Given the vectors P 5 3i 2 j 1 k, Q 5 4i 1 Qyj 2 2k, andS 5 2i 2 2j 1 2k, determine the

A crate of mass 80 kg is held in the position shown. Determine (a) the moment produced by the weight W of the crate about E, (b) the smallest force applied at B that creates a moment of equal magnitude and opposite sense about E.

A crate of mass 80 kg is held in the position shown. Determine (a) the moment produced by the weight W of the crate about E, (b) the smallest force applied at A that creates a moment of equal magnitude and opposite sense about E, (c) the magnitude, sense, and point of application on the bottom of the crate of the smallest vertical force that creates a moment of equal magnitude and opposite sense about E.

It is known that a vertical force of 200 lb is required to remove the nail at C from the board. As the nail first starts moving, determine (a) the moment about B of the force exerted on the nail, (b) the magnitude of the force P that creates the same moment about B if 5 10, and (c) the smallest force P that creates the same moment about B.

A 300-N force is applied at A as shown. Determine (a) the moment of the 300-N force about D, (b) the smallest force applied at B that creates the same moment about D.

A 300-N force is applied at A as shown. Determine (a) the moment of the 300-N force about D, (b) the magnitude and sense of the horizontal force applied at C that creates the same moment about D, (c) the smallest force applied at C that creates the same moment about D.

A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that 5 25, determine the moment of the force about point B by resolving the force into hori- zontal and vertical components.

A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that 5 25, determine the moment of the force about point B by resolving the force into com- ponents along AB and in a direction perpendicular to AB.

A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that the moment of the force about B is 120 lbin. clockwise, determine the value of .

Rod AB is held in place by the cord AC. Knowing that the tension in the cord is 1350 N and that c 5 360 mm, determine the moment about B of the force exerted by the cord at point A by resolving that force into horizontal and vertical components applied (a) at point A, (b) at point C.

The tailgate of a car is supported by the hydraulic lift BC. If the lift exerts a 125-lb force directed along its centerline on the ball and socket at B, determine the moment of the force about

The tailgate of a car is supported by the hydraulic lift BC. If the lift exerts a 125-lb force directed along its centerline on the ball and socket at B, determine the moment of the force about

It is known that the connecting rod AB exerts on the crank BC a 2.5-kN force directed down and to the left along the centerline of AB. Determine the moment of the force about C.

It is known that the connecting rod AB exerts on the crank BC a 2.5-kN force directed down and to the left along the centerline of AB. Determine the moment of the force about C.

Form the vector products B 3 C and B9 3 C, where B 5 B9, and use the results obtained to prove the identity

The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when (a) P 5 28i 1 4j 2 4k and Q 5 3i 1 3j 1 6k, (b) P 5 7i 2 6j 2 3k and Q 5 23i 1 6j 2 2k.

A plane contains the vectors A and B. Determine the unit vector normal to the plane when A and B are equal to, respectively, (a) 2i 1 3j 2 6k and 5i 2 8j 2 6k, (b) 4i 2 4j 1 3k and 23i 1 7j 2 5k.

A line passes through the points (12 m, 8 m) and (23 m, 25 m). Determine the perpendicular distance d from the line to the origin O of the system of coordinates.

Determine the moment about the origin O of the force F 5 4i 2 3j 1 5k that acts at a point A. Assume that the position vector of A is (a) r 5 2i 1 3j 2 4k, (b) r 5 28i 1 6j 2 10k, (c) r 5 8i 2 6j 1 5k.

Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tensions in cables AB and BC are 555 N and 660 N, respectively, determine the moment about O of the resultant force exerted on the tree by the cables at B.

The 12-ft boom AB has a fixed end A. A steel cable is stretched from the free end B of the boom to a point C located on the vertical wall. If the tension in the cable is 380 lb, determine the moment about A of the force exerted by the cable at B.

A 200-N force is applied as shown to the bracket ABC. Determine the moment of the force about A.

The wire AE is stretched between the corners A and E of a bent plate. Knowing that the tension in the wire is 435 N, determine the moment about O of the force exerted by the wire (a) on corner A, (b) on corner E.

6-ft-long fishing rod AB is securely anchored in the sand of a beach. After a fish takes the bait, the resulting force in the line is 6 lb. Deter- mine the moment about A of the force exerted by the line at B.

