Vector Mechanics for Engineers: Statics
12th Edition
ISBN: 9781259977268
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
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Chapter 3.4, Problem 3.141P
3.141 and *3.142 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.
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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.
3. Replace the force couple system at point O by a single force. Specify the coordinate ya of the point on the y-axis through which the line of action of this resultant passes.
Force P and couple M are applied at A as shown.
1. Suppose an equivalent system was made such that only force at B and a couple are present. What gives the magnitude of force at B and the couple in the equivalent system?
2. If the force P and couple M is to be replaced with a single force, where is the point of application of this single force along bar ABCD in order to have the same external effect as the original set of force P and couple M? (How many m to the left or right of B)
Chapter 3 Solutions
Vector Mechanics for Engineers: Statics
Ch. 3.1 - A foot valve for a pneumatic system is hinged at...Ch. 3.1 - 3.2A foot valve for a pneumatic system is hinged...Ch. 3.1 - It is known that a vertical force of 200 lb is...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - An 8-lb force P is applied to a shift lever....Ch. 3.1 - Prob. 3.7PCh. 3.1 - An 11-lb force P is applied to a shift lever. The...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...
Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.11 and 3.12The tailgate of a car is supported by...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - 3.13 and 3.14It is known that the connecting rod...Ch. 3.1 - Form the vector product P1 P2 and use the result...Ch. 3.1 - The vectors P and Q are two adjacent sides of a...Ch. 3.1 - Prob. 3.17PCh. 3.1 - Prob. 3.18PCh. 3.1 - Prob. 3.19PCh. 3.1 - Prob. 3.20PCh. 3.1 - Before the trunk of a large tree is felled, cables...Ch. 3.1 - The 12-ft boom AB has a fixed end A. A steel cable...Ch. 3.1 - A 200-N force is applied as shown to the bracket...Ch. 3.1 - A force P of magnitude 200 N acts along the...Ch. 3.1 - A 6-ft-long fishing rod AB is securely anchored in...Ch. 3.1 - A precast concrete wall section is temporarily...Ch. 3.1 - In Prob. 3.22, determine the perpendicular...Ch. 3.1 - In Prob. 3.23, determine the perpendicular...Ch. 3.1 - In Prob. 3.24, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.25, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - In Prob. 3.26, determine the perpendicular...Ch. 3.1 - Determine the value of a that minimizes the...Ch. 3.2 - Given the vectors P = 2i + j + 2k, Q = 3i + 4j ...Ch. 3.2 - Form the scalar product B C and use the result...Ch. 3.2 - Three cables are attached to the top of the tower...Ch. 3.2 - Prob. 3.38PCh. 3.2 - Knowing that the tension in cable AC is 280 lb,...Ch. 3.2 - Knowing that the tension in cable AD is 180 lb,...Ch. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - The 20-in. tube AB can slide along a horizontal...Ch. 3.2 - Solve Prob. 3.43 for the position corresponding to...Ch. 3.2 - Determine the volume of the parallelepiped of Fig....Ch. 3.2 - Prob. 3.46PCh. 3.2 - A crane is oriented so that the end of the 25-m...Ch. 3.2 - 3.48The 25-m crane boom AO lies in the yz plane....Ch. 3.2 - To loosen a frozen valve, a force F with a...Ch. 3.2 - 3.50When a force F is applied to the handle of the...Ch. 3.2 - The 0.61 1.00-m lid ABCD of a storage bin is...Ch. 3.2 - Prob. 3.52PCh. 3.2 - A farmer uses cables and winch pullers B and E to...Ch. 3.2 - Solve Prob. 3.53 when the tension in cable AB is...Ch. 3.2 - A force P of magnitude 520 lb acts on the frame...Ch. 3.2 - 3.56A force P acts on the frame shown at point E....Ch. 3.2 - The frame ACD is hinged at A and D and is...Ch. 3.2 - In Prob. 3.57, determine the moment about the...Ch. 3.2 - The triangular plate ABC is supported by...Ch. 3.2 - 3.60The triangular plate ABC is supported by...Ch. 3.2 - Prob. 3.61PCh. 3.2 - Prob. 3.62PCh. 3.2 - Two forces F1 and F2 in space have the same...Ch. 3.2 - Prob. 3.64PCh. 3.2 - Prob. 3.65PCh. 3.2 - In Prob. 3.57, determine the perpendicular...Ch. 3.2 - In Prob. 3.58, determine the perpendicular...Ch. 3.2 - In Prob. 3.59, determine the perpendicular...Ch. 3.2 - In Prob. 3.60, determine the perpendicular...Ch. 3.3 - Two 80-N forces are applied as shown to the...Ch. 3.3 - Two parallel 60-N forces are applied as shown to...Ch. 3.3 - A multiple-drilling machine is used to drill...Ch. 3.3 - Four pegs of the same diameter are attached to a...Ch. 3.3 - A piece of plywood in which several holes are...Ch. 3.3 - The shafts of an angle drive are acted upon by the...Ch. 3.3 - Prob. 3.76PCh. 3.3 - 3.77If P = 20 lb in the figure, replace the three...Ch. 3.3 - The two couples shown are to be replaced with a...Ch. 3.3 - Solve part a of Prob. 3.78, assuming that two 15-N...Ch. