Vectors & scalars: Force as vector NameReview

A) 16 N toward the right B) 16 N toward the leftC) 4 N toward the right D) 4 N toward the left

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

What additional force, when applied to the object, will establish equilibrium?

A) 0º B) 45º C) 90.º D) 180.º

2. Two 20.-newton forces act concurrently on an object.What angle between these forces will produce aresultant force with the greatest magnitude?

A) 3.3 m/s B) 5.0 m/sC) 6.0 m/s D) 8.3 m/s

3. A motorboat, which has a speed of 5.0 meters persecond in still water, is headed east as it crosses ariver flowing south at 3.3 meters per second. What isthe magnitude of the boat'sresultant velocity with respect to the starting point? A)

B)

C)

D)

4. The diagram below represents two concurrent forces.

Which vector represents the force that will produceequilibrium with these two forces?

A)

B)

C)

D)

5. Which diagram represents a box in equilibrium?

A) 0° B) 30° C) 90° D) 180°

6. Two forces act concurrently on an object. Theirresultant force has the largest magnitude when theangle between the forces is

A) 20. N, northeast B) 20. N, southwestC) 28 N, northeast D) 28 N, southwest

7. In the diagram below, a 20.-newton force due northand a 20.-newton force due east act concurrently onan object, as shown in the diagram below.

The additional force necessary to bring the object intoa state of equilibrium is

Base your answers to questions 8 and 9 on the information below.

A stream is 30. meters wide and its current flows southward at 1.5 meters per second. A toy boat islaunched with a velocity of 2.0 meters per second eastward from the west bank of the stream.

A) 8.6 s B) 12 s C) 15 s D) 60. s

8. How much time is required for the boat to reach the opposite bank of the stream?

A) 0.5 m/s B) 2.5 m/s C) 3.0 m/s D) 3.5 m/s

9. What is the magnitude of the boat's resultant velocity as it crosses the stream?

A) 1.0 m B) 5.0 mC) 3.0 m D) 11.0 m

10. A child walks 5.0 meters north, then 4.0 meters east,and finally 2.0 meters south. What is the magnitudeof the resultant displacement of the child after theentire walk?

A)

B)

C)

D)

11. Two 30.-newton forces act concurrently on an object.In which diagram would the forces produce aresultant with a magnitude of 30. newtons?

A)

B)

C)

D)

12. Which vector diagram best represents a cart slowingdown as it travels to the right on a horizontalsurface?

A) B)

C) D)

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

Which vector best represents the resultant of the twoforces?

A)

B)

C)

D)

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

Which diagram best represents a pair of componentvectors, A and B, that would combine to formresultant vector R?

A) 5.0 N B) 7.0 N C) 12 N D) 13 N

15. The diagram below represents a 5.0-newton forceand a 12-newton force acting on point P.

The resultant of the two forces has a magnitude of

A) 20. m south B) 20. m northC) 40. m south D) 40. m north

16. A girl leaves a history classroom and walks 10.meters north to a drinking fountain. Then she turnsand walks 30. meters south to an art classroom.What is the girl’s total displacement from the historyclassroom to the art classroom?

A)

B)

C)

D)

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

Which vector best represents force B?

A) B)

C) D)

18. Which vector diagram represents the greatest magnitude of displacement for an object?

A)

B)

C)

D)

19. A force vector was resolved into two perpendicularcomponents, F1 and F2, as shown in the diagrambelow.

Which vector best represents the original force?

A) B)

C) D)

20. Which combination of initial horizontal velocity, (vH) and initial vertical velocity, (vv) results in thegreatest horizontal range for a projectile over levelground? [Neglect friction.]

A) 7.5 m/s vertical and 13 m/s horizontalB) 13 m/s vertical and 7.5 m/s horizontalC) 6.0 m/s vertical and 9.0 m/s horizontalD) 9.0 m/s vertical and 6.0 m/s horizontal

21. The components of a 15-meters-per-second velocityat an angle of 60.° above the horizontal are

A) 0 N B) 2.1 N C) 7.7 N D) 8.0 N

22. An 8.0-newton block is accelerating down africtionless ramp inclined at 15° to the horizontal, asshown in the diagram below.

What is the magnitude of the net force causing theblock's acceleration?

A) 11 N B) 13 N C) 18 N D) 22 N

23. A child pulls a wagon at a constant velocity along alevel sidewalk. The child does this by applying a22-newton force to the wagon handle, which isinclined at 35° to the sidewalk as shown below.

What is the magnitude of the force of friction on thewagon?

A) FH = 3.5 N and FV = 4.9 NB) FH = 4.9 N and FV = 3.5 NC) FH = 14 N and FV = 20. ND) FH = 20. N and FV = 14 N

24. The vector diagram below represents the horizontalcomponent, FH, and the vertical component, FV, of a24-newton force acting at 35° above the horizontal.

What are the magnitudes of the horizontal andvertical components?

