If and , determine the magnitude and direction measured clockwise from the positive x

Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis. F

Two forces act on the hook. Determine the magnitude of the resultant force. F

Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. F

Resolve the 30-lb force into components along the u and axes, and determine the magnitude of each of these components. F

The force acts on the frame. Resolve this force into components acting along members AB and AC, and determine the magnitude of each component. F

If force F is to have a component along the u axis of , determine the magnitude of F and the magnitude of its component Fv along the v axis.

If and , determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

If and , determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

If the magnitude of the resultant force is to be 9 kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle u. u = 60 T = 5 kN u = 30 T = 6 kN *

Determine the magnitude of the resultant force acting on the bracket and its direction measured counterclockwise from the positive u axis.

Resolve F1 into components along the u and axes, and determine the magnitudes of these components.

Resolve F2 into components along the u and axes, and determine the magnitudes of these components.

If and the resultant force acts along the positive u axis, determine the magnitude of the resultant force and the angle . *

If the resultant force is required to act along the positive u axis and have a magnitude of 5 kN, determine the required magnitude of FB and its direction u.

The plate is subjected to the two forces at A and B as shown. If , determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal.

Determine the angle of for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right.Also, what is the magnitude of the resultant force?

If the tension in the cable is 400 N, determine the magnitude and direction of the resultant force acting on the pulley. This angle is the same angle of line AB on the tailboard block. u *

The device is used for surgical replacement of the knee joint. If the force acting along the leg is 360 N, determine its components along the x and y axes.

The device is used for surgical replacement of the knee joint. If the force acting along the leg is 360 N, determine its components along the x and y axes.

Determine the design angle for strut AB so that the 400-lb horizontal force has a component of 500 lb directed from A towards C.What is the component of force acting along member AB? Take .

Determine the design angle between struts AB and AC so that the 400-lb horizontal force has a component of 600 lb which acts up to the left, in the same direction as from B towards A.Take u = 30. *

Resolve F1 into components along the u and axes and determine the magnitudes of these components.

Resolve F2 into components along the u and axes and determine the magnitudes of these components.

The truck is to be towed using two ropes. Determine the magnitudes of forces FA and FB acting on each rope in order to develop a resultant force of 950 N directed along the positive x axis.Set .

The truck is to be towed using two ropes. If the resultant force is to be 950 N, directed along the positive x axis, determine the magnitudes of forces FA and FB acting on each rope and the angle of FB so that the magnitude of FB is a minimum. FA acts at 20 from the x axis as shown. u u = 50 *

If , , and the resultant force is 6 kN directed along the positive y axis, determine the required magnitude of F2 and its direction .

If and the resultant force is to be 6 kN directed along the positive y axis, determine the magnitudes of F1 and F2 and the angle if F2 is required to be a minimum.

If , , and the resultant force is to be directed along the positive y axis, determine the magnitude of the resultant force if F2 is to be a minimum. Also, what is F2 and the angle u?

If and , determine the magnitude of the resultant force acting on the plate and its direction measured clockwise from the positive x axis. *

If the resultant force FR is directed along a line measured 75 clockwise from the positive x axis and the magnitude of F2 is to be a minimum, determine the magnitudes of FR and F2 and the angle u 90.

Two forces F1 and F2 act on the screw eye. If their lines of action are at an angle apart and the magnitude of each force is determine the magnitude of the resultant force FR and the angle between FR and F1.

The log is being towed by two tractors A and B. Determine the magnitudes of the two towing forces FA and FB if it is required that the resultant force have a magnitude and be directed along the x axis. Set .

The resultant FR of the two forces acting on the log is to be directed along the positive x axis and have a magnitude of 10 kN, determine the angle of the cable, attached to B such that the magnitude of force FB in this cable is a minimum. What is the magnitude of the force in each cable for this situation? u FR = 10 kN u = 15 *

The beam is to be hoisted using two chains. Determine the magnitudes of forces FA and FB acting on each chain in order to develop a resultant force of 600 N directed along the positive y axis.Set .

The beam is to be hoisted using two chains. If the resultant force is to be 600 N directed along the positive y axis, determine the magnitudes of forces FA and FB acting on each chain and the angle of FB so that the magnitude of FB is a minimum. FA acts at 30 from the y axis, as shown.

Three chains act on the bracket such that they create a resultant force having a magnitude of 500 lb. If two of the chains are subjected to known forces, as shown, determine the angle of the third chain measured clockwise from the positive x axis, so that the magnitude of force F in this chain is a minimum. All forces lie in the xy plane. What is the magnitude of F? Hint: First find the resultant of the two known forces. Force F acts in this direction.