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - A 500-N force is applied to a bent plate as shown....Ch. 3.3 - A crane column supports a 16-kip load as shown....Ch. 3.3 - A dirigible is tethered by a cable attached to its...Ch. 3.3 - A 30-lb vertical force P is applied at A to the...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - A worker tries to move a rock by applying a 360-N...Ch. 3.3 - The shearing forces exerted on the cross section...Ch. 3.3 - Knowing that = 60, replace the force and couple...Ch. 3.3 - Three control rods attached to a lever ABC exert...Ch. 3.3 - A rectangular plate is acted upon by the force and...Ch. 3.3 - While tapping a hole, a machinist applies the...Ch. 3.3 - A hexagonal plate is acted upon by the force P and...Ch. 3.3 - Replace the 250-kN force P with an equivalent...Ch. 3.3 - A 2.6-kip force is applied at point D of the...Ch. 3.3 - Replace the 150-N force with an equivalent...Ch. 3.3 - To keep a door closed, a wooden stick is wedged...Ch. 3.3 - A 46-lb force F and a 2120-lbin. couple M are...Ch. 3.3 - A 110-N force acting in a vertical plane parallel...Ch. 3.3 - The 12-ft boom AB has a fixed end A, and the...Ch. 3.3 - The jib crane shown is oriented so that its boom...Ch. 3.4 - 3.101A 4-m-long beam is subjected to a variety of...Ch. 3.4 - Prob. 3.102PCh. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - Five separate force-couple systems act at the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Three stage lights are mounted on a pipe as shown....Ch. 3.4 - A beam supports three loads of given magnitude and...Ch. 3.4 - A 6 12-in. plate is subjected to four loads as...Ch. 3.4 - Gear C is rigidly attached to arm AB. If the...Ch. 3.4 - To test the strength of a 625 500-mm suitcase,...Ch. 3.4 - Two cables exert forces of 90 kN each on a truss...Ch. 3.4 - Pulleys A and B are mounted on bracket CDEF. The...Ch. 3.4 - The roof of a building frame is subjected to the...Ch. 3.4 - A couple of magnitude M = 80 lbin. and the three...Ch. 3.4 - A couple M and the three forces shown are applied...Ch. 3.4 - A machine component is subjected to the forces and...Ch. 3.4 - Solve Prob. 3.116, assuming that P = 60 N.Ch. 3.4 - As follower AB rolls along the surface of member...Ch. 3.4 - A machine component is subjected to the forces...Ch. 3.4 - Two 150-mm-diameter pulleys are mounted on line...Ch. 3.4 - As an adjustable brace BC is used to bring a wall...Ch. 3.4 - In order to unscrew the tapped faucet A, a plumber...Ch. 3.4 - Assuming = 60 in Prob. 3.122, replace the two...Ch. 3.4 - Four forces are applied to the machine component...Ch. 3.4 - A blade held in a brace is used to tighten a screw...Ch. 3.4 - A mechanic uses a crowfoot wrench to loosen a bolt...Ch. 3.4 - Prob. 3.127PCh. 3.4 - Prob. 3.128PCh. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 3.130PCh. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Determine the magnitude and the point of...Ch. 3.4 - Prob. 3.133PCh. 3.4 - A piece of sheet metal is bent into the shape...Ch. 3.4 - Prob. 3.135PCh. 3.4 - Prob. 3.136PCh. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Two bolts at A and B are tightened by applying the...Ch. 3.4 - Prob. 3.139PCh. 3.4 - A flagpole is guyed by three cables. If the...Ch. 3.4 - 3.141 and 3.142Determine whether the...Ch. 3.4 - 3.141 and 3.142Determine whether the...Ch. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Show that, in general, a wrench can be replaced...Ch. 3.4 - Show that a wrench can be replaced with two...Ch. 3.4 - Show that a wrench can be replaced with two...Ch. 3 - A 300-N force P is applied at point A of the bell...Ch. 3 - A winch puller AB is used to straighten a fence...Ch. 3 - A small boat hangs from two davits, one of which...Ch. 3 - Prob. 3.150RPCh. 3 - A single force P acts at C in a direction...Ch. 3 - The 23-in. vertical rod CD is welded to the...Ch. 3 - In a manufacturing operation, three holes are...Ch. 3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3 - Prob. 3.155RPCh. 3 - A 77-N force F1 and a 31-Nm couple M1 are applied...Ch. 3 - Three horizontal forces are applied as shown to a...Ch. 3 - While using a pencil sharpener, a student applies...
