32 + Mcqs in Force Vectors Page 1 McqOptions

1.	The cable AO exerts a force on the top of the pole of F = {120i 90j 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.
A.	x = 16 ft, y = 16 ft, z = 25 ft
B.	x = 12 ft, y = 9 ft, z = 8 ft
C.	x = 20 ft, y = 10 ft, z = 14 ft
D.	x = 24 ft, y = 18 ft, z = 16 ft
Answer» E.

Discussion

2.	The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is horizontal and the force at A is directed at = 30°, determine the magnitude and direction of the resultant force.
A.	R = 458 N, = 97.5° CCW
B.	R = 252 N, = 82.5° CCW
C.	R = 252 N, = 97.5° CCW
D.	R = 458 N, = 82.5° CCW
Answer» D. R = 458 N, = 82.5° CCW

Discussion

3.	If = 20° and = 35°, determine the magnitudes of F1 and F2 so that the resultant force has a magnitude of 20 lb and is directed along the positive x axis.
A.	F1 = 20.0 lb, F2 = 22.9 lb
B.	F1 = 25.6 lb, F2 = 26.6 lb
C.	F1 = 28.5 lb, F2 = 11.91 lb
D.	F1 = 14.00 lb, F2 = 8.35 lb
Answer» E.

Discussion

4.	Determine the design angle (
A.	FAB = 321 lb, = 40.0°
B.	FAB = 383 lb, = 36.9°
C.	FAB = 171.1 lb, = 20.0°
D.	FAB = 215 lb, = 52.7°
Answer» E.

Discussion

5.	Determine the magnitude of the x and y components of the 2kN force.
A.	Fx = -1.414 kN, Fy = -1.414 kN
B.	Fx = -1.000 kN, Fy = -1.732 kN
C.	Fx = -1.732 kN, Fy = -1.000 kN
D.	Fx = -4.000 kN, Fy = -2.312 kN
Answer» C. Fx = -1.732 kN, Fy = -1.000 kN

Discussion

6.	Two forces act on a block. Determine the angle between them.
A.	= 135.0¬∞
B.	= 65.1¬∞
C.	= 45.0¬∞
D.	= 114.9¬∞
Answer» E.

Discussion

7.	Determine the magnitude and direction angles of F2, so that the resultant of the two forces acts upward along the z axis of the pole and has a magnitude of 275 N.
A.	F2 = 246 N, = 54.9¬∞, = 114.0¬∞, = 44.7¬∞
B.	F2 = 200 N, = 45.0¬∞, = -60.0¬∞, = 29.0¬∞
C.	F2 = 200 N, = 45.0¬∞, = 120.0¬∞, = 29.0¬∞
D.	F2 = 246 N, = 54.9¬∞, = 66.0¬∞, = 44.7¬∞
Answer» B. F2 = 200 N, = 45.0¬∞, = -60.0¬∞, = 29.0¬∞

Discussion

8.	If = 20¬∞ and = 35¬∞, determine the magnitudes of F1 and F2 so that the resultant force has a magnitude of 20 lb and is directed along the positive x axis.
A.	F1 = 20.0 lb, F2 = 22.9 lb
B.	F1 = 25.6 lb, F2 = 26.6 lb
C.	F1 = 28.5 lb, F2 = 11.91 lb
D.	F1 = 14.00 lb, F2 = 8.35 lb
Answer» E.

Discussion

9.	The antenna tower is supported by three cables. The forces in these cables are as follows: FB = 520 N, FC = 680 N, and FD = 560 N. Write the resultant of these three forces as a vector.
A.	R = (4i +16j-72k) N
B.	R = (-120i +40 j-960k) N
C.	R = (560i +720j+1440k) N
D.	R = (80i +320j-1440k) N
Answer» E.

