Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 3, Problem 3.153RP
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.
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Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x axis.Replace the couples applied to the shafts by a single equivalent couple, specifying its magnitude and the direction of its axis.
Replace the two couples shown by a single equivalent couple.
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 and Dynamics
Ch. 3.1 - 3.1 A crate of mass 80 kg is held in the position...Ch. 3.1 - 3.2 A crate of mass 80 kg is held in the position...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 - 3.6 A 20-lb force is applied to the control rod AB...Ch. 3.1 - 3.7 A 20-lb force is applied to the control rod AB...Ch. 3.1 - Prob. 3.8PCh. 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 - Prob. 3.15PCh. 3.1 - Prob. 3.16PCh. 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 - Prob. 3.24PCh. 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 - 3.28 In Prob. 3.24, determine the perpendicular...Ch. 3.1 - 3.29 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 - 3.35 Given the vectors P = 2i + 3j − k, Q = 5i −...Ch. 3.2 - Form the scalar product B C and use the result...Ch. 3.2 - 3.37 Three cables are used to support a container...Ch. 3.2 - 3.38 Three cables are used to support a container...Ch. 3.2 - Knowing that the tension in cable AC is 280 lb,...Ch. 3.2 - Prob. 3.40PCh. 3.2 - Ropes AB and BC are two of the ropes used to...Ch. 3.2 - Prob. 3.42PCh. 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 - 3.45 Determine the volume of the parallelepiped of...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 - Prob. 3.51PCh. 3.2 - 3.52 To lift a heavy crate, a man uses a block and...Ch. 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 - Prob. 3.55PCh. 3.2 - Prob. 3.56PCh. 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 - A regular tetrahedron has six edges of length a. A...Ch. 3.2 - Prob. 3.62PCh. 3.2 - Prob. 3.63PCh. 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 - Prob. 3.71PCh. 3.3 - Prob. 3.72PCh. 3.3 - Four pegs of the same diameter are attached to a...Ch. 3.3 - Prob. 3.74PCh. 3.3 - Prob. 3.75PCh. 3.3 - If P = 0 in the figure, replace the two remaining...Ch. 3.3 - 3.77If P = 20 lb in the figure, replace the three...Ch. 3.3 - Prob. 3.78PCh. 3.3 - Prob. 3.79PCh. 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 - Prob. 3.82PCh. 3.3 - Prob. 3.83PCh. 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 - 3.88 A force and a couple are applied as shown to...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 - Prob. 3.92PCh. 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 - Prob. 3.95PCh. 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 - Prob. 3.98PCh. 3.3 - 3.99 An antenna is guyed by three cables as shown....Ch. 3.3 - Prob. 3.100PCh. 3.4 - Prob. 3.101PCh. 3.4 - Prob. 3.102PCh. 3.4 - 3.103 Determine the single equivalent force and...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 - 3.109 A 32-lb motor is mounted on the floor. Find...Ch. 3.4 - To test the strength of a 625 500-mm suitcase,...Ch. 3.4 - 3.111 Solve Prob. 3.110, assuming that P = 138...Ch. 3.4 - Prob. 3.112PCh. 3.4 - 3.113 A truss supports the loading shown....Ch. 3.4 - Prob. 3.114PCh. 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 - Prob. 3.117PCh. 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 - Prob. 3.123PCh. 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 - Prob. 3.129PCh. 3.4 - Prob. 3.130PCh. 3.4 - A concrete foundation mat of 5-m radius supports...Ch. 3.4 - Prob. 3.132PCh. 3.4 - Three forces of the same magnitude P act on a cube...Ch. 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 - Prob. 3.140PCh. 3.4 - Prob. 3.141PCh. 3.4 - Prob. 3.142PCh. 3.4 - Replace the wrench shown with an equivalent system...Ch. 3.4 - Prob. 3.144PCh. 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 - 3.152 A small boat hangs from two davits, one of...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 - The force and couple shown are to be replaced by...Ch. 3 - Prob. 3.156RPCh. 3 - Prob. 3.157RPCh. 3 - While using a pencil sharpener, a student applies...
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- Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x axis. Replace the couples applied to the shafts by a single equivalent couple, specifying its magnitude and the direction of its axis.arrow_forwardReplace the two couples shown by a single equivalent couplearrow_forwardThe indicated force-couple system is applied to a small shaft at the center of the plate. Replace this system by a single force R and specify the coordinate x of the point on the x-axis through which the line of action of this resultant force passes.arrow_forward
- The indicated force-couple system is applied to a small shaft at the center of the plate. Replace this system by a single force R and specify the coordinate x of the point on the x-axis through which the line of action of this resultant force passes.arrow_forwardThe two shafts of a speed-reducer unit are subjected to couples of magnitude M1 =15 lb.ft and M2=3 lb.ft, respectively. Replace the two couples with a single equivalent couple, specifying its magnitude and the direction of its axis.arrow_forwardDetermine 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_forward
- The two shafts of a speed-reducer unit are subjected to couples of magnitude M1 = 15 lb·ft and M2 = 3 lb·ft, respectively. Replace the two couples with a single equivalent couple, specifying its magnitude and the direction of its axis.arrow_forwardThe magnitude of the moment produced by force F about segment AB of the pipe assembly is equal to.arrow_forwardProblem 3. If M = 48000 N-mm, then replace the loading below with an equivalent resultant force and couple moment at point O (i.e., a force-couple system at point O). Express both in Cartesian form. Note: The depiction of M shown is another way to indicate the moment of a force couple rather than a curved arrow. It attempts to illustrate the two forces that make up the couple, without specifying the forces themselves. 150 mm 150 M mm 60° 30° 320 N 160 400 N mmarrow_forward
- Determine the couple-vector that is equivalent to thethree couples acting on the gear box, given that C1 = 200 lb.in, C2 = 140 lb.in, C3= 220 lb.inarrow_forwardThe force-couple system shown acts on a trapezoidal plate. a. Determine the value of M1 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 M1 in this case is 120 kip-in counterclockwise, determine the point of action of the resultant force R along line CD.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_forward
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