A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tension in cable BD is 900 N, determine the moment about point O of the force exerted by the cable at B.

In Prob. 3.22, determine the perpendicular distance from point A to cable BC.

In Prob. 3.24, determine the perpendicular distance from point O to wire AE.

In Prob. 3.24, determine the perpendicular distance from point B to wire AE.

In Prob. 3.25, determine the perpendicular distance from point D to a line drawn through points B and C.

In Prob. 3.26, determine the perpendicular distance from point O to cable BD.

In Prob. 3.26, determine the perpendicular distance from point C to cable BD.

Determine the value of a that minimizes the perpendicular distance from point C to a section of pipeline that passes through points A and B.

Given the vectors P 5 2i 1 3j 2 k, Q 5 5i 2 4j 1 3k, and S 5 23i 1 2j 2 5k, compute the scalar products P ? Q, P ? S, and Q ? S.

Form the scalar product B ? C and use the result obtained to prove the identity

Three cables are used to support a container as shown. Determine the angle formed by cables AB and AD.

Three cables are used to support a container as shown. Determine the angle formed by cables AC and AD.

Knowing that the tension in cable AC is 280 lb, determine (a) the angle between cable AC and the boom AB, (b) the projection on AB of the force exerted by cable AC at point A.

Ropes AB and BC are two of the ropes used to support a tent. The two ropes are attached to a stake at B. If the tension in rope BC is 490 N, determine (a) the angle between rope BC and the stake, (b) the projection on the stake of the force exerted by rope BC at point B.

Ropes AB and BC are two of the ropes used to support a tent. The two ropes are attached to a stake at B. If the tension in rope BC is 490 N, determine (a) the angle between rope BC and the stake, (b) the projection on the stake of the force exerted by rope BC at point B.

The 20-in. tube AB can slide along a horizontal rod. The ends A and B of the tube are connected by elastic cords to the fixed point C. For the position corresponding to x 5 11 in., determine the angle formed by the two cords, (a) using Eq. (3.30), (b) applying the law of cosines to triangle ABC.

Solve Prob. 3.43 for the position corresponding to x 5 4 in.

Determine the volume of the parallelepiped of Fig. 3.20b when (a) P 5 4i 2 3j 1 2k, Q 5 22i 2 5j 1 k, and S 5 7i 1 j 2 k, (b) P 5 5i 2 j 1 6k, Q 5 2i 1 3j 1 k, and S 5 23i 2 2j 1 4k.

Given the vectors P 5 3i 2 j 1 k, Q 5 4i 1 Qyj 2 2k, and S 5 2i 2 2j 1 2k, determine the value of Qy for which the three vectors are coplanar.

A crane is oriented so that the end of the 25-m boom AO lies in the yz plane. At the instant shown, the tension in cable AB is 4 kN. Determine the moment about each of the coordinate axes of the force exerted on A by cable AB.

The 25-m crane boom AO lies in the yz plane. Determine the maxi- mum permissible tension in cable AB if the absolute value of moments about the coordinate axes of the force exerted on A by cable AB must be |Mx| # 60 kN?m, |My| # 12 kN?m, |Mz| # 8 kN?m

To loosen a frozen valve, a force F with a magnitude of 70 lb is applied to the handle of the valve. Knowing that 5 25, Mx 5 261 lb?ft, and Mz 5 243 lb?ft, determine and d.

To lift a heavy crate, a man uses a block and tackle attached to the bottom of an I-beam at hook B. Knowing that the moments about the y and the z axes of the force exerted at B by portion AB of the rope are, respectively, 120 N?m and 2460 N?m, determine the distance a.

To lift a heavy crate, a man uses a block and tackle attached to the bottom of an I-beam at hook B. Knowing that the man applies a 195-N force to end A of the rope and that the moment of that force about the y axis is 132 N?m, determine the distance a.

A farmer uses cables and winch pullers B and E to plumb one side of a small barn. If it is known that the sum of the moments about the x axis of the forces exerted by the cables on the barn at points A and D is equal to 4728 lb?ft, determine the magnitude of TDE when TAB 5 255 lb.

