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engineering
engineering mechanics statics 15th

Engineering Mechanics Statics 15th Edition Russell C. Hibbeler - Solutions

The power line is supported at A by the tower. If the cable weighs 0.75 lb/ft, determine the total length of the cable, BAC. Set s = 3 ft. B A 7 ft
The crate has a weight of 550 lb. Determine the force in each supporting cable. B 30 D
The members of a truss are pin connected at joint O. Determine the magnitude of and its angle θ for equilibrium. Set F2 = 6 kN. 5 kN 7 kN 5 30° y 70° 0 F₁ F₂ ·X
Knowing the forces in members A and C, determine the forces FB and FD acting on members B and D that are required for equilibrium. The force system is concurrent at point O. FD 2 kN C D 45° A 4 kN 60° B FB
If the 5-kg block is suspended from the pulley B and the sag of the cord is d = 0.15 m. determine the force in cord ABC. Neglect the size of the pulley. 0.4 m B D C 0.15 m
The beam has a weight of 700 1h. Determine the shortest cable ABC that can be used to lift it if the maximum force the cable can sustain is 1500 lb. B -10 ft- of
The block has a mass of 5 kg and rests on a smooth plane. Determine the upstretched length of the spring. k= 200 N/m 45° 0.3 m 0.4 m
If the mass of cylinder C is 40 kg, determine the mass of cylinder A in order to hold the assembly in the position shown. D A E 30° Ho B 40 kg
Determine the maximum weight W that can be supported in the position shown if each chain AC and AB can support a maximum tension of 600 lb before it fails. B 12 13 A 30%
The man attempts to pull down the tree using the cable and small pulley arrangement shown. If the tension in AB is 60 lb determine the tension in cable CAD and the angle θ that the cable makes at the pulley. D 0 20° 30°
Determine the normal force, shear force, and moment in the shaft at points B and D. These points lie just to the right of the 150-lb force and the bearing at C, respectively. There is a thrust bearing at A and a journal bearing at C. A -15 in.. 150 lb B 15 in.. 75 lb 10 in..
The structural connections transmit the loads shown to the column. Determine the normal force, shear force, and moment acting in the column at a section passing horizontally through point A. 30 mm 16 kN -250 mm A 125 mm 40 mm 6 kN 23 kN 185 mm 6 kN
The pliers are used to grip the tube at B. If a force of 20 lb is applied to the handles, determine the shear force and moment at point C. Assume the jaws of the pliers exert only normal forces on the tube.zzz 20 lb 20 lb 10 in. -40° Cecco 0.5 in. C 1 in. B
The beam-column is fixed to the floor and supports the load shown. Determine the normal force, shear force, and moment at points A and B. 5 kN 0.6 m 0.2 m 2m A B 0.8 kN. m 2.5 kN 0.4 m
Determine the shear and moment as a function of x,and then draw the shear and moment diagrams. РА -3m- Prob. F7-7 6 kN
Determine the distance a as a fraction of the beam’s length L for locating the roller support so that the moment in the beam at B is zero. P -L- P B -L3-
Determine the shear and moment as a function of x, and then draw the shear and moment diagrams. 15 kN.m 2 kN/m 3 m Prob. F7-8 A
Determine the shear and moment as a function of x, and then draw the shear and moment diagrams. A 6 m- Prob. F7-10 12 kN-m
The cable will fail when subjected to a tension of 2 kN. Determine the largest vertical load P the frame will and calculate the normal force, shear force, and moment at point C for this loading. P 0.1 m -0.75 m- 0.5 m -0.75 m- C -0.75 m- B A
Determine the normal force, shear force, and moment acting at point C. Al 8 kN 18 kN m 1.25 m 5 kN/m 0.75 m C -0.5 m B
