Two-Dimensional Rectangular Components

2/1 The force F has a magnitude of 800 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F.

2/2 The magnitude of the force F is 600 N. Express F as a vector in terms of the unit vectors i and j. Identify both the scalar and vector components of F.

2/3 The slope of the 4.8-kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and j.

2/4 The line of action of the 9.6-kN force F runs through the points A and B as shown in the figure. Determine the x and y scalar components of F.

2/5 A cable stretched between the fixed supports A and B is under a tension T of 900 N. Express the tension as a vector using the unit vectors i and j, first, as a force TA acting on A and second, as a force TB acting on B.

2/6 The 1800-N force F is applied to the end of the I beam. Express F as a vector using the unit vectors i and j.

2/7 The two structural members, one of which is in tension and the other in compression, exert the indicated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle  which R makes with the positive x-axis.

2/8 Two forces are applied to the construction bracket as shown. Determine the angle which makes the resultant of the two forces with the vertical. Determine the magnitude R of the resultant.

2/9 In the design of a control mechanism, it is determined that rod AB transmits a 260-N force P to the crank BC. Determine the x and y scalar components of P.

2/10 For the mechanism of Prob. 2/9, determine the scalar components Pt and Pn of P which are tangent and normal, respectively, to crank BC.

2/11 The t-component of the force F is known to be 75N. Determine the n-component and the magnitude of F.

2/12 A force F of magnitude 800 N is applied to point C of the bar AB as shown. Determine both the x-y and the n-t components of F.

2/13 The two forces shown act at point A of the bent bar. Determine the resultant R of the two forces.

2/14 To satisfy design limitations it is necessary to determine the effect of the 2-kN tension in the cable on the shear, tension, and bending of the fixed I-beam. For this purpose replace this force by its equivalent of two forces at A, Ft parallel and Fn perpendicular to the beam. Determine Ft and Fn.

2/15 Determine the magnitude Fs of the tensile spring force in order that the resultant of Fs
and F is a vertical force. Determine the magnitude R of this vertical resultant force.

2/16 The ratio of the lift force L to the drag force D for the simple airfoil is L/D 10. If the lift force on a short section of the airfoil is 200 N, compute the magnitude of the resultant force R and the angle which it makes with the horizontal.

2/17 Determine the components of the 2-kN force along the oblique axes a and b. Determine the projections of F onto the a- and b-axes.

2/18 Determine the scalar components Ra and Rb of the force R along the nonrectangular axes a and b. Also determine the orthogonal projection Pa of R onto axis a.

2/19 Determine the resultant R of the two forces shown by (a) applying the parallelogram rule for vector addition and (b) summing scalar components.

2/20 It is desired to remove the spike from the timber by applying force along its horizontal axis. An obstruction A prevents direct access, so that two forces, one 1.6kN and the other P, are applied by cables as shown. Compute the magnitude of P necessary to ensure a resultant T directed along the spike. Also find T.

2/21 At what angle must the 800-N force be applied in order that the resultant R of the two forces has a
magnitude of 2000 N? For this condition, determine the angle β between R and the vertical.

2/22 The unstretched length of the spring of modulus k 1.2 kN/m is 100 mm. When pin P is in the position 30, determine the x- and y-components of the force which the spring exerts on the pin. (The force in a spring is given by F kx, where x is the deflection from the unstretched length.)

2/23 Refer to the statement and figure of Prob. 2/22. When pin P is in the position 20, determine the n- and t-components of the force F which the spring of modulus k 1.2 kN/m exerts on the pin.

2/24 The cable AB prevents bar OA from rotating clockwise about the pivot O. If the cable tension is 750 N, determine the n- and t-components of this force acting on point A of the bar.

2/25 At what angle must the 400-N force be applied in order that the resultant R of the two forces have a magnitude of 1000 N? For this condition what will be the angle β between R and the horizontal?

2/26 In the design of the robot to insert the small cylindrical part into a close-fitting circular hole, the robot arm must exert a 90-N force P on the part parallel to the axis of the hole as shown. Determine the components of the force which the part exerts on the robot along axes (a) parallel and perpendicular to the arm AB, and (b) parallel and perpendicular to the arm BC.

2/27 The guy cables AB and AC are attached to the top of the transmission tower. The tension in cable AC is 8kN. Determine the required tension T in cable AB such that the net effect of the two cable tensions is a downward force at point A. Determine the magnitude R of this downward force.

2/28 The gusset plate is subjected to the two forces shown. Replace them by two equivalent forces, Fx in
the x-direction and Fa in the a-direction. Determine the magnitudes of Fx and Fa. Solve geometrically or graphically.