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physics
mechanics
Vector Mechanics for Engineers Statics and Dynamics 11th edition Ferdinand Beer, E. Russell Johnston Jr., David Mazurek, Phillip Cornwell, Brian Self - Solutions
Rod AB is held in place by the cord AC. Knowing that c = 840 mm and that the moment about B of the force exerted by the cord at point A is 756 N∙m, determine the tension in the cord.
An antenna is guyed by three cables as shown. Knowing that the tension in cable AD is 270 lb, replace the force exerted at A by cable AD 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)(b) (c) (d) (e) (f) (g) (h)
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, (a) Replace each loading with an equivalent force-couple system at end A of the beam.(b) Prob. 3.101b, which of the loadings are
Five separate force-couple systems act at the corners of a piece of sheet metal, which has been bent into the shape shown. Determine which of these systems is equivalent to a force F = (10 lb)i and a couple of moment M = (15 lb ‹… ft)j + (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 = 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
A beam supports three loads of given magnitude and a fourth load whose magnitude is a function of position. If b = 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
A 6 × 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.
To test the strength of a 625 × 500-mm suitcase, forces are applied as shown. If P = 88 N,(a) Determine the resultant of the applied forces,(b) Locate the two points where the line of action of the resultant intersects the edge of the suitcase.
Solve Prob. 3.110, assuming that P = 138 N.Problem 3.110 To test the strength of a 625 × 500-mm suitcase, forces are applied as shown. If P = 88 N,(a) Determine the resultant of the applied forces,(b) Locate the two points where the line of action of the resultant intersects the edge of the
A couple of magnitude M = 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 resultant 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 = 0, determine the location of the rivet hole if it is to be located(a) On line FG,(b) On line GH.
Solve Problem 3.116, assuming that P = 60 N.PROBLEM 3.116 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 = 0, determine the location of the rivet hole if it is to be located(a)
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 Point D obtained by drawing the perpendicular from the point of contact to the x-axis.(b) For a = 1 m and b = 2 m, determine the
Two 150-mm-diameter pulleys are mounted on line shaft AD. The belts at B and C lie in vertical planes parallel to the yz-plane. Replace the belt forces shown 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 = 21.2 lb and M = 13.25 Ib ( 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 perpendicular to the pipe and to the wrench, he prevents the pipe from rotating, and thus avoids
Assuming θ = 60° in Prob. 3.122, replace the two 40-lb forces with an equivalent force-couple system at D and determine whether the plumber's 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.PROBLEM 3.122
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 equivalent to a force-couple system at A consisting of R = −(25 N)i + Ryj + Rzk and MRA = - (13.5 N·m)i.(b) Find the corresponding values of Ry and Rz.(c) What
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 equivalent to a force-couple system at C consisting of the force C = - (8 Ib)i + (4 Ib)k and the couple MC = (360
Three children are standing on a 5 × 5-m raft. If the weights of the children at Points A, B, and C are 375 N, 260 N, and 400 N, respectively, determine the magnitude and the point of application of the resultant of the three weights.
Three children are standing on a 5 × 5-m raft. The weights of the children at Points A, B, and C are 375 N, 260 N, and 400 N, respectively. If a fourth child of weight 425 N climbs onto the raft, determine where she should stand if the other children remain in the positions shown and the line
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 = 1 ft and b = 12 ft.
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 a and b so that the point of application of the resultant of the four forces is at G.
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 by an equivalent wrench and determine(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 magnitude 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
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.
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.
A flagpole is guyed by three cables. If the tensions in the cables have the same magnitude P, replace the forces exerted on the pole 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 xz-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 so reduced, replace the given system with an equivalent wrench and determine its resultant,
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 resolving that force into horizontal and vertical components applied(a) At Point C,(b) At Point E.
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 θ = 65°, knowing that My = −15 N · m and Mz = −36 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 resultant force RA exerted on the davit at A must not exceed 279 lb â‹… ft in absolute value. Determine the largest allowable tension in line ABAD when x = 6 ft.
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 = 2Q, determine the required value of α 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 â‹… m couple M1 are applied to corner E of the bent plate shown. If F1 and M1 are to be replaced with an equivalent force-couple system (F2, M2) at corner B and if (M2)z = 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 = 200 N,(b) P = 2400 N,(c) P = 1000 N.
While using a pencil sharpener, a student applies the forces and couple shown.(a) Determine the forces exerted at B and C knowing that these forces and the couple are equivalent to a force-couple system at A consisting of the force (2.6 lb)i + = Ryj(0.7 lb)k and the couple MRA = Mxi (1.0 lb ·
The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when(a) P = -8i + 4j - 4k and Q = 3i + 3j + 6k,(b) P = 7i - 6j - 3k and Q = -3i + 6j - 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 + 3j - 6k and 5i - 8j - 6k,(b) 4i - 4j + 3k and -3i + 7j - 5k.
