point P. 33. A 6-newton force and an 8-newton force act concurrently on a box located on a frictionless horizontal surface. Which top-view diagram shows the forces producing the smallest magnitude of acceleration of the box? Which diagram best represents the resultant of these two forces? 31. Two students push on a sled. One pushes with a force of 30. newtons east and the other exerts a force of 40. newtons south, as shown in the topview diagram below. Which vector best represents the resultant of these two forces? 34. As shown in the diagram below, a painter climbs 7.3 meters up a vertical scaffold A to B and then walks 11.0 meters from B to C along a level platform 32. The map below shows the route traveled by a school bus. The magnitude of the painter's total displacement while moving from A to C is 3.7 m 13.2 m 18.3 m 25.6 m 35. A person walks 5.0 kilometers north, then 5.0 kilometers east. His displacement is closest to What is the magnitude of the total displacement of the school bus from the start to the end of its trip? 400 m 500 m 800 m 1,800 m 7.1 kilometers northeast 7.1 kilometers northwest 10 kilometers northeast 10 kilometers northwest 36. A mass is moved 9.0 meters north and 12.0 meters east. The magnitude of the displacement is 12.0 m 15.0 m 3.0 m 21.0 m

6 37. Forces F1 and F2 act concurrently on point P, as shown in the diagram below. 43. A 150.-newton force, F1, and a 200.-newton force, F2, are applied simultaneously to the same point on a large crate resting on a frictionless, horizontal surface. Which diagram shows the forces positioned to give the crate the greatest acceleration? The equilibrant of F1 and F2 is 14 N southwest 14 N southeast 20. N southwest 20. N southeast 38. A car travels 12 kilometers due north and then 8 kilometers due west going from town A to town B. What is the magnitude of the displacement of a helicopter that flies in a straight line from town A to town B? 20. km 14 km 10. km 4 km 39. A ball is fired with a velocity of 12 meters per second from a cannon pointing north, while the cannon is moving eastward at a velocity of 24 meters per second. Which vector best represents the resultant velocity of the ball as it leaves the cannon? 44. A river flows due east at 1.5 meters per second. A motorboat leaves the north shore of the river and heads due south at 2.0 meters per second, as shown in the diagram below. Which vector best represents the resultant velocity of the boat relative to the riverbank? 40. A man walks 40 meters north, then 70 meters east, and then 40 meters south. What is his displacement from the starting point? 150 meters east 150 meters west 70 meters east 70 meters west 41. Which pair of concurrent forces could produce a resultant force having a magnitude of 10. Newtons? 10. N. 10. N 10. N. 30. N 4.7 N. 4.7 N 4.7 N. 5.0 N 42. A student walks 40. meters along a hallway that heads due north, then turns and walks 30. meters along another hallway that heads due east. What is the magnitude of the student's resultant displacement? 10. m 35 m 50. m 70. m 45. A 3.0-newton force and a 4.0-newton force act concurrently on a point. In which diagram below would the orientation of these forces produce the greatest net force on the point? 46. A boat heads directly eastward across a river at 12 meters per second. If the current in the river is flowing at 5.0 meters per second due south, what is the magnitude of the boat's resultant velocity? 7.0 m/s 8.5 m/s 13 m/s 17 m/s