Discussion

10.	Determine the magnitudes of the resultant force and its direction measured from the positive x axis.
A.	R = 12.49 kN, = 43.9¬∞ CW
B.	R = 13.6 kN, = 21.5¬∞ CW
C.	R = 14.00 kN, = 60.0¬∞ CW
D.	R = 10.80 kN, = 68.2¬∞ CW
Answer» B. R = 13.6 kN, = 21.5¬∞ CW

Discussion

11.	Cable BC exerts a force of F = 28 N on the top of the flagpole. Determine the projection of this force along the positive z axis of the pole.
A.	F = 24 N
B.	F = -24 N
C.	F = 12 N
D.	F = 12 N
Answer» C. F = 12 N

Discussion

12.	The ball joint is subjected to the three forces shown. Find the magnitude of the resultant force.
A.	R = 5.30 kN
B.	R = 5.74 kN
C.	R = 5.03 kN
D.	R = 6.20 kN
Answer» E.

Discussion

13.	Determine the design angle (
A.	FAB = 321 lb, = 40.0¬∞
B.	FAB = 383 lb, = 36.9¬∞
C.	FAB = 171.1 lb, = 20.0¬∞
D.	FAB = 215 lb, = 52.7¬∞
Answer» E.

Discussion

14.	Determine the projection of the position vector r along the aa axis.
A.	raa = 35.3 m
B.	raa = 6.28 m
C.	raa = 5.42 m
D.	raa = 5.61 m
Answer» D. raa = 5.61 m

Discussion

15.	Express the Force F2 in Cartesian vector form.
A.	F2 = (155 i + 155 j + 300 k) lb
B.	F2 = (212 i + 212 j - 519 k) lb
C.	F2 = (155 i + 155 j - 300 k) lb
D.	F2 = (367 i + 367 j - 300 k) lb
Answer» E.

Discussion

16.	Determine the magnitude and direction of F so that this force has components of 40 lb acting from A toward B and 60lb acting from A toward C on the frame.
A.	F = 44.7 lb, = 22.9¬∞
B.	F = 80.3 lb, = 46.2¬∞
C.	F = 62.9 lb, = 37.1¬∞
D.	F = 72.1 lb, = 56.3¬∞
Answer» C. F = 62.9 lb, = 37.1¬∞

Discussion

17.	Determine the design angle for connecting member A to the plate if the resultant force is to be directed vercially upward. Also, what is the magnitude of the resultant?
A.	R = 400 N, = 53.5¬∞
B.	R = 250 N, = 30.0¬∞
C.	R = 300 N, = 36.9¬∞
D.	R = 640 N, = 38.6¬∞
Answer» D. R = 640 N, = 38.6¬∞

Discussion

18.	Determine the angle between the pole AC and the wire AB.
A.	= 131.8¬∞
B.	= 70.5¬∞
C.	= 109.5¬∞
D.	= 48.2¬∞
Answer» C. = 109.5¬∞

Discussion

19.	Determine the magnitude of the x and y components of the 700-lb force.
A.	Fx = -350 lb, Fy = 606 lb
B.	Fx = -404 lb, Fy = 571 lb
C.	Fx = -606 lb, Fy = 350 lb
D.	Fx = -571 lb, Fy = 404 lb
Answer» D. Fx = -571 lb, Fy = 404 lb

Discussion

20.	What is the projection of the force F2 along the positive axis?
A.	F2y = 170.0 N
B.	F2y = ‚Äî80.0 N
C.	F2y = 90.0 N
D.	F2y = 120.0 N
Answer» D. F2y = 120.0 N

Discussion

21.	The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is horizontal and the force at A is directed at = 30¬∞, determine the magnitude and direction of the resultant force.
A.	R = 458 N, = 97.5¬∞ CCW
B.	R = 252 N, = 82.5¬∞ CCW
C.	R = 252 N, = 97.5¬∞ CCW
D.	R = 458 N, = 82.5¬∞ CCW
Answer» D. R = 458 N, = 82.5¬∞ CCW