Determine the normal force, shear force, and moment at point C. Take P = 8 kN. P 0.1 m -0.75 m- 0.5 m -0.75 m- C -0.75 m- B A
Determine the normal force, shear force, and moment at points F and E. A 3 ft E 2 ft B 50 lb/ft 6 ft C + 4 ft F D 2 ft
The cantilevered rack is used to support each end of a smooth pipe that has a total weight of 300 lb. Determine the normal force, shear force, and moment that act in the arm at its fixed support A along a vertical section. 6 in. A В 30°
The 9-kip force is supported by the floor panel DE, which in turn is simply supported at its ends by floor beams. These beams transmit their loads to the girder AB. Determine the shear and moment acting at point C in the girder. A 6 ft-6 ft- 6 ft- -8 ft- с. D 9 kip 2 ft -24 ft -4 ft--6 ft- E B
Determine the normal force, shear force, and moment in the beam at points C and D. The beam is supported at A and B. 4 kip 3 ft C 250 lb/ft -4 ft4 ft- A -6 ft D 4 ft B
Rod AB is fixed to a smooth collar D, which slides freely along the vertical guide. Determine the normal force, shear force, and moment at point C, which is located just to the left of the 60-lb concentrated load. 4 ft A B 1.5 ft F 1.5 ft 1.5 ft 1.5 ft C E D 0.4 ft
Determine the normal force, shear force, and moment at points E and F of the compound beam. Point E is located just to the left of 800-N force. A 800 N E -1.5 m-1 1200 N 4 5 3 B m2 m- 400 N/m \F -1 m1.5 m 1.5 m- D
Determine the normal force, shear force, and moment at point C of the beam. 200 N/m -3m IC -3 m- 400 N/m B
Determine the shear force and moment acting at point D of the beam. - 6 ft- 9 ft D 2 kip/ft 9 ft- B
Determine the shear force and moment acting at point C of the beam. For the calculation use Simpson’s rule to evaluate the integrals. W 2 kip/ft Α' W = 1/2 (2x³ +√√x + 4) 2 ft C 2 ft 11.58 kip/ft B X
Determine the distance a in terms of the beam’s length L between the symmetrically placed supports A and B so that the moment at the center of the beam is zero. Wo A- ㅏ을 a -L- 을이 B Wo
Determine the normal force, shear force, and moment in the beam at points D and E. Point E is just to the right of the 3-kip load. -6 ft- D 1.5 kip/ft -6 ft- B 4 ft 3 kip E C -4 ft- Ab
Determine the angle θ at which the 500-N force must act at A so that the moment of this force about point B is equal to zero. Im B 2 m- 10.3 E 500 N
Determine the tension developed in cables AB. AC. nd AD. F₂ = 450 N 45° F₁ = 300 N 3 Prob. F2-7 F3 = 600 N
Determine the moment of each of the three forces about point A. F₁=250 N 30% A -2 m- -3 m B F₂ = 300 N 60° 4'm 5 F3 = 500 N
Determine the force in cables AB and AC necessary to support the 12-kg traffic light. г 25 24 12° B
Determine the moment of each of the three forces about point B. F₁ = 250 N 30% A -2 m -3 mr B F2₂ = 300 N 60° 4 m F3 = 500 N
The man exerts the wo forces on the handle of the shovel. Determine the resultant moment of these forces about the blade at A. 800 mm 65° 450 mm F = 12 N F = 30 N 30⁰ 20°
If FB = 30 and Fc = 45 Ib determine the resultant moment about the bolt located at A. 2.5 ft 20⁰ FB 0.75 ft 30° Fc
Friction on the concrete surface creates a couple moments of Mo = 100 N · m on the blades of the trowel. Determine the magnitude of the couple forces so that the resultant couple moment on the trowel is zero. The forces lie in a horizontal plane and act perpendicular to the handle of the trowel.
Two forces act on the skew caster. Determine the resultant moment of these forces about point A and about point B. 1.25 in. 2.5 in. 60 80 lb B 10 lb 2 in.