A line passes through the points (12 m, 8 m) and (-3 m, -5 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 = 4i − 3j + 5k that acts at a Point A. Assume that the position vector of A is(a) r = 2i + 3j − 4k,(b) r = −8i + 6j − 10k,(c) r = 8i − 6j + 5k.
Determine the moment about the origin O of the force F = 2i + 3j − 4k that acts at a Point A. Assume that the position vector of A is(a) r = 3i − 6j + 5k,(b) r = i − 4j − 2k,(c) r = 4i + 6j − 8k.
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.
A 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. Determine 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.PROBLEM 3.22 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
In Prob. 3.24, determine the perpendicular distance from point O to wire AE.PROBLEM 3.24 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.
In Prob. 3.24, determine the perpendicular distance from point B to wire AE.PROBLEM 3.24 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.
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 α = 10°,(c) The smallest
In Prob. 3.25, determine the perpendicular distance from point A to a line drawn through points B and C.PROBLEM 3.25 A 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. Determine the moment about A of the
In Prob. 3.25, determine the perpendicular distance from point D to a line drawn through points B and C.PROBLEM 3.25 A 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. Determine the moment about A of the
In Prob. 3.26, determine the perpendicular distance from point O to cable BD.PROBLEM 3.26 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. 3.26, determine the perpendicular distance from point C to cable BD.PROBLEM 3.26 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.
Given the vectors P = 2i + 3j - k, Q = 5i - 4j + 3k, and S = -3i + 2j - 5k, compute the scalar products P · Q, P · S, and Q · S?
Knowing that the tension in cable AC is 280 lb, determine(a) The angle between cable AC and the boom AB,(b) Projection on AB of the force exerted by cable AC at point A.
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.
Knowing that the tension in cable AD is 180 lb, determine(a) The angle between cable AD and the boom AB,(b) The projection on AB of the force exerted by cable AD 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 AB is 540 N, determine(a) The angle between rope AB and the stake,(b) The projection on the stake of the force exerted by rope AB 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 = 11 in., determine the angle formed by the two cords(a) Using Eq. (3.32),(b) Applying the law of cosines to triangle ABC.
Solve Prob. 3.43 for the position corresponding to x = 4 in.PROBLEM 3.43 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 = 11 in., determine the angle formed by the two
Determine the volume of the parallelepiped of Fig. 3.25 when(a) P = 4i − 3j + 2k, Q = −2i − 5j + k, and S = 7i + j − k,(b) P = 5i − j + 6k, Q = 2i + 3j + k, and S = −3i − 2j + 4k.
Given the vectors P = 3i - j + k, Q = 4i + Qyj - 2k, and S = 2i - 2j + 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 maximum 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 of magnitude 70 lb is applied to the handle of the valve. Knowing that θ = 25, Mx = - 61 lb ( ft, and Mz = - 43 Ib ( ft, determine φ and 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.
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 â‹… m, determine the distance a.
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 Problem 3.57, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable.PROBLEM 3.57 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
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 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that α = 25°, determine the moment of the force about Point B by resolving the force into horizontal and vertical components.
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 CF at C is 33 N, determine the moment of that force about the line joining Points D and B.
In Prob. 3.55, determine the perpendicular distance between rod AB and the line of action of P.PROBLEM 3.55 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.
In Prob. 3.56, determine the perpendicular distance between rod AB and the line of action of Q.PROBLEM 3.56 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.
In Problem 3.58, determine the perpendicular distance between portion BG of the cable and the diagonal AD.PROBLEM 3.58 In Problem 3.57, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable.PROBLEM 3.57 The frame ACD is hinged at A and D and is
In Problem 3.59, determine the perpendicular distance between cable AE and the line joining Points D and B.PROBLEM 3.59 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,
In Problem 3.60, determine the perpendicular distance between cable CF and the line joining Points D and B.PROBLEM 3.60 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 CF at C is 33 N,
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 α = 25°, determine the moment of the force about Point B by resolving the force into components along AB and in a direction perpendicular to AB.
Two 80-N forces are applied as shown to the corners B and D of a rectangular plate.(a) Determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples.(b) Use the result obtained to
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
Four 1 ½ -in. -diameter pegs are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated.(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
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 resultant couple applied to the board is 1132.5 lb · in. counterclockwise.
If P = 20 lb, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
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.PROBLEM 3.78 Replace the two couples shown with a single equivalent couple, specifying its magnitude and the direction of its axis.
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