7 47. A student walks 1.0 kilometer due east and 1.0 kilometer due south. Then she runs 2.0 kilometers due west. The magnitude of the student's resultant displacement is closest to 0 km 1.4 km 3.4 km 4.0 km 48. Two perpendicular forces act on an object as shown in the diagram. 54. The diagram below represents two forces acting concurrently on an object. The magnitude of the resultant force is closest to 20. N 40. N 45. N 60. N 55. If a woman runs 100 meters north and then 70 meters south, her total displacement will be What is the magnitude of the resultant force on the object? 17 N 13 N 7.0 N 5.0 N 49. A force of 6.0 Newtons north and a force of 8.0 Newtons east act concurrently on an object. The magnitude of the resultant of the two forces is 1.3 N 2.0 N 10. N 14 N 50. A student walks 3 blocks south, 4 blocks west, and 3 blocks north. What is the, displacement of the student? 10 blocks east 10 blocks west 4 blocks east 4 blocks west 51. Two forces (OA and OB) act simultaneously at point O as shown on the diagram. 30 m north 30 m south 170 m north 170 m south 56. The resultant of two forces acting on the same point at the same time will be greatest when the angle between the forces is 0º 45º 90º 180º 57. The diagram below represents two concurrent forces acting on a point. Which vector best represents their resultant? The magnitude of the resultant force is closest to 8.0 N 11 N 15 N 16 N 52. Which vector best represents the resultant of forces F1 and F2 acting concurrently on point P as shown in the diagram below? 53. A force of 3 Newtons and a force of 5 Newtons act concurrently to produce a resultant of 8 Newtons. The angle between the forces must be 0º 60º 90º 180º 58. Two concurrent forces act at right angles to each other. If one of the forces is 40 Newtons and the resultant of the two forces is 50 Newtons, the magnitude of the other force must be 10 N 20 N 30 N 40 N 59. If a man walks 17 meters east then 17 meters south, the magnitude of the man's displacement is 17 m 24 m 30. m 34 m 60. As the angle between two concurrent forces of 5.0 Newtons and 7.0 Newtons increases from 0º to 180º, the magnitude of their resultant changes from 0 N to 35 N 2.0 N to 12 N 12 N to 2.0 N 12 N to 0 N 61. The resultant of two concurrent forces is minimum when the angle between them is 0º 45º 90º 180º

8 62. What is the magnitude of the vector sum of the two concurrent forces represented in the diagram to the right? 70. Which vector below best represents the resultant of the two vectors shown to the right? 2.5 Newtons 3.5 Newtons 3.0 Newtons 4.0 Newtons 63. An object is displaced 12 meters to the right and then 16 meters upward. The magnitude of the resultant displacement is 1.3 meters 20 meters 28 meters 4.0 meters 64. As the angle between two concurrent forces increases from 45º to 90º, the magnitude of their resultant decreases increases remains the same 65. A girl attempts to swim directly across a stream 15 meters wide. When she reaches the other side, she is 15 meters downstream. The magnitude of her displacement is closest to 30 m 21 m 17 m 15 m 66. Two forces of 100 Newtons and 25 Newtons act concurrently on an object. These two forces could have a resultant force of 0 N 50 N 100 N 150 N 67. Two concurrent forces of 40 Newtons and X Newtons have a resultant of 100 Newtons. Force X could be 20 Newtons 40 Newtons 80 Newtons 150 Newtons 68. As the angle between two concurrent forces is increased from 10º to 75º, the magnitude of the resultant force decreases increases remains the same 69. Which pair of concurrent forces may have a resultant of 20. Newtons? 5.0 N and 10. N 20. N and 20. N 20. N and 50. N 30. N and 5.0 N 71. Forces A and B have a resultant R. Force A and resultant R are shown in the diagram below. Which vector below best represents force B? 72. A unit used for a vector quantity is watt newton kilogram second

9 73. An object is displaced 3 meters to the west and then 4 meters to the south. 75. A displacement vector with a magnitude of 20. meters could have perpendicular components with magnitudes of Which vector shown below best represents the resultant displacement of the block? 10. m and 10. m 12 m and 8.0 m 12 m and 16 m 16 m and 8.0 m 76. A box weighing 46 newtons rests on an incline that makes an angle of 25 with the horizontal. What is the magnitude of the component of the box's weight perpendicular to the incline? 19 N 21 N 42 N 46 N 77. Which combination of initial horizontal velocity, (vh) and initial vertical velocity, (vv) results in the greatest horizontal range for a projectile over level ground? [Neglect friction.] 74. An airplane traveling north at 220. meters per second encounters a 50.0-meters-per-second crosswind from west to east, as represented in the diagram below. 78. The components of a 15-meters-per-second velocity at an angle of 60. above the horizontal are What is the resultant speed of the plane? 170. m/s 214 m/s 226 m/s 270. m/s 7.5 m/s vertical and 13 m/s horizontal 13 m/s vertical and 7.5 m/s horizontal 6.0 m/s vertical and 9.0 m/s horizontal 9.0 m/s vertical and 6.0 m/s horizontal 79. A ball is thrown with an initial speed of 10. meters per second. At what angle above the horizontal should the ball be thrown to reach the greatest height?