The cable exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If θ = 30°, determine the placement x of the hook at B so that this force creates a maximum moment about point O. What is this moment? A P = 6 kN B 8m I'm O
Determine the moment of the force F about point O. Express the result as a Cartesian vector. F = (-6i+4j+ 8k) kN 6 m X -2 m- N 4 m 1m P 3 m
If F₁ = {100i-120j +75k} lb and F₂ = {-200i+250j + 100k} lb, determine the resultant momentproduced by these forces about point O. Express the resultas a Cartesian vector. 3 ft 4 ft 5 ft F₂ -y
The cable exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If x = 10 m, determine the position θ of the boom so that this force creates a maximum moment about point O. What is this moment? A P = 6 kN B 8m -x- 1'm OR m
Two men exert forces of F = 80 Ib and P = 50 Ib on the ropes. Determine the moment of each force about A. Which way will the pole rotate, clockwise or counterclockwise? 12 ft 6 ft A C
Determine the orientation θ (0° < θ < 180°) of the 40-lb force F so that it produces (a) The maximum moment about point A (b) No moment about point A. Find the moment in case (a). 8 ft- 2 ft
If the man at B exerts a force of p = 30 Ib on his rope, determine the magnitude of the force F the man at C must exert to prevent the pole from rotating, i.e., so the resultant moment about A of both forces is zero. 12 ft A 6 ft
The handle of the hammer is subjected to the force of F = 20 Ib Determine the moment of this force about the point A. 18 in. 30° 5 in. B
A force of 80 N acts on the handle of the paper cutter at A. Determine the moment created by this force about the hinge at O, if θ = 60° At what angle θ should the force be applied so that the moment it creates about point O is a maximum (clockwise)? What is this maximum moment? F=80 N. 400
If the tension in the belt is 52 lb, determine the moment of each of these forces about the pin at A. 8 in. A 30º 20 -5 in.- F₁ = 52 lb 6 in. MAFU F₂ = 52 lb
The tower crane is used to hoist a 2-Mg load upward at constant velocity. The 1.5-Mg jib BD and 0.5-Mg jib BC have centers of mass at G1 and G2, respectively. Determine the required mass of the counterweight C so that the resultant moment produced by the load and the weight of the tower crane jibs
Determine the moment of the force F about point A as a function of θ. Plot the result of M (ordinate) versus θ (abscissa) for 0° < θ < 180°. 8 ft- 2 ft F = 40 lb
In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 500 lb·in. about point A. Determine the required magnitude of force F. 18 in. 30° 5 in. B
The force F = {400i - 100j - 700k} lb acts at the end of the beam. Determine the moment of this force about point O. 1.5 ft X B -0.25 ft F 8 ft
Determine the magnitude of F so that the resultantcouple moment acting on the beam is 1.5 kN · m clockwise. FA 0.9 m 2 kN Prob. F4-22 B -F 0.3 m 2 kN
The force F = {400i - 100j - 700} Ib acts at the end of the beam. Determine the moment of this force about point A. T 1.5 ft B -0.25 ft 8 ft N
Determine the couple moment acting on the pipeassembly and express the result as a Cartesian vector. x B FA = 450 N 0.4 m 35 4 5 0.3 m 0 FB = 450 N C
Determine the smallest force F that must be applied to the rope in order to create a moment of M = 900 N · m at point O. x B 1.5 m m F A 10.5 m
Determine the moment of the force F about point P. Express the result as a Cartesian vector. F = (-6i+4j+ 8k) kN 6 m x A -2 m- O N 4 m 1m P 3 m
If F = {550i + 60j + 30k} lb, determine the magnitude and coordinate direction angles of the moment of F about point A. 1 ft, z A -2 ft- 3 ft 45° B -y
The man pulls on the rope with a force of F = 20 N. Determine the moment of this force about the base of the pole at O. Solve the problem two ways, i.e., by using a position vector from O to A, then O to B. B 1.5 m F A 4 m 10.5 m 19
Determine the coordinate direction angles of the force F applied at the end of the pipe such that the moment of F about point A is zero. 1 ft -A -2 ft- 3 ft 45° B F
Given the three nonzero vectors A, B, and C, show that if ,A · (B X C) = 0 the three vectors must lie in the same plane.
