To determine Find the magnitude of the couple ( M ) and direction of its axis after replacing the two couples in single equivalent couple. Explanation Given information: The inclined force acting at point B ( F B ) is 50 N. The inclined force acting at point C ( F C ) is 50 N. The force acting at the point E ( F E ) is 12.5 N. The force acting at the point D ( F D ) is 12.5 N. The height between point C and F ( CF ) is 120 mm. The height between point F and A ( FA ) is 120 mm. The horizontal distance between point E and D ( ED ) is 192 mm. The height between point E and B ( EB ) is 144 mm. The distance between point C and D ( CD ) is 160 mm. Calculation: Replace the couple in the ABCD plane with two couple’s P and Q . Show the couple ABCD by replacing with two couple’s P and Q as Figure 1. Calculate the distance CG using the formula: Use Pythagoras theorem, C G = C D 2 + C F 2 Substitute 160 mm for CD and 120 mm for CF. C G = ( 160 ) 2 + ( 120 ) 2 = 200 mm Calculate the force ( P ) acting at the point B using the formula: P = F B C D C G Substitute 50 N for F B , 160 mm for CD and 200 mm for CG . P = 50 ( 160 200 ) = 40 N Calculate the force ( Q ) acting at the point C using the formula: Q = F C C F C G Substitute 50 N for F C , 120 mm for CF and 200 mm for CG . Q = 50 ( 120 200 ) = 30 N Show the axis by showing the moments and angle acting as Figure 2. Calculate the angle ( θ ) using the relation: tan θ = E B E D Substitute 144 mm for EB and 192 mm for ED . tan θ = 144 192 θ = tan − 1 ( 0.75 ) = 36.87 ° Calculate the couple vector ( M 1 ) perpendicular to plane ABCD using the relation: M 1 = [ P × ( C F + F A ) ] − [ Q ( C D ) ] Substitute 40 N for P , 120 mm for CF , 120 mm for FA , 30 N for Q , 160 mm for CD . M 1 = [ 40 × ( 120 + 120 ) ] − [ 30 ( 160 ) ] = 4800 N ⋅ mm × 1 1000 m mm = 4.80 N ⋅ m Write the couple vector ( M 1 ) perpendicular to plane ABCD in vector form: M 1 = ( M 1 cos θ ) j + ( M 1 sin θ ) k Substitute 4.80 N ⋅ m for M 1 and 36.87 ° for θ

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 3.3, Problem 3.78P

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Find the magnitude of the couple (M) and direction of its axis after replacing the two couples in single equivalent couple.

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Chapter 3.3, Problem 3.77P

Chapter 3.3, Problem 3.79P

Chapter 3 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

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 - Prob. 3.6P Ch. 3.1 - Prob. 3.7P Ch. 3.1 - Prob. 3.8P 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 - 3.15 Form the vector products B × C and B′ × C,...Ch. 3.1 - Prob. 3.16P Ch. 3.1 - 3.17 A plane contains the vectors A and B....Ch. 3.1 - Prob. 3.18P Ch. 3.1 - Prob. 3.19P Ch. 3.1 - 3.20 Determine the moment about the origin O of...Ch. 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. 3.24P 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 - Prob. 3.28P Ch. 3.1 - Prob. 3.29P 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 - Prob. 3.37P Ch. 3.2 - Prob. 3.38P Ch. 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 - Prob. 3.45P Ch. 3.2 - Prob. 3.46P Ch. 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 - 3.51 To lift a heavy crate, a man uses a block and...Ch. 3.2 - Prob. 3.52P 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. 3.55P Ch. 3.2 - Prob. 3.56P 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. 3.61P Ch. 3.2 - Prob. 3.62P Ch. 3.2 - Two forces F1 and F2 in space have the same...Ch. 3.2 - Prob. 3.64P Ch. 3.2 - Prob. 3.65P Ch. 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. 3.71P Ch. 3.3 - 3.72 Four pegs are attached to a board as shown....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 - Prob. 3.75P Ch. 3.3 - Prob. 3.76P Ch. 3.3 - 3.77If P = 20 lb in the figure, replace the three...Ch. 3.3 - 3.78 Replace the two couples shown with a single...Ch. 3.3 - Prob. 3.79P 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 - Prob. 3.82P 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 - Prob. 3.88P 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 - Prob. 3.99P Ch. 3.3 - Prob. 3.100P Ch. 3.4 - Prob. 3.101P Ch. 3.4 - Prob. 3.102P Ch. 3.4 - Prob. 3.103P 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 - Prob. 3.109P Ch. 3.4 - To test the strength of a 625 500-mm suitcase,...Ch. 3.4 - Prob. 3.111P Ch. 3.4 - Pulleys A and B are mounted on bracket CDEF. The...Ch. 3.4 - 3.113 A truss supports the loading shown....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. 3.127P Ch. 3.4 - Prob. 3.128P Ch. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 3.130P Ch. 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. 3.133P Ch. 3.4 - A piece of sheet metal is bent into the shape...Ch. 3.4 - Prob. 3.135P Ch. 3.4 - Prob. 3.136P Ch. 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. 3.139P Ch. 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. 3.150RP Ch. 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 - Prob. 3.155RP Ch. 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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