Solve Prob. 3.53 when the tension in cable AB is 306 lb.

The 23-in. vertical rod CD is welded to the midpoint C of the 50-in. rod AB. Determine the moment about AB of the 235-lb force P.

The 23-in. vertical rod CD is welded to the midpoint C of the 50-in. rod AB. Determine the moment about AB of the 174-lb force Q.

The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable.

In Prob. 3.57, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable.

The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the position shown by cables AE and CF. If the force exerted by cable AE at A is 55 N, determine the moment of that force about the line joining points D and B.

A regular tetrahedron has six edges of length a. A force P is directed as shown along edge BC. Determine the moment of P about edge OA.

regular tetrahedron has six edges of length a. (a) Show that two opposite edges, such as OA and BC, are perpendicular to each other. (b) Use this property and the result obtained in Prob. 3.61 to deter- mine the perpendicular distance between edges OA and BC.

Two forces F1 and F2 in space have the same magnitude F. Prove that the moment of F1 about the line of action of F2 is equal to the moment of F2 about the line of action of F1.

In Prob. 3.55, determine the perpendicular distance between rod AB and the line of action of P.

In Prob. 3.56, determine the perpendicular distance between rod AB and the line of action of Q.

In Prob. 3.57, determine the perpendicular distance between portion BH of the cable and the diagonal AD.

3.7

In Prob. 3.59, determine the perpendicular distance between cable AE and the line joining points D and B.

In Prob. 3.60, determine the perpendicular distance between cable CF and the line joining points D and B.

Two parallel 40-N forces are applied to a lever as shown. Determine the moment of the couple formed by the two forces (a) by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples, (b) by using the perpendicular distance between the two forces, (c) by summing the moments of the two forces about point A.

Four 112-in.-diameter pegs are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indi- cated. (a) Determine the resultant couple acting on the board. (b) If only one string is used, around which pegs should it pass and in what directions should it be pulled to create the same couple with the minimum tension in the string? (c) What is the value of that minimum tension?

Four pegs of the same diameter are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated. Determine the diameter of the pegs knowing that the resul- tant couple applied to the board is 1132.5 lb?in. counterclockwise.

A piece of plywood in which several holes are being drilled succes- sively has been secured to a workbench by means of two nails. Knowing that the drill exerts a 12-Nm couple on the piece of plywood, determine the magnitude of the resulting forces applied to the nails if they are located (a) at A and B, (b) at B and C, (c) at A and C.

The two shafts of a speed-reducer unit are subjected to couples of magnitude M1 5 15 lbft and M2 5 3 lbft, respectively. Replace the two couples with a single equivalent couple, specifying its magnitude and the direction of its axis.

If P 5 0 in the figure, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis.

"If P 5 20 lb in the figure, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its"

Replace the two couples shown with a single equivalent couple, specifying its magnitude and the direction of its axis.

Solve Prob. 3.78, assuming that two 10-N vertical forces have been added, one acting upward at C and the other downward at B.

A 500-N force is applied to a bent plate as shown. Determine (a) an equivalent force-couple system at B, (b) an equivalent system formed by a vertical force at A and a force at B.

The tension in the cable attached to the end C of an adjustable boom ABC is 560 lb. Replace the force exerted by the cable at C with an equivalent force-couple system (a) at A, (b) at B.

A dirigible is tethered by a cable attached to its cabin at B. If the tension in the cable is 1040 N, replace the force exerted by the cable at B with an equivalent system formed by two parallel forces applied at A and C.

30-lb vertical force P is applied at A to the bracket shown, which is held by screws at B and C. (a) Replace P with an equivalent force- couple system at B. (b) Find the two horizontal forces at B and C that are equivalent to the couple obtained in part a.

A worker tries to move a rock by applying a 360-N force to a steel bar as shown. (a) Replace that force with an equivalent force-couple system at D. (b) Two workers attempt to move the same rock by applying a vertical force at A and another force at D. Determine these two forces if they are to be equivalent to the single force of part a.

A worker tries to move a rock by applying a 360-N force to a steel bar as shown. If two workers attempt to move the same rock by applying a force at A and a parallel force at C, determine these two forces so that they will be equivalent to the single 360-N force shown in the figure.