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- 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.arrow_forward1. Replace the assigned forces by a single force R at the rotation axis O.Determine:(a) the corresponding magnitude of R(b) the angle of R with respect to x-axis(c) the rotation of couple M2. from your answer above replace the force couple system by a single force.(a) Transmit the “tail” of the resultant R in the x-axis and determine the distance from tail to point O.(b) Transmit the “tail” of the resultant R in the y-axis and determine the distance from tail to point O. SOLVE F2=2N, F3=3N, F6=6N, F8=8N --> FORCE DEGREE: a=10, b=20, c=25, d=30 REFER TO THE IMAGE FIGUREarrow_forward1. Replace the assigned forces by a single force R at the rotation axis O.Determine:(a) the corresponding magnitude of R(b) the angle of R with respect to x-axis(c) the rotation of couple M2. from your answer above replace the force couple system by a single force.(a) Transmit the “tail” of the resultant R in the x-axis and determine the distance from tail to point O.(b) Transmit the “tail” of the resultant R in the y-axis and determine the distance from tail to point O. FORCES: F2=2N, F3=3N, F6=6N, F8=8N DEGREE: B=20, C=25 REFER TO THE IMAGEarrow_forward
- 5 3.67 Replace the coplanar force system that acts on the casting with an equiva- lent force-couple system, with the force acting at (a) point O: and (b) point A. 90 lb 2.5 ft 150 lb 800 lb-ft 3 ft 200 lbarrow_forwardDetermine the force-couple system, with the force acting at point O, that is equivalent to the force and couple acting on the arm CD of the industrial robot. Note that the arm ABCD lies in a vertical plane that is inclined at 40◦ to the yz-plane; the arm CD makes an angle of 30◦ with the vertical.arrow_forward4. Reduce the given loading system to a force-couple system at point A. Then determine the distance x to the right of point A at which the resultant of the three forces acts. gON 72ON 200mm 500 mm 450 mm 1200Narrow_forward
- (a) Replace the force system shown with a force-couple system with the force acting at point O. (b) Determine the wrench that is equivalent to this force system. Find the coordinates of the point where the axis of the wrench crosses the xy-plane. 200 lb 5 ft 250 lb 300 lb 2 ft- 300 lb 200 lbarrow_forwardPROBLEM 3 The force-couple system shown acts on a trapezoidal plate. a. Determine the value of M, if the system shown is equivalent to a single force acting at point C. b. The system shown is equivalent to a force-couple system consisting of R and M2 = 3000 kip-in clockwise. If M, in this case is 120 kip-in counterclockwise, determine the point of action of the resultant force Ralong line CD. 50° 1YZ kips 10 in 1X in 10 in A |20 kips 35 kips 8x kips 2Y in M, 50° 1YZ kips C D Parameters X = 4, Y = 8, Z = 7 1X in 13 in 2Y in 24 in 8X kips 83 kips 145 kips 1YZ kips 18 inarrow_forward3. Determine the equivalent single force of the shown system of forces and couples. Determine and draw its line of action on the x-y plane. F₁ = 20 lb 3 ft 4 ft F2=10 lb 5 ft M₂=100 lb-ft -3 ft- F3 = 50 lb M₁ = 170 lb-ft Xarrow_forward
- 6 in. 6 in. 160 lb-in. 18 in. B 30 lb 34 lb H 18 in. 12 in. D 6 in. 8 in. in. 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, its pitch, and the point where its axis intersects the yz-plane.arrow_forwardQ4: Determine the force-couple system at O which is equivalent to the two forces applied to the bracket. 150 mm 200 mm 1.6 kN 2.4 kN 200 mmarrow_forwardthe force and a couple are applied to the beam in an attempt to lift it. replace this force system by an equivalent force-couple system with the force acting at (a) point A; and (b) pointBarrow_forward
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