10 80. An 8.0-newton block is accelerating down a frictionless ramp inclined at 15 to the horizontal, as shown in the diagram below. 83. The diagram below shows a newton truck at rest on a hill that makes an angle of 8.0 with the horizontal. What is the magnitude of the net force causing the block's acceleration? 0 N 2.1 N 7.7 N 8.0 N 81. A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force to the wagon handle, which is inclined at 35 to the sidewalk as shown below. What is the component of the truck's weight parallel to the hill? N N N N 84. A block weighing 10.0 newtons is on a ramp inclined at 30.0 to the horizontal. A 3.0-newton force of friction, Ff, acts on the block as it is pulled up the ramp at constant velocity with force F, which is parallel to the ramp, as shown in the diagram below. What is the magnitude of the force of friction on the wagon? 11 N 13 N 18 N 22 N 82. The vector diagram below represents the horizontal component, FH, and the vertical component, FV, of a 24-newton force acting at 35 above the horizontal. What are the magnitudes of the horizontal and vertical components? FH = 3.5 N and FV = 4.9 N FH = 4.9 N and FV = 3.5 N FH = 14 N and FV = 20. N FH = 20. N and FV = 14 N What is the magnitude of force F? 7.0 N 8.0 N 10 N 13 N 85. An airplane flies with a velocity of 750. kilometers per hour, 30.0º south of east. What is the magnitude of the eastward component of the plane s velocity? 866 km/h 650 km/h 433 km/h 375km/h 86. A soccer player kicks a ball with an initial velocity of 10. meters per second at an angle of 30. above the horizontal. The magnitude of the horizontal component of the ball s initial velocity is 5.0 m/s 8.7 m/s 9.8 m/s 10. m/s 87. A 3-newton force and a 4-newton force are acting concurrently on a point. Which force could not produce equilibrium with these two forces? 1 N 7 N 9 N 4 N

11 88. The diagram below represents a force vector, A and resultant vector, R. 91. The diagram below shows a force of magnitude F applied to a mass at angle relative to a horizontal frictionless surface. Which force vector B below could be added to force vector A to produce resultant vector, R. 89. The diagram below represents a block at rest on an incline. As angle is increased, the horizontal acceleration of the mass decreases increases remains the same 92. The diagram below shows a 10.0-kilogram mass held at rest on a frictionless 30.0 incline by force F. Which diagram best represents the forces acting on the block? (Ff = frictional force, FN = normal force, and Fw = weight.) What is the approximate magnitude of force F? 9.81 N 49.1 N 85.0 N 98.1 N 93. In the diagram below, a box is at rest on an inclined plane. Which vector best represents the direction of the normal force acting on the box? A B C D 94. Two students are pushing a car. What should be the angle of each student s arms with respect to the flat ground to maximize the horizontal component of the force? 0º 30º 45º 90º 95. Into how many possible components can a single force be resolved? 90. A 5.0-newton force could have perpendicular components of 1.0 N and 4.0 N 2.0 N and 3.0 N 3.0 N and 4.0 N 5.0 N and 5.0 N an unlimited number two components three components four components at right angles to each other

