Two-Dimensional Rectangular Components

Basic Concept : Two-Dimensional Rectangular Components

2/99 Express F as a vector in terms of the unit vectors i, j, and k. Determine the angle between F and the

y-axis.

2/100 The 70-m microwave transmission tower is steadied by three guy cables as shown. Cable AB carries a tension of 12 kN. Express the corresponding force on point B as a vector.

2/101 Express the force F as a vector in terms of the unit vectors i, j, and k. Determine the angles x, y, and z which F makes with the positive x-, y-, and z-axes.

2/102 Express F as a vector in terms of the unit vectors i, j, and k. Determine the projection, both as a scalar and as a vector, of F onto line OA, which lies in the x-y plane.

2/103 The force F has a magnitude of 900 N and acts along the diagonal of the parallelepiped as shown. Express F in terms of its magnitude times the appropriate unit vector and determine its x-, y-, and z-components.

2/104 The turnbuckle is tightened until the tension in the cable AB equals 2.4 kN. Determine the vector

expression for the tension T as a force acting on member AD. Also find the magnitude of the projection of T along the line AC.

2/105 The rigid pole and cross-arm assembly is supported by the three cables shown. A turnbuckle at D is tightened until it induces a tension T in CD of 1.2 kN. Express T as a vector. Does it make any difference in the result which coordinate system is used?

2/106 Use the result cited for Prob. 2/105 and determine the magnitude TGF of the projection of T onto line GF.

2/107 The tension in the supporting cable AB is 10 kN. Write the force which the cable exerts on the boom BC as a vector T. Determine the angles θx, θy, and θz which the line of action of T forms with the positive x-, y-, and z-axes.

2/108 The cable BC carries a tension of 750 N. Write this tension as a force T acting on point B in terms of the unit vectors i, j, and k. The elbow at A forms a right angle.

2/109 Derive the expression for the projection FDC of the force F onto the line directed from D to C.

2/110 If M is the center of the face ABCD of the rectangular solid, express F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projection of F along line AE. The quantities F, a, b, and c are known.

2/111 Determine the angle between the 200-N force and line OC.

2/112 The rectangular plate is supported by hinges along its side BC and by the cable AE. If the cable tension is 300 N, determine the projection onto line BC of the force exerted on the plate by the cable. Note that E is the midpoint of the horizontal upper edge of the structural support.

2/113 The access door is held in the 30 open position by the chain AB. If the tension in the chain is 100 N, determine the projection of the tension force onto the diagonal axis CD of the door.

2/114 The spring of constant k 2.6 kN/m is attached to the disk at point A and to the end fitting at point B as shown. The spring is unstretched when θA and θB are both zero. If the disk is rotated 15 clockwise

and the end fitting is rotated 30 counterclockwise, determine a vector expression for the force F which
the spring exerts at point A. The magnitude of the spring force is the constant k multiplied by the deflection (lengthening or shortening) of the spring.

2/115 Determine the x-, y-, and z-components of force F which acts on the tetrahedron as shown. The quantities a, b, c, and F are known, and M is the midpoint of edge AB.

2/116 A force F is applied to the surface of the sphere as shown. The angles θ and ϕ locate point P, and point M is the midpoint of ON. Express F in vector form, using the given x-, y-, and z-coordinates.