The shearing forces exerted on the cross section of a steel channel can be represented by a 900-N vertical force and two 250-N hori- zontal forces as shown. Replace this force and couple with a single force F applied at point C, and determine the distance x from C to line BD. (Point C is defined as the shear center of the section.)

A force and a couple are applied as shown to the end of a cantilever beam. (a) Replace this system with a single force F applied at point C, and determine the distance d from C to a line drawn through points D and E. (b) Solve part a if the directions of the two 360-N forces are reversed.

Three control rods attached to a lever ABC exert on it the forces shown. (a) Replace the three forces with an equivalent force-couple system at B. (b) Determine the single force that is equivalent to the force-couple system obtained in part a, and specify its point of appli- cation on the lever.

While tapping a hole, a machinist applies the horizontal forces shown to the handle of the tap wrench. Show that these forces are equivalent to a single force, and specify, if possible, the point of application of the single force on the handle.

hexagonal plate is acted upon by the force P and the couple shown. Determine the magnitude and the direction of the smallest force P for which this system can be replaced with a single force at E.

Replace the 250-kN force P with an equivalent force-couple system at G.

A 2.6-kip force is applied at point D of the cast-iron post shown. Replace that force with an equivalent force-couple system at the center A of the base section.

Replace the 150-N force with an equivalent force-couple system at A.

To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts at B a 175-N force directed along line AB. Replace that force with an equivalent force-couple system at C.

46-lb force F and a 2120-lb?in. couple M are applied to corner A of the block shown. Replace the given force-couple system with an equivalent force-couple system at corner H.

A 110-N force acting in a vertical plane parallel to the yz plane is applied to the 220-mm-long horizontal handle AB of a socket wrench. Replace the force with an equivalent force-couple system at the origin O of the coordinate system.

An antenna is guyed by three cables as shown. Knowing that the tension in cable AB is 288 lb, replace the force exerted at A by cable AB with an equivalent force-couple system at the center O of the base of the antenna.

A 3-m-long beam is subjected to a variety of loadings. (a) Replace each loading with an equivalent force-couple system at end A of the beam. (b) Which of the loadings are equivalent?

A 3-m-long beam is loaded as shown. Determine the loading of Prob. 3.101 that is equivalent to this loading.

Determine the single equivalent force and the distance from point A to its line of action for the beam and loading of (a) Prob. 3.101a, (b) Prob. 3.101b, (c) Prob. 3.102.

Five separate force-couple systems act at the corners of a piece of sheet metal that has been bent into the shape shown. Determine which of these systems is equivalent to a force F 5 (10 lb)i and a couple of moment M 5 (15 lb?ft)j 1 (15 lb?ft)k located at the origin.

The weights of two children sitting at ends A and B of a seesaw are 84 lb and 64 lb, respectively. Where should a third child sit so that the resultant of the weights of the three children will pass through C if she weighs (a) 60 lb, (b) 52 lb?

Three stage lights are mounted on a pipe as shown. The lights at A and B each weigh 4.1 lb, while the one at C weighs 3.5 lb. (a) If d 5 25 in., determine the distance from D to the line of action of the resultant of the weights of the three lights. (b) Determine the value of d so that the resultant of the weights passes through the midpoint of the pipe.

A beam supports three loads of given magnitude and a fourth load whose magnitude is a function of position. If b 5 1.5 m and the loads are to be replaced with a single equivalent force, determine (a) the value of a so that the distance from support A to the line of action of the equivalent force is maximum, (b) the magnitude of the equivalent force and its point of application on the beam.

A 6 3 12-in. plate is subjected to four loads as shown. Find the resultant of the four loads and the two points at which the line of action of the resultant intersects the edge of the plate.

A 32-lb motor is mounted on the floor. Find the resultant of the weight and the forces exerted on the belt, and determine where the line of action of the resultant intersects the floor.

Solve Prob. 3.110, assuming that P 5 138 N.

Pulleys A and B are mounted on bracket CDEF. The tension on each side of the two belts is as shown. Replace the four forces with a single equivalent force, and determine where its line of action inter- sects the bottom edge of the bracket.

truss supports the loading shown. Determine the equivalent force acting on the truss and the point of intersection of its line of action with a line drawn through points A and G.