A) 1.4 103 N B) 1.0 104 NC) 1.4 104 N D) 9.9 104 N

25. The diagram below shows a 1.0 × 105-newton truckat rest on a hill that makes an angle of 8.0° with thehorizontal.

What is the component of the truck's weight parallelto the hill?

A) 7.0 N B) 8.0 N C) 10 N D) 13 N

26. A block weighing 10.0 newtons is on a rampinclined at 30.0° to the horizontal. A 3.0-newtonforce of friction, Ff, acts on the block as it is pulledup the ramp at constant velocity with force F, whichis parallel to the ramp, as shown in the diagrambelow.

What is the magnitude of force F?

A) 866 km/h B) 650 km/hC) 433 km/h D) 375km/h

27. An airplane flies with a velocity of 750. kilometersper hour, 30.0º south of east. What is the magnitudeof the eastward component of the plane’s velocity?

A) 5.0 m/s B) 8.7 m/sC) 9.8 m/s D) 10. m/s

28. A soccer player kicks a ball with an initial velocityof 10. meters per second at an angle of 30.° abovethe horizontal. The magnitude of the horizontalcomponent of the ball’s initial velocity is

A) 1 N B) 7 N C) 9 N D) 4 N

29. A 3-newton force and a 4-newton force are actingconcurrently on a point. Which force could notproduce equilibrium with these two forces?

A)

B)

C)

D)

30. The diagram below represents a block at rest on anincline.

Which diagram best represents the forces acting onthe block? (Ff = frictional force, FN = normal force,and Fw = weight.)

A) 3.2 km B) 3.6 kmC) 5.0 km D) 7.0 km

31. A hiker travels 1.0 kilometer south, turns and travels3.0 kilometers west, and then turns and travels 3.0kilometers north. What is the total distance traveledby the hiker?

A) watt B) newtonC) kilogram D) second

32. A unit used for a vector quantity is

A) power B) kinetic energyC) speed D) weight

33. Which quantity is a vector?

A) mass B) forceC) momentum D) acceleration

34. Which quantity is scalar?

A) displacement B) momentumC) velocity D) time

35. Which term identifies a scalar quantity?

36. 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.

A) 0.0 m B) 30. m C) 60. m D) 180 m

The magnitude of the player's total displacement after running the drill is

A) speed is to velocityB) displacement is to distanceC) displacement is to velocityD) speed is to distance

37. Scalar is to vector as

A) impulse B) powerC) speed D) time

38. Which quantity is a vector?

A) less B) greaterC) the same

39. A student on her way to school walks four blockseast, three blocks north, and another four blockseast, as shown in the diagram.

Compared to the distance she walks, the magnitudeof her displacement from home to school is

Base your answers to questions 40 through 42 on the information and diagram below and on yourknowledge of physics.

A 150-newton force, applied to a wooden crate at an angle of 30.° above the horizontal, causesthe crate to travel at constant velocity across a horizontal wooden floor, as represented below.

40. Calculate the magnitude of the normal force exerted by the floor on the crate. [Show all work,including the equation and substitution with units.]

41. Determine the magnitude of the frictional force acting on the crate.

42. Calculate the magnitude of the horizontal component of the 150-newton force. [Show all work,including the equation and substitution with units.]

Base your answers to questions 43 through 45 on the information and diagram below.

The scaled diagram below represents two forces acting concurrently at point P. The magnitudeof force A is 32 newtons and the magnitude of force B is 20. newtons. The angle between thedirections of force A and force B is 120°.

43. On the diagram use a protractor and a ruler to construct a scaled vector to represent the resultant offorces A and B. Label the vector R.

44. Determine the linear scale used in the diagram.

45. Determine the magnitude of the resultant force.

Base your answers to questions 46 through 49 on the information and vector diagram below and onyour knowledge of physics.

A hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north. Thevectors in the diagram below represent these two displacements.

46. Using a protractor, determine the angle between east and the hiker's resultant displacement.

47. Determine the magnitude of the hiker's resultant displacement.

48. On the diagram above, use a ruler to construct the vector representing the hiker's resultantdisplacement.

49. Using a metric ruler, determine the scale used in the vector diagram.

Answer KeyVectors & scalars

1. D2. A3. C4. C5. C6. A7. D8. C9. B10. B11. C12. B13. B14. A15. D16. A17. B18. B19. D20. D21. B22. B23. C24. D25. C26. B27. B28. B29. C30. D31. D32. B33. D34. A35. D36. A

37. A38. A39. A40.

41. 130 N42.

43.

44. 1.0 cm = 4.0 N(Within 0.2 N)

45. 28 N +/- 2 N46. 35° 2° or for an

answer that is theangle between the2.0-km vector andthe student'sresponse to question67.

47. 2.4 km 0.2 km or for an answer that isthe product of thelength of theresultant (in cm)drawn by the studentfor question 67 andthe student'sresponse to question66.

48. Constructing anarrow starting atpoint P and endingwith an arrowhead atthe top of the 1.4 kmvector or for a vector6.1 cm 0.2 cmlong at an angle of35° north of the 2.0km vector.

49. 0.40 km 0.02 km