Discussion

22.	Determine the magnitude and direction of the position vector r which points from point A to point B.
A.	r = 12 ft, = 70.5¬∞, = 48.2¬∞, = 131.8¬∞
B.	r = 12 ft, = 109.5¬∞, = 131.8¬∞, = 48.2¬∞
C.	r = 12 ft, = 70.5¬∞, = 48.2¬∞, = 48.2¬∞
D.	r = 12 ft, = 109.5¬∞, = 131.8¬∞, = 131.8¬∞
Answer» B. r = 12 ft, = 109.5¬∞, = 131.8¬∞, = 48.2¬∞

Discussion

23.	The cable AO exerts a force on the top of the pole of F = {‚Äî120i ‚Äî 90j ‚Äî 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.
A.	x = 16 ft, y = 16 ft, z = 25 ft
B.	x = 12 ft, y = 9 ft, z = 8 ft
C.	x = 20 ft, y = 10 ft, z = 14 ft
D.	x = 24 ft, y = 18 ft, z = 16 ft
Answer» E.

Discussion

24.	Determine the magnitude of the x and y components of the 2‚ÄîkN force.
A.	Fx = -1.414 kN, Fy = -1.414 kN
B.	Fx = -1.000 kN, Fy = -1.732 kN
C.	Fx = -1.732 kN, Fy = -1.000 kN
D.	Fx = -4.000 kN, Fy = -2.312 kN
Answer» C. Fx = -1.732 kN, Fy = -1.000 kN

Discussion

25.	Determine the magnitude of the resultant force by adding the rectangular components of the three forces.
A.	R = 29.7 N
B.	R = 54.2N
C.	R = 90.8 N
D.	R = 24.0 N
Answer» B. R = 54.2N

Discussion

26.	Express force F as a Cartesian vector; then determine its direction angles.
A.	F = (-2i +j+2k) kN, = 48.2¬∞, = 70.5¬∞, = 48.2¬∞
B.	F = (-2i +j+2k) kN, = 131.8¬∞, = 70.5¬∞, = 48.2¬∞
C.	F = (-4i +j+4k) kN, = 48.2¬∞, = 70.5¬∞, = 48.2¬∞
D.	F = (-4i +2j+4k) kN, = 131.8¬∞, = 70.5¬∞, = 48.2¬∞
Answer» C. F = (-4i +j+4k) kN, = 48.2¬∞, = 70.5¬∞, = 48.2¬∞

Discussion

27.	Determine the magnitude and direction of the resultant force.
A.	R = 80.3 lb, = 106.2¬∞ CCW
B.	R = 80.3 lb, = 73.8¬∞ CCW
C.	R = 72.1 lb, = 63.6¬∞ CCW
D.	R = 72.1 lb, = 116.4¬∞ CCW
Answer» B. R = 80.3 lb, = 73.8¬∞ CCW

Discussion

28.	Express the force F1 in Cartesian vector form.
A.	F1 = (200 i - 200 j + 283 k) lb
B.	F1 = (200 i + 200 j + 283 k) lb
C.	F1 = (-200 i + 200 j + 565 k) lb
D.	F1 = (-200 i + 200 j + 283 k) lb
Answer» E.

Discussion

29.	Force F acts on peg A such that one of its components, lying in the x-y plane, has a magnitude of 50 lb. Express F as a Cartesian vector.
A.	F = (43.3 i + 25.0 j + 25.0 k) lb
B.	F = (43.3 i + 25.0 j + 28.9 k) lb
C.	F = (43.3 i - 25.0 j + 25.0 k) lb
D.	F = (43.3 i - 25.0 j + 28.9 k) lb
Answer» E.