A couple of magnitude M 5 80 lb?in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resul- tant intersects line AB and line BC.

A couple M and the three forces shown are applied to an angle bracket. Find the moment of the couple if the line of action of the resultant of the force system is to pass through (a) point A, (b) point B, (c) point C.

A machine component is subjected to the forces and couples shown. The component is to be held in place by a single rivet that can resist a force but not a couple. For P 5 0, determine the location of the rivet hole if it is to be located (a) on line FG, (b) on line GH.

Solve Prob. 3.116, assuming that P 5 60 N.

As follower AB rolls along the surface of member C, it exerts a constant force F perpendicular to the surface. (a) Replace F with an equivalent force-couple system at the point D obtained by drawing the perpendicular from the point of contact to the x axis. (b) For a 5 1 m and b 5 2 m, determine the value of x for which the moment of the equivalent force-couple system at D is maximum.

A machine component is subjected to the forces shown, each of which is parallel to one of the coordinate axes. Replace these forces with an equivalent force-couple system at A.

As an adjustable brace BC is used to bring a wall into plumb, the force-couple system shown is exerted on the wall. Replace this force- couple system with an equivalent force-couple system at A if R 5 21.2 lb and M 5 13.25 lb?ft.

In order to unscrew the tapped faucet A, a plumber uses two pipe wrenches as shown. By exerting a 40-lb force on each wrench at a distance of 10 in. from the axis of the pipe and in a direction per- pendicular to the pipe and to the wrench, he prevents the pipe from rotating, and thus he avoids loosening or further tightening the joint between the pipe and the tapped elbow C. Determine (a) the angle that the wrench at A should form with the vertical if elbow C is not to rotate about the vertical, (b) the force-couple system at C equiva- lent to the two 40-lb forces when this condition is satisfied.

Assuming 5 60 in Prob. 3.122, replace the two 40-lb forces with an equivalent force-couple system at D and determine whether the plumbers action tends to tighten or loosen the joint between (a) pipe CD and elbow D, (b) elbow D and pipe DE. Assume all threads to be right-handed.

Four forces are applied to the machine component ABDE as shown. Replace these forces with an equivalent force-couple system at A.

A blade held in a brace is used to tighten a screw at A. (a) Determine the forces exerted at B and C, knowing that these forces are equiva- lent to a force-couple system at A consisting of R 5 2(25 N)i 1 Ry j 1 Rzk and MR A 5 2(13.5 N?m)i. (b) Find the corresponding values of Ry and Rz. (c) What is the orientation of the slot in the head of the screw for which the blade is least likely to slip when the brace is in the position shown?

A mechanic uses a crowfoot wrench to loosen a bolt at C. The mechanic holds the socket wrench handle at points A and B and applies forces at these points. Knowing that these forces are equiva- lent to a force-couple system at C consisting of the force C 5 2(8 lb)i 1 (4 lb)k and the couple MC 5 (360 lb?in.)i, determine the forces applied at A and at B when Az 5 2 lb.

Three children are standing on a 5 3 5-m raft. If the weights of the children at points A, B, and C are 375 N, 260 N, and 400 N, respec- tively, determine the magnitude and the point of application of the resultant of the three weights.

Three children are standing on a 5 3 5-m raft. The weights of the children at points A, B, and C are 375 N, 260 N, and 400 N, respec- tively. If a fourth child weighing 425 N climbs onto the raft, deter- mine where she should stand if the other children remain in the positions shown and if the line of action of the resultant of the four weights is to pass through the center of the raft.

Four signs are mounted on a frame spanning a highway, and the magnitudes of the horizontal wind forces acting on the signs are as shown. Determine the magnitude and the point of application of the resultant of the four wind forces when a 5 1 ft and b 5 12 ft.

A concrete foundation mat of 5-m radius supports four equally spaced columns, each of which is located 4 m from the center of the mat. Determine the magnitude and the point of application of the resultant of the four loads.

Determine the magnitude and the point of application of the smallest additional load that must be applied to the foundation mat of Prob. 3.131 if the resultant of the five loads is to pass through the center of the mat.

Three forces of the same magnitude P act on a cube of side a as shown. Replace the three forces with an equivalent wrench and deter- mine (a) the magnitude and direction of the resultant force R, (b) the pitch of the wrench, (c) the axis of the wrench.