Three cables pull on the pipe such that they create a resultant force having a magnitude of 900 lb. If two of the cables are subjected to known forces, as shown in the figure, determine the angle of the third cable so that the magnitude of force F in this cable is a minimum. All forces lie in the xy plane.What is the magnitude of F? Hint: First find the resultant of the two known forces. F

Resolve each force acting on the post into its x and y components. F

Determine the magnitude and direction of the resultant force. F

Determine the magnitude of the resultant force acting on the corbel and its direction measured counterclockwise from the x axis. F

If the resultant force acting on the bracket is to be 750 N directed along the positive x axis, determine the magnitude of F and its direction u. F

If the magnitude of the resultant force acting on the bracket is to be 80 lb directed along the u axis, determine the magnitude of F and its direction u. F

Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. *

Determine the magnitude of the resultant force acting on the pin and its direction measured clockwise from the positive x axis.

If and , determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

If the magnitude of the resultant force acting on the eyebolt is 600 N and its direction measured clockwise from the positive x axis is , determine the magnitude of F1 and the angle f.

The contact point between the femur and tibia bones of the leg is at A. If a vertical force of 175 lb is applied at this point, determine the components along the x and y axes. Note that the y component represents the normal force on the load-bearing region of the bones. Both the x and y components of this force cause synovial fluid to be squeezed out of the bearing space. *

If and , determine the magnitude of the resultant force acting on the plate and its direction measured clockwise from the positive x axis.

If the magnitude for the resultant force acting on the plate is required to be 6 kN and its direction measured clockwise from the positive x axis is , determine the magnitude of F2 and its direction .

If and the resultant force acting on the gusset plate is directed along the positive x axis, determine the magnitudes of F2 and the resultant force.

Determine the magnitude of F1 and its direction f = 30 F1 = 250 lb so that the resultant force is directed vertically upward and has a magnitude of 800 N. *

Determine the magnitude and direction measured counterclockwise from the positive x axis of the resultant force of the three forces acting on the ring A. Take F1 = 500 N and u = 20.

Determine the magnitude and direction of FB so that the resultant force is directed along the positive y axis and has a magnitude of 1500 N.

Determine the magnitude and angle measured counterclockwise from the positive y axis of the resultant force acting on the bracket if FB = 600 N and u = 20.

If and , determine the magnitude of the resultant force acting on the bracket and its direction measured clockwise from the positive x axis. *

If the magnitude of the resultant force acting on the bracket is 400 lb directed along the positive x axis, determine the magnitude of F1 and its direction .

If the resultant force acting on the bracket is to be directed along the positive x axis and the magnitude of F1 is required to be a minimum, determine the magnitudes of the resultant force and F1.

The three concurrent forces acting on the screw eye produce a resultant force . If and F1 is to be 90 from F2 as shown, determine the required magnitude of F3 expressed in terms of F1 and the angle u.

Determine the magnitude of FA and its direction so that the resultant force is directed along the positive x axis and has a magnitude of 1250 N. *

Determine the magnitude and direction measured counterclockwise from the positive x axis of the resultant force acting on the ring at O if FA = 750 N and u = 45.

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

The three forces are applied to the bracket. Determine the range of values for the magnitude of force P so that the resultant of the three forces does not exceed 2400 N.

If and ,determine the magnitude of the resultant force acting on the bracket and its direction measured clockwise from the positive x axis. *

If the magnitude of the resultant force acting on the bracket is to be 450 N directed along the positive u axis, determine the magnitude of F1 and its direction .

If the resultant force acting on the bracket is required to be a minimum, determine the magnitudes of F1 and the resultant force. Set f = 30.

Three forces act on the bracket. Determine the magnitude and direction of F2 so that the resultant force is directed along the positive u axis and has a magnitude of 50 lb.

If and , determine the magnitude and direction measured clockwise from the positive x axis of the resultant force of the three forces acting on the bracket. *

The three concurrent forces acting on the post produce a resultant force . If , and F1 is to be 90 from F2 as shown, determine the required magnitude of F3 expressed in terms of F1 and the angle u.

Determine the magnitude of force F so that the resultant force of the three forces is as small as possible. What is the magnitude of this smallest resultant force?

Express each of the three forces acting on the bracket in Cartesian vector form with respect to the x and y axes. Determine the magnitude and direction of F1 so that the resultant force is directed along the positive axis and has a magnitude of FR = 600 N. F

Determine its coordinate direction angles of the force. F

Express the force as a Cartesian vector. F

Express the force as a Cartesian vector. F

Express the force as a Cartesian vector. F

Express the force as a Cartesian vector. F

Determine the resultant force acting on the hook.

Determine the coordinate angle for F2 and then express each force acting on the bracket as a Cartesian vector. *

Determine the magnitude and coordinate direction angles of the resultant force acting on the bracket. g

Express each force acting on the pipe assembly in Cartesian vector form.

Determine the magnitude and direction of the resultant force acting on the pipe assembly.