12 96. The diagram below shows a sled and rider sliding down a snow-covered hill that makes an angle of 30. with the horizontal. Which vector best represents the direction of the normal force, FN, exerted by the hill on the sled? 97. The diagram below shows a block on a horizontal frictionless surface. A newton force acts on the block at an angle of 30. above the horizontal. 100.The vector below represents the resultant of two forces acting concurrently on an object at point P. What is the magnitude of force F if it establishes equilibrium? 50.0 N 86.6 N 100. N 187 N 98. Equilibrium exists in a system where three forces are acting concurrently on an object. If the system includes a 5.0-newton force due north and a 2.0-newton force due south, the third force must be 7.0 N south 7.0 N north 3.0 N south 3.0 N north 99. A 100.-newton force acts on point P, as shown in the diagram below. Which pair of vectors best represents two concurrent forces that combine to produce this resultant force vector? The magnitude of the vertical component of this force is approximately 30. N 50. N 71 N 87 N

13 101.Two aluminum spheres of identical mass and identical charge q hang from strings of equal length. If the spheres are in equilibrium, which diagram best represents the direction of each force acting on the spheres? 102. In the diagram below, a force, F, is applied to the handle of a lawnmower inclined at angle to the ground The diagram below shows a child pulling a 50.-kilogram friend on a sled by applying a 300.-newton force on the sled rope at an angle of 40. with the horizontal. The magnitude of the horizontal component of force F depends on the magnitude of force F, only the measure of angle, only both the magnitude of force F and the measure of angle neither the magnitude of force F nor the measure of angle 103. As the angle between a force and level ground decreases from 60º to 30º, the vertical component of the force decreases increases remains the same 104. Which quantity is a vector? power kinetic energy speed weight The vertical component of the 300.-newton force is approximately 510 N 230 N 190 N 32 N 106. A block is at rest on an inclined plane as shown in the diagram at the right. As angle is increased, the component of the block's weight parallel to the plane decreases increases remains the same

14 107. In the diagram below, a block rests on a ramp, making angle with the horizontal The handle of a lawn roller is held at 45 from the horizontal. A force, F, of 28.0 Newtons is applied to the handle as the roller is pushed across a level lawn, as shown in the diagram below. If angle is increased, what will occur? The block's mass will decrease. The block's weight will increase. The block's component of weight parallel to the ramp will decrease. The block's component of weight parallel to the ramp will increase A force of 100. Newtons is applied to an object at an angle of 30 from the horizontal as shown in the diagram below. What is the magnitude of the vertical component of this force? What is the magnitude of the force moving the roller forward? 7.00 N 14.0 N 19.8 N 39.0 N 112. The diagram represents a force acting at point P. Which pair of concurrent forces would produce equilibrium when added to the force acting at point P? 0 N 50.0 N 86.7 N 100. N 109. The diagram below shows a person exerting a 300.-newton force on the handle of a shovel that makes an angle of 60. with the horizontal ground In the diagram below, the weight of a box on a plane inclined at 30. is represented by the vector W. What is the magnitude of the component of the weight (W) that acts parallel to the incline? The component of the 300.-newton force that acts perpendicular to the ground is approximately 150. N 260. N 300. N 350. N 110. A resultant force of 10. Newtons is made up of two component forces acting at right angles to each other. If the magnitude of one of the components is 6.0 Newtons, the magnitude of the other component must be 16 N 8.0 N 6.0 N 4 N W 0.50 W 0.87 W 1.5 W 114. A lawnmower is pushed with a constant force of F, as shown in the diagram below: As angle between the lawnmower handle and the horizontal increases, the horizontal component of F decreases increases remains the same