Determine the moment of the force F about point P. Express the result as a Cartesian vector. P X 2 m -3 m- 0 3 m- T A 1 m F = {2i + 4j6k) kN 3 m
Determine the moment of the force F about the door hinge at B. Express the result as a Cartesian vector. 45° 7 ft F = 80 lb 3 ft X B Z 1.5 ft 5 ft y 4 ft 1.5 ft D
Determine the moment of the force of F = 600 N about point A. X 6 m B 45⁰ 4 m F N A 4 m 6 m
Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has a radius of 5 ft, to fail at the support C. This requires a moment of M = 80 Ib to be developed at C. X 5 ft -7 ft Z 60° 5 ft B A 60 lb 6 ft
Determine the smallest force F that must be applied along the rope in order to develop a moment of M = 1500 N · m at A. x 6 m B 45° 4 m F C A 4m 6 m- y
The curved rod has a radius of 4 ft. If the cable AB exerts a force of 80 lb on the rod, determine the moment of this force about point C. Solve the problem by using two different position vectors. F = 80 lb/ x B Z 4 ft 4 ft -C y
The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point A. x 200 mm 30° N F = 80 N 400 mm 40° 250 mm 300 mm 200 mm y
The curved rod has a radius of 5 ft. If a force of 60 lb acts at its end as shown, determine the moment of this force about point C. 5 ft -7 ft C 60° 5 ft B 60 lb 6 ft
The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point B. + 200 mm 30° N F = 80 N 400 mm 40° 250 mm 300 mm 200 mm y
A force of F = {6i - 2j + 1k} k · N produces a moment MO = {4i + 5j - 14k} of about the origin of coordinates, point O. If the force acts at a point having an x coordinate of x = 1 m, determine the y and z coordinates. Mo X Z y N F 1 m
The force F = {6i + 8j + 10k} creates a moment about point O of MO = {-14i + 8j + 2k} N · m. If the force passes through a point having an x coordinate of 1 m, determine the y and z coordinates of the point. Also, realizing that determine the perpendicular distance d from point and MO in an
The cable exerts a 140-N force on the telephone pole. Determine the moment of this force about point A. Solve the problem using two different position vectors. F = 140 N/ 3 m B Z 6 m 2m -y
Determine the moment of each force acting on the handle of the wrench about the z-axis. Take F1 = {-2i + 4j - 8k} lb, F2 = {3i + 2j - 6k} lb. F₁ F₂ B A - 45° 3.5 in. Z 4 in. 6 in.
Determine the moment about point O of each force acting on the pipe assembly. Add these moments and calculate the magnitude and coordinate direction angles of the resultant moment. 0.8 m Z F₁ = {30i + 20j - 30k} N 1.20 m 0.4 m y F₂ (60i 10j 35k) N -
Determine the moment of each force about point A. Add these moments and calculate the magnitude and coordinate direction angles of the resultant moment. X 0.8 m F₁ = {30i+20j - 30k} N A 1.20 m 0.4 m y F₂ (60i 10j - 35k} N =
Determine the resultant moment of the two forces about the Oa axis. Express the result as a Cartesian vector. F₂ = 50 lb 5 ft 30° 0 4 ft- B 30° 45° 120* 6 ft F₁ = 80 lb 60° y
Determine the moment of each force acting on the handle of the wrench about the axis. Take F1 = {-2i + 4j - 8k} Ib, F2 = {3i + 2j - 6k} lb. X F₁. F₂. B 45° 3.5 in. 4 in. 6 in.