The force F acts on the bracket within the octant shown.If , ,and ,determine the x, y, z components of F. *

The force F acts on the bracket within the octant shown. If the magnitudes of the x and z components of F are and , respectively,and , determine the magnitude of F and its y component. Also, find the coordinate direction angles a and g.

The two forces F1 and F2 acting at A have a resultant force of . Determine the magnitude and coordinate direction angles of F2.

Determine the coordinate direction angles of the force F1 and indicate them on the figure.

The spur gear is subjected to the two forces caused by contact with other gears. Express each force as a Cartesian vector. *

The spur gear is subjected to the two forces caused by contact with other gears. Determine the resultant of the two forces and express the result as a Cartesian vector.

If the resultant force acting on the bracket is , determine the magnitude and coordinate direction angles of F.

If the resultant force acting on the bracket is to be , determine the magnitude and coordinate direction angles of F.

If , , , and , determine the magnitude and coordinate direction angles of the resultant force acting on the hook. *

If the resultant force acting on the hook is , determine the magnitude and coordinate direction angles of F.

The shaft S exerts three force components on the die D. Find the magnitude and coordinate direction angles of the resultant force. Force \(F_2\) acts within the octant shown.

The mast is subjected to the three forces shown. Determine the coordinate direction angles of F1 so that the resultant force acting on the mast is .

The mast is subjected to the three forces shown. Determine the coordinate direction angles of F1 so that the resultant force acting on the mast is zero. *

Determine the magnitude and coordinate direction angles of F2 so that the resultant of the two forces acts along the positive x axis and has a magnitude of 500 N.

Determine the magnitude and coordinate direction angles of F2 so that the resultant of the two forces is zero.

If the resultant force acting on the bracket is directed along the positive y axis, determine the magnitude of the resultant force and the coordinate direction angles of F so that b 6 90.

Specify the magnitude of F3 and its coordinate direction angles so that the resultant force FR = 59j6 kN. *

If , , and = 45, determine the magnitude and coordinate direction angles of the resultant force acting on the ball-and-socket joint.

The pole is subjected to the force F, which has components acting along the x, y, z axes as shown. If the magnitude of F is 3 kN, , and , determine the magnitudes of its three components.

The pole is subjected to the force F which has components and .If , determine the magnitudes of F and Fy.

Three forces act on the ring. If the resultant force FR has a magnitude and direction as shown, determine the magnitude and the coordinate direction angles of force F3. *

Determine the coordinate direction angles of F1 and FR.

Two forces F1 and F2 act on the bolt. If the resultant force FR has a magnitude of 50 lb and coordinate direction angles and , as shown, determine the magnitude of F2 and its coordinate direction angles. F

Express the position vector in Cartesian vector form, then determine its magnitude and coordinate direction angles. F

Determine the length of the rod and the position vector directed from A to B.What is the angle u? F

Express the force as a Cartesian vector. F

Express the force as a Cartesian vector. F

Determine the magnitude of the resultant force at A. F

Determine the resultant force at A.

Determine the position vector r directed from point A to point B and the length of cord AB.Take .

If the cord AB is 7.5 m long, determine the coordinate position +z of point B z = 4 m *

Determine the distance between the end points A and B on the wire by first formulating a position vector from A to B and then determining its magnitude.

Determine the magnitude and coordinate direction angles of the resultant force acting at A.

Determine the magnitude and coordinate direction angles of the resultant force.

Determine the magnitude and coordinate direction angles of the resultant force acting at A. *

Determine the magnitude and coordinate direction angles of the resultant force.

The chandelier is supported by three chains which are concurrent at point O. If the force in each chain has a magnitude of 60 lb, express each force as a Cartesian vector and determine the magnitude and coordinate direction angles of the resultant force.

The chandelier is supported by three chains which are concurrent at point O. If the resultant force at O has a magnitude of 130 lb and is directed along the negative z axis, determine the force in each chain.

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

The tower is held in place by three cables. If the force of each cable acting on the tower is shown, determine the magnitude and coordinate direction angles of the resultant force.Take x = 20 m, y = 15 m. a, b, g

The door is held opened by means of two chains. If the tension in AB and CDis and , respectively, express each of these forces in Cartesian vector form. FA = 300 N FC = 250 N

The guy wires are used to support the telephone pole. Represent the force in each wire in Cartesian vector form. Neglect the diameter of the pole.

Two cables are used to secure the overhang boom in position and support the 1500-N load. If the resultant force is directed along the boom from point A towards O, determine the magnitudes of the resultant force and forces FB and FC.Set and . *

Two cables are used to secure the overhang boom in position and support the 1500-N load. If the resultant force is directed along the boom from point A towards O, determine the values of x and z for the coordinates of point C and the magnitude of the resultant force. Set FB = 1610 N and FC = 2400 N.