15 115. The diagram below represents a car resting on a hill The vector diagram below represents the velocity of a car traveling 24 meters per second east of north. Which vector best represents the weight of the car? A B C D 116. Which diagram represents the vector with the largest downward component? [Assume each vector has the same magnitude.] 117. The diagram below represents a constant force F acting on a box located on a frictionless horizontal surface. As the angle between the force and the horizontal increases, the acceleration of the box will decrease increase remain the same 118. A constant force is exerted on a box as shown in the diagram. As the angle decreases to 0, the magnitude of the horizontal component of the force decreases increases remains the same 119. Which quantity is scalar? mass force momentum acceleration What is the magnitude of the component of the car's velocity that is directed eastward? 121. A hiker travels 1.0 kilometer south, turns and travels 3.0 kilometers west, and then turns and travels 3.0 kilometers north. What is the total distance traveled by the hiker? 3.2 km 3.6 km 5.0 km 7.0 km 122. Which term identifies a scalar quantity? displacement momentum velocity time 123. Scalar is to vector as speed is to velocity displacement is to distance displacement is to velocity speed is to distance 124. Which quantity is a vector? impulse power speed time 125. Which is a vector quantity? speed work mass displacement

16 126. Base your answer to the following question on the information below. In a drill during basketball practice, a player runs the length of the 30.-meter court and back. The player does this three times in 60. seconds. The magnitude of the player's total displacement after running the drill is 0.0 m 30. m 60. m 180 m 129. The speedometer in a car does not measure the car s velocity because velocity is a 127. If the force vector shown in the diagram above is resolved into two components, these two components could best be represented by which diagram below? vector quantity and has a direction associated with it vector quantity and does not have a direction associated with it scalar quantity and has a direction associated with it scalar quantity and does not have a direction associated with it 130. Which is a vector quantity? electric charge electric field strength electric potential difference electric resistance 131. A student on her way to school walks four blocks east, three blocks north, and another four blocks east, as shown in the diagram Which is not a vector quantity? electric charge magnetic field strength velocity displacement Compared to the distance she walks, the magnitude of her displacement from home to school is less greater the same 132. Which is a scalar quantity? acceleration momentum speed displacement

17 133. Velocity is to speed as displacement is to 140. Which terms both represent scalar quantities? acceleration time momentum distance 134. The diagram below shows a worker using a rope to pull a cart. displacement and velocity distance and speed displacement and speed distance and velocity 141. Which terms represent a vector quantity and its respective unit? weight kilogram mass kilogram force newton momentum newton 142. Which quantity includes both magnitude and direction? The workers pull on the handle of the cart can best be described as a force having magnitude, only direction, only both magnitude and direction neither magnitude nor direction 135. Which term represents a scalar quantity? distance displacement force weight 136. Which is a vector quantity? distance speed power force 137. Which two terms represent a vector quantity and the scalar quantity of the vector s magnitude, respectively? mass time distance velocity 143. A ship changes direction several times and finishes 20 miles north of its starting point. This displacement is a vector quantity because it has both magnitude and direction magnitude but no direction direction but no magnitude neither magnitude nor direction 144. Which term represents a vector quantity? work power force distance 145. A car is driven from Buffalo to Albany and on to New York City, as shown in the diagram below. acceleration and velocity weight and force speed and time displacement and distance 138. Which is a vector quantity? gravitational field strength of Earth mass of a jogger charge of an electron kinetic energy of a freely falling body 139. A softball player leaves the batter's box, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player's total displacement from the batter's box is smaller larger the same Compared to the magnitude of the car's total displacement, the distance driven is shorter longer the same 146. Which is a vector quantity? distance time speed acceleration

18 147. Which is a scalar quantity? 152. Which is a scalar quantity? displacement distance force acceleration 148. Which pair of terms are vector quantities? force and mass distance and displacement momentum and acceleration speed and velocity 149. Distance is to displacement as force is to weight speed is to velocity velocity is to acceleration impulse is to momentum 150. Which is a vector quantity? momentum energy speed power 151. Which is a vector quantity? acceleration due to gravity mechanical equivalent of heat rest mass of an electron speed of an object force energy displacement velocity 153. Which is a scalar quantity? kinetic energy momentum force weight 154. Which is a vector quantity? displacement mass speed energy 155. Which is a scalar quantity? speed displacement force momentum 156. Which quantities are scalar? speed and work velocity and force distance and acceleration momentum and power

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