Determine the components Fa and Fb of the 4-kN force along the oblique axes a and b

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.

The force F has a magnitude of 7 kN and acts at the location indicated. Express F as a vector in terms of the unit vectors i and j. Next, determine the x and y scalar components of F.

The slope of the 6.5-kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and j.

The force F has a magnitude of 1250 lb and has the indicated line of action. Write the unit vector n associated with F and use n to determine the x and y scalar components of F.

The control rod AP exerts a force F on the sector as shown. Determine both the x-y and the n-t components of the force.

Two forces are applied to the construction bracket as shown. Determine the angle \(\theta\) which makes the resultant of the two forces vertical. Determine the magnitude R of the resultant.

Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If \(F_1 = 500 N\) and \(F_2 = 350 N\), determine the vector expression for the resultant R of the two forces. Then determine the magnitude of the resultant and the angle which it makes with the positive x-axis.

The y-component of the force F which a person exerts on the handle of the box wrench is known to be 70 lb. Determine the x-component and the magnitude of F.

Determine the x-y and n-t components of the 13-kip force F acting on the simply-supported beam.

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 \(\theta\) which R makes with the positive x-axis.

The guy cables AB and AC are attached to the top of the transmission tower. The tension in cable AB is 8 kN. Determine the required tension T in cable AC 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.

If the equal tensions T in the pulley cable are 400 N, express in vector notation the force R exerted on the pulley by the two tensions. Determine the magnitude of R.

Two people exert the forces shown on the potted shrub. Determine the vector expression for the resultant R of the forces and determine the angle which the resultant makes with the positive y-axis.

A compressive force F is transmitted via the coupler arm AB to disk OA. Develop the general expression for the n - and t-components of F as they act on the disk. Evaluate your expressions for (a) F = 500 N, \(\theta=60^{\circ}, \phi=20^{\circ}\) and (b) F = 800 N, \(\theta=45^{\circ}\), \(\phi=150^{\circ}\)

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

The two forces shown act in the x-y plane of the T-beam cross section. If it is known that the resultant R of the two forces has a magnitude of 3.5 kN and a line of action that lies \(15^{\circ}\) above the negative x-axis, determine the magnitude of \(\mathbf{F}_1\) and the inclination \(\theta\) of \(\mathbf{F}_2\).

Determine the x- and y-components of the tension T which is applied to point A of the bar OA. Neglect the effects of the small pulley at B. Assume that r and \(\theta\) are known.

Refer to the mechanism of the previous problem. Develop general expressions for the n- and t-components of the tension T applied to point A. Then evaluate your expressions for T = 100 N and \(\theta = 35^{\circ}\).

Determine the magnitude \(F_s\) of the tensile spring force in order that the resultant of \(F_s\) and F is a vertical force. Determine the magnitude R of this vertical resultant force.

Determine the resultant R of the two forces applied to the bracket. Write R in terms of unit vectors along the x- and y-axes shown.

A sheet of an experimental composite is subjected to a simple tension test to determine its strength along a particular direction. The composite is reinforced by the Kevlar fibers shown, and a close-up showing the direction of the applied tension force F in relation to the fiber directions at point A is shown. If the magnitude of F is 2.5 kN, determine the components \(F_a\) and \(F_b\) of the force F along the oblique axes a and b. Also determine the projections \(P_a\) and \(P_b\) of F onto the a-b axes.

Determine the scalar components \(R_a\) and \(R_b\) of the force R along the non rectangular axes a and b. Also determine the orthogonal projection \(P_a\) of R onto axis a.

Determine the components \(F_a\) and \(F_b\) of the 4-kN force along the oblique axes a and b. Determine the projections \(P_a\) and \(P_b\) of F onto the a- and b-axes.

If the projection \(P_a\) and component \(F_b\) of the force F along oblique axes a and b are both 325 N, determine the magnitude F and the orientation \(\theta\) of the b-axis.

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 400 lb 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.

At what angle \(\theta\) must the 800-lb force be applied in order that the resultant R of the two forces have a magnitude of 2000 lb? For this condition, determine the angle \(\beta\) between R and the vertical.

Power is to be transferred from the pinion A to the output gear C inside a mechanical drive. Because of output motion requirements and space limitations, an idler gear B is introduced as shown. A force analysis has determined that the total contact force between each pair of meshing teeth has a magnitude \(F_n = 5500 N\), and these forces are shown acting on idler gear B. Determine the magnitude of the resultant R of the two contact forces acting on the idler gear. Complete both a graphical and a vector solution.

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.

The unstretched length of the spring is r. When pin P is in an arbitrary position \(\theta\), determine the x - and y-components of the force which the spring exerts on the pin. Evaluate your general expressions for r = 400 mm, k = 1.4 kN/m, and \(\theta=40^{\circ}\). (Note: The force in a spring is given by \(F = k \delta\), where \(\delta\) is the extension from the unstretched length.)