Multiple Choice

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Chapter 2

Multiple Choice

This activity contains 29 questions.

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

R = 12.49 kN, = 43.9° CWR = 13.6 kN, = 21.5° CWR = 14.00 kN, = 60.0° CWR = 10.80 kN, = 68.2° CW

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

Fx = -1.414 kN, Fy = -1.414 kNFx = -1.000 kN, Fy = -1.732 kNFx = -1.732 kN, Fy = -1.000 kNFx = -4.000 kN, Fy = -2.312 kN

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

Fx = -350 lb, Fy = 606 lbFx = -404 lb, Fy = 571 lbFx = -606 lb, Fy = 350 lbFx = -571 lb, Fy = 404 lb

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.

F = 44.7 lb, = 22.9°F = 80.3 lb, = 46.2°F = 62.9 lb, = 37.1°F = 72.1 lb, = 56.3°

Determine the design angle ( <90°) bretween the two struts so that the 500-lb horizontal force has a component of 600lb directed from A toward C. That is the component of force acting along member AB?

F_AB = 321 lb, = 40.0°F_AB = 383 lb, = 36.9°F_AB = 171.1 lb, = 20.0°F_AB = 215 lb, = 52.7°

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.

F₁ = 20.0 lb, F₂ = 22.9 lbF₁ = 25.6 lb, F₂ = 26.6 lbF₁ = 28.5 lb, F₂ = 11.91 lbF₁ = 14.00 lb, F₂ = 8.35 lb

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.

R = 458 N, = 97.5° CCWR = 252 N, = 82.5° CCWR = 252 N, = 97.5° CCWR = 458 N, = 82.5° CCW

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?

R = 400 N, = 53.5°R = 250 N, = 30.0°R = 300 N, = 36.9°R = 640 N, = 38.6°

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

R = 29.7 NR = 54.2NR = 90.8 NR = 24.0 N

Determine the magnitude and direction of the resultant force.

R = 251 N, = 85.5° CCWR = 251 N, = 94.5° CCWR = 421 N, = 67.7° CCWR = 421 N, = 112.3° CCW

Determine the magnitude and direction of the resultant force.

R = 80.3 lb, = 106.2° CCWR = 80.3 lb, = 73.8° CCWR = 72.1 lb, = 63.6° CCWR = 72.1 lb, = 116.4° CCW

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 F_R = 20 lb.

= = 70.5° = = 41.4° = = 19.47° = = 18.43°

Express each force in Cartesian vector form.

F₁ = (2.50 i + 3.54 j + 2.50 k) kN, F₂ = -2 j kNF₁ = (4.33 i + 3.54 j + 4.33 k) kN, F₂ = -2 j kNF₁ = (2.17 i + 3.75 j + 4.33 k) kN, F₂ = -2 j kNF₁ = (4.33 i + 3.75 j + 2.17 k) kN, F₂ = -2 j kN

Express the force F₁ in Cartesian vector form.

F₁ = (200 i - 200 j + 283 k) lbF₁ = (200 i + 200 j + 283 k) lbF₁ = (-200 i + 200 j + 565 k) lbF₁ = (-200 i + 200 j + 283 k) lb

Express the Force F₂ in Cartesian vector form.

F₂ = (155 i + 155 j + 300 k) lbF₂ = (212 i + 212 j - 519 k) lbF₂ = (155 i + 155 j - 300 k) lbF₂ = (367 i + 367 j - 300 k) lb

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

R = 5.30 kNR = 5.74 kNR = 5.03 kNR = 6.20 kN

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.

F₂ = 246 N, = 54.9°, = 114.0°, = 44.7°F₂ = 200 N, = 45.0°, = -60.0°,

= 29.0°F₂ = 200 N, = 45.0°, = 120.0°,

= 29.0°F₂ = 246 N, = 54.9°, = 66.0°,

= 44.7°

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.

F = (43.3 i + 25.0 j + 25.0 k) lbF = (43.3 i + 25.0 j + 28.9 k) lbF = (43.3 i - 25.0 j + 25.0 k) lbF = (43.3 i - 25.0 j + 28.9 k) lb

Specify the magnitude and direction angles ₁, ₁ and ₁ of F₁ so that the resultant of the three forces acting on the post is F_R = {-350k}lb. Note that F3 lies in the x—y plane.

F₁ = 429 lb, = 62.2°, = 70.0°, = 35.3°F₁ = 429 lb, = 62.2°, = 110.0°, = 144.7°F₁ = 447 lb, = 30.0°, = 120.0°, = 141.5°F₁ = 447 lb, = 30.0°, = 60.0°, = 38.5°

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

r = 12 ft, = 70.5°, = 48.2°, = 131.8°r = 12 ft, = 109.5°, = 131.8°, = 48.2°r = 12 ft, = 70.5°, = 48.2°, = 48.2°r = 12 ft, = 109.5°, = 131.8°, = 131.8°

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

x = 7.75 mx = 7.68 mx = 6.93 mx = 7.94 m

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

F = (-2i +j+2k) kN, = 48.2°, = 70.5°, = 48.2° F = (-2i +j+2k) kN, = 131.8°, = 70.5°, = 48.2° F = (-4i +j+4k) kN, = 48.2°, = 70.5°, = 48.2° F = (-4i +2j+4k) kN, = 131.8°, = 70.5°, = 48.2°

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

R = (4i +16j-72k) NR = (-120i +40 j-960k) NR = (560i +720j+1440k) NR = (80i +320j-1440k) N

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.

x = 16 ft, y = 16 ft, z = 25 ftx = 12 ft, y = 9 ft, z = 8 ftx = 20 ft, y = 10 ft, z = 14 ftx = 24 ft, y = 18 ft, z = 16 ft

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

= 131.8° = 70.5° = 109.5° = 48.2°

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

r_aa = 35.3 mr_aa = 6.28 mr_aa = 5.42 mr_aa = 5.61 m

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.

F = 24 NF = -24 NF = 12 NF = 12 N

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

= 135.0° = 65.1° = 45.0° = 114.9°

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

F_2y = 170.0 NF_2y = —80.0 NF_2y = 90.0 NF_2y = 120.0 N

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Multiple Choice

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

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

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

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

Determine the magnitude and direction of the resultant force.

Determine the magnitude and direction of the resultant force.

Express each force in Cartesian vector form.

Express the force F1 in Cartesian vector form.

Express the Force F2 in Cartesian vector form.

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

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.

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.

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

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

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

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.

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 angle between the pole AC and the wire AB.

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

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

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

Express the force F₁ in Cartesian vector form.

Express the Force F₂ in Cartesian vector form.

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.

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

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