JMAP Physics Regents Exam Math Questions: Vectors



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| |Two forces act concurrently on an object. Their resultant force has the largest magnitude when the angle between the |

| |forces is |

| |(1) 0° (3) 90° |

| |(2) 30° (4) 180° |

| |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. |

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| |The additional force necessary to bring the object into a state of equilibrium is |

| |(1) 20. N, northeast (3) 28 N, northeast |

| |(2) 20. N, southwest (4) 28 N, southwest |

| |A 100.-newton force acts on point P, as shown in the diagram below. |

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| |[pic] |

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| |The magnitude of the vertical component of this force is approximately |

| |(1) 30. N (3) 71 N |

| |(2) 50. N (4) 87 N |

| |A force of 60. newtons is applied to a rope to pull a sled across a horizontal surface at a constant velocity. The rope |

| |is at an angle of 30. degrees above the horizontal. |

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| |[pic] |

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| |Calculate the magnitude of the component of the 60.-newton force that is parallel to the horizontal surface. [Show all |

| |work, including the equation and substitution with units.] |

| |A vector makes an angle, θ, with the horizontal. The horizontal and vertical components of the vector will be equal in |

| |magnitude if angle θ is |

| |(1) 30° (3) 60° |

| |(2) 45° (4) 90° |

| |A 20.-newton force due north and a 40.-newton force due east act concurrently on a 10.-kilogram object, located at point|

| |P. |

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| |[pic] |

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| |a) Using a ruler, determine the scale used in the vector diagram by finding the number of newtons represented by each |

| |centimeter. |

| |b) On the vector diagram on your answer paper, use a ruler and protractor to construct the vector that represents the |

| |resultant force. |

| |c) What is the magnitude of the resultant force? |

| |d) What is the measure of the angle (in degrees) between east and the resultant force? |

| |e) Calculate the magnitude of the acceleration of the object. [Show all calculations, including the equation and |

| |substitution with units.] |

| |Forces F1 and F2 act concurrently on point P, as shown in the diagram below. |

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| |[pic] |

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| |The equilibrant of F1 and F2 is |

| |(1) 14 N southwest (3) 20. N southwest |

| |(2) 14 N southeast (4) 20. N southeast |

| |Which combination of three concurrent forces acting on a body could not produce equilibrium? |

| |(1) 1 N, 3 N, 5 N (3) 3 N, 4 N, 5 N |

| |(2) 2 N, 2 N, 2 N (4) 4 N, 4 N, 5 N |

| |The vector below represents the resultant of two forces acting concurrently on an object at point P. |

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| |Which pair of vectors best represents two concurrent forces that combine to produce this resultant force vector? |

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| |[pic] |

| |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 |

| |(1) 5 N northeast (3) 7 N northeast |

| |(2) 10. N southwest (4) 7 N southwest |

| |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 |

| |(1) 0.0 N to 12.0 N (3) 12.0 N to 2.0 N |

| |(2) 2.0 N to 12.0 N (4) 12.0 N to 0.0 N |

| |A 5.0-newton force could have perpendicular components of |

| |(1) 1.0 N and 4.0 N (3) 3.0 N and 4.0 N |

| |(2) 2.0 N and 3.0 N (4) 5.0 N and 5.0 N |

| |Two 30.-newton forces act concurrently on an object. In which diagram would the forces produce a resultant with a |

| |magnitude of 30. newtons? |

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| |[pic] |

| |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 top-view diagram below. |

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| |[pic] |

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| |Which vector best represents the resultant of these two forces? |

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| |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? |

| |(1) 0 N and 45 N (3) 20. N and 25 N |

| |(2) 5 N and 9 N (4) 0 N and 50. N |

| |Which is a vector quantity? |

| |(1) distance (3) power |

| |(2) speed (4) force |

| |The diagram below represents a force vector, A, and a resultant vector, R, |

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| |Which force vector B below could be added to force vector A to produce resultant vector R? |

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| |A force vector was resolved into two perpendicular components, F1 and F2, as shown in the diagram below. |

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| |[pic] |

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| |Which vector best represents the original force? |

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| |Which pair of forces acting concurrently on an object will produce the resultant of greatest magnitude? |

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| |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) 1 N (3) 9N |

| |(2) 7 N (4) 4N |

| |A force of [pic] newton due south and a force of [pic] newton due east act concurrently on an electron, e–. |

| |a) On the diagram, draw a force diagram to represent the two forces acting on the electron. (The electron is |

| |represented by a dot.) Use a metric ruler and the scale of |

| |1.0 centimeter = [pic] newton. Begin each vector at the dot representing the electron and label its magnitude in |

| |newtons. |

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| |[pic] |

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| |b) Determine the resultant force on the electron, graphically. Label the resultant vector R. |

| |c) Determine the magnitude of the resultant vector R. |

| |d) Determine the angle between the resultant and the [pic]-newton vector. |

| |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? |

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| |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 |

| |(1) decreases |

| |(2) increases |

| |(3) remains the same |

| |Forces A and B have a resultant R. Force A and resultant R are represented in the diagram below. |

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| |[pic] |

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| |Which vector best represents force B? |

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| |[pic] |

| |The diagram below represents a 5.0-newton force and a 12-newton force acting on point P. |

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| |[pic] |

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| |The resultant of the two forces has a magnitude of |

| |(1) 5.0 N (3) 12 N |

| |(2) 7.0 N (4) 13 N |

| |The diagram below shows a resultant vector, R. |

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| |[pic] |

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| |Which diagram best represents a pair of component vectors, A and B, that would combine to form resultant vector R? |

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| |The vector diagram below represents two forces, F1 and F2, simultaneously acting on an object. |

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| |Which vector best represents the resultant of the two forces? |

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| |As the angle between two concurrent forces decreases, the magnitude of the force required to produce equilibrium |

| |(1) decreases |

| |(2) increases |

| |(3) remains the same |

| |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. |

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| |[pic] |

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| |What are the magnitudes of the horizontal and vertical components? |

| |(1) FH = 3.5 N and FV = 4.9 N |

| |(2) FH = 4.9 N and FV = 3.5 N |

| |(3) FH = 14 N and FV = 20. N |

| |(4) FH = 20. N and FV = 14 N |

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| |(1) |

| |(4) |

| |(2) |

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| |(2) |

| |a) 5 newtons (+/- 0.2 N) |

| |b) |

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| |c) 45 N (+/-2 N) |

| |d) 27˚(+-2˚) |

| |e) |

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| |(3) |

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| |(3) |

| |a) |

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| |b) [pic] ± [pic] N |

| |c) 53° ± 2° |

| |(4) |

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| |(2) |

| |(4) |

| |(1) |

| |(2) |

| |(2) |

| |(4) |

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