The cable AO exerts a force on the top of the pole of . If the cable has a length of 34 ft, determine the height z of the pole and the location (x, y) of its base. F = 5-120i - 90j - 80k6 lb

If the force in each chain has a magnitude of 450 lb, determine the magnitude and coordinate direction angles of the resultant force.

If the resultant of the three forces is , determine the magnitude of the force in each chain. FR = 5-900k6 lb *

The antenna tower is supported by three cables. If the forces of these cables acting on the antenna are , ,and ,determine the magnitude and coordinate direction angles of the resultant force acting at A. FB = 520 N FC = 680 N FD = 560 N

If the force in each cable tied to the bin is 70 lb, determine the magnitude and coordinate direction angles of the resultant force.

If the resultant of the four forces is , determine the tension developed in each cable. Due to symmetry, the tension in the four cables is the same.

The pipe is supported at its end by a cord AB. If the cord exerts a force of on the pipe at A, express this force as a Cartesian vector. F = 12 lb *

The load at A creates a force of 200 N in wire AB. Express this force as a Cartesian vector, acting on A and directed towards B.

The cylindrical plate is subjected to the three cable forces which are concurrent at point D. Express each force which the cables exert on the plate as a Cartesian vector, and determine the magnitude and coordinate direction angles of the resultant force.

The cable attached to the shear-leg derrick exerts a force on the derrick of . Express this force as a Cartesian vector. F

Determine the angle between the force and the line AO. . F

Determine the angle between the force and the line AB. u F

Determine the angle between the force and the line . F

Determine the component of projection of the force along the line OA. OA U u F

Find the magnitude of the projected component of the force along the pipe F

Determine the components of the force acting parallel and perpendicular to the axis of the pole.

Given the three vectors A, B, and D, show that . *

Determine the projected component of the force acting along cable AC. Express the result as a Cartesian vector. FAB = 560 N A # (B + D) = (A # B) + (A # D)

Determine the length of side BC of the triangular plate. Solve the problem by finding the magnitude of rBC; then check the result by first finding q , rAB, and rAC and then using the cosine law.

Determine the magnitudes of the components of force F = 56 N acting along and perpendicular to line AO.

Determine the magnitudes of the components of acting along and perpendicular to segment DE of the pipe assembly. *

Two forces act on the hook. Determine the angle between them.Also, what are the projections of F1 and F2 along the y axis?

Two forces act on the hook. Determine the magnitude of the projection of F2 along F1. u

Determine the projection of force along line BC. Express the result as a Cartesian vector. F = 80 N

The clamp is used on a jig. If the vertical force acting on the bolt is , determine the magnitudes of its components F1 and F2 which act along the OA axis and perpendicular to it. F = {-500k} N *

Determine the magnitude of the projected component of force FAB acting along the z axis.

Determine the magnitude of the projected component of force FAC acting along the z axis.

Determine the projection of force acting along line AC of the pipe assembly. Express the result as a Cartesian vector.

Determine the magnitudes of the components of force acting parallel and perpendicular to segment BC of the pipe assembly. F = 400 N F = 400 N *

Cable OA is used to support column OB. Determine the angle it makes with beam OC.

Cable OA is used to support column OB. Determine the angle f it makes with beam OD. u

The cables each exert a force of 400 N on the post. Determine the magnitude of the projected component of F1 along the line of action of F2.

Determine the angle between the two cables attached to the post. u *

A force of is applied to the handle of the wrench. Determine the angle between the tail of the force and the handle AB.

Determine the angle between cables AB and AC.

If F has a magnitude of 55 lb, determine the magnitude of its projected components acting along the x axis and along cable AC. u

Determine the magnitudes of the projected components of the force acting along the x and y axes. F = 300 N *

Determine the magnitude of the projected component of the force F = 300 N acting along line OA.

Two cables exert forces on the pipe. Determine the magnitude of the projected component of F1 along the line of action of F2.

Determine the angle between the two cables attached to the pipe.

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

Determine the magnitude of the projected component of the 100-lb force acting along the axis BC of the pipe.

Determine the angle between pipe segments BA and BC

Determine the magnitude and direction of the resultant of the three forces by first finding the resultant and then forming . Specify its direction measured counterclockwise from the positive x axis. FR = F + F2 F = F1 + F3 FR = F1 + F2 + F3

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

Determine the magnitude and direction of the smallest force F3 so that the resultant force of all three forces has a magnitude of 20 lb.

Resolve the 250-N force into components acting along the u and axes and determine the magnitudes of these components.

Cable AB exerts a force of 80 N on the end of the 3-m-long boom OA. Determine the magnitude of the projection of this force along the boom.

The three supporting cables exert the forces shown on the sign. Represent each force as a Cartesian vector.