The tool is used to shut off gas valves that are difficult to access. If the force F is applied to the handle, determine the component of the moment created about the z axis of the valve. z 0.25 m 30° F = (-60i + 20j + 15k) N 0.4 m y
The A-frame is being hoisted into an upright position by the vertical force of F = 80 lb. Determine the moment of this force about the x axis when the frame is in the position shown. x² x N A 6 ft 30° 15% B 6 ft -y
The Rollerball skate is an in-line tandem skate that uses two large spherical wheels on each skate, rather than traditional wafer-shape wheels. During skating the two forces acting on the wheel of one skate consist of a 78-lb normal force and a 13-lb friction force. Determine the moment of both of
The A-frame is being hoisted into an upright position by the vertical force of F = 80 lb. Determine the moment of this force about the y' axis passing through points A and B when the frame is in the position shown. X'. N A 6 ft 30° 6 ft
The crossbar wrench is used to remove a lug nut from the automobile wheel. The mechanic applies a couple to the wrench such that his hands are a constant distance apart. Is it necessary that a = b in order to produce the most effective turning of the nut? Explain. Also, what is the effect of
The hanger H is used to support the end of the floor beam B. If the loading on the hanger consists of two couples, determine the magnitude of the horizontal forces F and - F so that the resultant couple moment on the hanger is zero. HA B
The cord passing over the two small pegs A and B on the board is subjected to a tension of 10 lb. Determine the minimum tension P and the orientation θ of the cord passing over pegs C and D, so that the resultant couple produced by both cords is 20 lb · in. clockwise. -P 10 lb 30° A 15
If the valve can be opened with a couple moment of 25 N · m within, determine the required magnitude of each couple forces that must be applied to the wheel. F -150 mm-150 mm. F
Replace the loading by an equivalent resultant force and specify its location on the beam, measured from point O. 5 kN/m 6 m 2 kN/m 3m- 4 kN/m
Two couples act on the beam. If the resultant couple is to be zero, determine the magnitudes of P and F, and the distance d between A and B. 60⁰ F 0.2 m A d PA 30° B 1m 300 N 2 m 500 N
Three couple moments act on the pipe assembly. Determine the magnitude of the resultant couple moment if M2 = 50 N and M3 = 35 N · m. M3 0 120⁰° 120° 120° (M₂ M₁= 80 N·m
Three couple moments act on the pipe assembly. Determine the magnitudes of M2 and M3 so that the resultant couple moment is zero. My 0-2 120⁰ 120⁰ 120* M₂ M₁-80N m
Two couples act on the frame. If the resultant couple moment is to be zero, determine the distance d between the 100-lb couple forces. 100 lb -3 ft-+d- 30° 30% 100 Ib 150 Ib -3 ft- B T 4 ft 150 Ib
Two couples act on the frame. If d = 4 ft, determine the resultant couple moment by (a) Summing the moments of the two couples (b) Resolving each force into x and y components and then summing the moments about A of all the force components. -3 ft- 100 lb 30° 30⁰ 100 lb 150 lb. -3
If F = 80N, determine the magnitude and coordinate direction angles of the couple moment. The pipe assembly lies in the x–y plane. X F 3 in. 3 in. 4 in. 10 lb Z -F 10 lb 30° -P 6 in. y
Two couples act on the frame. If d = 6 ft, determine the resultant couple moment by (a) Summing the moments of the two couples (b) Resolving each force into x and y components and then summing the moments about B of all the force components. 100 lb -3 ft- -31-+-а- 30⁰ -30% 100 lb 150
Express the moment of the couple acting on the pipe assembly in Cartesian vector form. What is the magnitude of the couple moment? X Z 3 ft 1.5 ft X 1 ft. 20 lb. B 20 lb 1 ft 2 ft
Determine the magnitude and coordinate direction angles of the resultant couple moment. M₁ = 40 lb-ft 20° 15° X Z M₂ = 30 lb-ft 130° y
Determine the force in each member of the truss.State if the members are in tension or compression. A -4 ft- B D -4 ft- 450 lb 4 ft

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