A piece of sheet metal is bent into the shape shown and is acted upon by three forces. If the forces have the same magnitude P, replace them with an equivalent wrench and determine (a) the mag- nitude and the direction of the resultant force R, (b) the pitch of the wrench, (c) the axis of the wrench.

The forces and couples shown are applied to two screws as a piece of sheet metal is fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz plane.

"The forces and couples shown are applied to two screws as a piece of sheet metal is fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz plane."

Two bolts at A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine (a) the resultant R, (b) the pitch of the single equivalent wrench, (c) the point where the axis of the wrench intersects the xz plane.

Two bolts at A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine (a) the resultant R, (b) the pitch of the single equivalent wrench, (c) the point where the axis of the wrench intersects the xz plane.

Two ropes attached at A and B are used to move the trunk of a fallen tree. Replace the forces exerted by the ropes with an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the yz plane.

Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz plane. If it cannot be reduced, replace the given system with an equivalent wrench and determine its resultant, its pitch, and the point where its axis intersects the yz plane.

Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz plane. If it cannot be reduced, replace the given system with an equivalent wrench and determine its resultant, its pitch, and the point where its axis intersects the yz plane.

Replace the wrench shown with an equivalent system consisting of two forces perpendicular to the y axis and applied respectively at A and B.

Show that, in general, a wrench can be replaced with two forces chosen in such a way that one force passes through a given point while the other force lies in a given plane.

Show that a wrench can be replaced with two perpendicular forces, one of which is applied at a given point.

Show that a wrench can be replaced with two forces, one of which has a prescribed line of action.

A 300-N force P is applied at point A of the bell crank shown. (a) Compute the moment of the force P about O by resolving it into horizontal and vertical components. (b) Using the result of part a, determine the perpendicular distance from O to the line of action of P.

A winch puller AB is used to straighten a fence post. Knowing that the tension in cable BC is 1040 N and length d is 1.90 m, determine the moment about D of the force exerted by the cable at C by resolv- ing that force into horizontal and vertical components applied (a) at point C, (b) at point E.

A small boat hangs from two davits, one of which is shown in the figure. The tension in line ABAD is 82 lb. Determine the moment about C of the resultant force RA exerted on the davit at A.

A single force P acts at C in a direction perpendicular to the handle BC of the crank shown. Determine the moment Mx of P about the x axis when 5 65, knowing that My 5 215 N?m and Mz 5 236 N?m.

A small boat hangs from two davits, one of which is shown in the figure. It is known that the moment about the z axis of the resul- tant force RA exerted on the davit at A must not exceed 279 lb?ft in absolute value. Determine the largest allowable tension in line ABAD when x 5 6 ft.

In a manufacturing operation, three holes are drilled simultaneously in a workpiece. If the holes are perpendicular to the surfaces of the workpiece, replace the couples applied to the drills with a single equivalent couple, specifying its magnitude and the direction of its axis.

A 260-lb force is applied at A to the rolled-steel section shown. Replace that force with an equivalent force-couple system at the center C of the section.

The force and couple shown are to be replaced by an equivalent single force. Knowing that P 5 2Q, determine the required value of if the line of action of the single equivalent force is to pass through (a) point A, (b) point C.

A 77-N force F1 and a 31-N?m couple M1 are applied to corner E of the bent plate shown. If F1 and M1 are to be replaced with an equiva- lent force-couple system (F2, M2) at corner B and if (M2)z 5 0, determine (a) the distance d, (b) F2 and M2.

Three horizontal forces are applied as shown to a vertical cast-iron arm. Determine the resultant of the forces and the distance from the ground to its line of action when (a) P 5 200 N, (b) P 5 2400 N, (c) P 5 1000 N.

While using a pencil sharpener, a student applies the forces and couple shown. (a) Determine the forces exerted at B and C know- ing that these forces and the couple are equivalent to a force-couple system at A consisting of the force R 5 (2.6 lb)i 1 Ry j 2 (0.7 lb)k and the couple MR A 5 Mxi 1 (1.0 lb?ft)j 2 (0.72 lb?ft)k. (b) Find the corresponding values of Ry and Mx.