Discussion

30.	If F1 = F2 = 30lb, determine the angles and so that the resultant force is directed along the positive x axis and has a magnitude of FR = 20 lb.
A.	= = 70.5¬∞
B.	= = 41.4¬∞
C.	= = 19.47¬∞
D.	= = 18.43¬∞
Answer» B. = = 41.4¬∞

Discussion

31.	Express each force in Cartesian vector form.
A.	F1 = (2.50 i + 3.54 j + 2.50 k) kN, F2 = -2 j kN
B.	F1 = (4.33 i + 3.54 j + 4.33 k) kN, F2 = -2 j kN
C.	F1 = (2.17 i + 3.75 j + 4.33 k) kN, F2 = -2 j kN
D.	F1 = (4.33 i + 3.75 j + 2.17 k) kN, F2 = -2 j kN
Answer» B. F1 = (4.33 i + 3.54 j + 4.33 k) kN, F2 = -2 j kN

Discussion

32.	The cord is attached between two walls. If it is 8 m long, determine the distance x to the point of attachment at B.
A.	x = 7.75 m
B.	x = 7.68 m
C.	x = 6.93 m
D.	x = 7.94 m
Answer» C. x = 6.93 m

Discussion

Explore topic-wise MCQs in Engineering Mechanics.

The cable AO exerts a force on the top of the pole of F = {120i  90j  80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is horizontal and the force at A is directed at = 30°, determine the magnitude and direction of the resultant force.

If = 20° and = 35°, determine the magnitudes of F1 and F2 so that the resultant force has a magnitude of 20 lb and is directed along the positive x axis.

Determine the design angle (

Determine the magnitude of the x and y components of the 2kN force.

Two forces act on a block. Determine the angle between them.

Determine the magnitude and direction angles of F2, so that the resultant of the two forces acts upward along the z axis of the pole and has a magnitude of 275 N.

If = 20¬∞ and = 35¬∞, determine the magnitudes of F1 and F2 so that the resultant force has a magnitude of 20 lb and is directed along the positive x axis.

The antenna tower is supported by three cables. The forces in these cables are as follows: FB = 520 N, FC = 680 N, and FD = 560 N. Write the resultant of these three forces as a vector.

Determine the magnitudes of the resultant force and its direction measured from the positive x axis.

Cable BC exerts a force of F = 28 N on the top of the flagpole. Determine the projection of this force along the positive z axis of the pole.

The ball joint is subjected to the three forces shown. Find the magnitude of the resultant force.

Determine the design angle (

Determine the projection of the position vector r along the aa axis.

Express the Force F2 in Cartesian vector form.

Determine the magnitude and direction of F so that this force has components of 40 lb acting from A toward B and 60lb acting from A toward C on the frame.

Determine the design angle for connecting member A to the plate if the resultant force is to be directed vercially upward. Also, what is the magnitude of the resultant?

Determine the angle between the pole AC and the wire AB.

Determine the magnitude of the x and y components of the 700-lb force.

What is the projection of the force F2 along the positive axis?

The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is horizontal and the force at A is directed at = 30¬∞, determine the magnitude and direction of the resultant force.

Determine the magnitude and direction of the position vector r which points from point A to point B.

The cable AO exerts a force on the top of the pole of F = {‚Äî120i ‚Äî 90j ‚Äî 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

Determine the magnitude of the x and y components of the 2‚ÄîkN force.

Determine the magnitude of the resultant force by adding the rectangular components of the three forces.

Express force F as a Cartesian vector; then determine its direction angles.

Determine the magnitude and direction of the resultant force.

Express the force F1 in Cartesian vector form.

Force F acts on peg A such that one of its components, lying in the x-y plane, has a magnitude of 50 lb. Express F as a Cartesian vector.

If F1 = F2 = 30lb, determine the angles and so that the resultant force is directed along the positive x axis and has a magnitude of FR = 20 lb.

Express each force in Cartesian vector form.

The cord is attached between two walls. If it is 8 m long, determine the distance x to the point of attachment at B.

The cable AO exerts a force on the top of the pole of F = {120i 90j 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

Determine the magnitude of the x and y components of the 2kN force.