Statics and Mechanics of Materials
2nd Edition
ISBN: 9780073398167
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek
Publisher: McGraw-Hill Education
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Chapter 3.4, Problem 78P
To determine
The systems that is equivalent to a force
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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.
A force P (200 + R)i + (250+ R)j + 300 k N, is
acting at origin of the co-ordinate
system, and a moment M = (10+ R)i + (100 -
R)j + 30 k N-m, is acting at (0.5,1.0, -0.5) m
from origin. Replace the given force system
by equivalent wrench system, and
determine the point where the axis of
wrench will pass through x-z plane. (R = 41)
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.
380 lb
9"
15"
HJ
12"
640 lb
A
Answers:
Force-couple system at A. The force is positive if up, and the moment is positive if counterclockwise.
R=
M=
i
X=
i
Resultant
330 lb
i
lb
lb-in.
in.
Chapter 3 Solutions
Statics and Mechanics of Materials
Ch. 3.1 - A 20-lb force is applied to the control rod AB as...Ch. 3.1 - A 20-lb force is applied to the control rod AB as...Ch. 3.1 - A 300-N force P is applied at point A of the bell...Ch. 3.1 - A 400-N force P is applied at point A of the bell...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 - 3.7 and 3.8 The tailgate of a car is supported by...Ch. 3.1 - 3.7 and 3.8 The tailgate of a car is supported by...Ch. 3.1 - 3.9 and 3.10 It is known that the connecting rod...Ch. 3.1 - 3.9 and 3.10 It is known that the connecting rod...
Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Prob. 12PCh. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Determine the moment about the origin O of the...Ch. 3.1 - Prob. 15PCh. 3.1 - Prob. 16PCh. 3.1 - Prob. 17PCh. 3.1 - A wooden board AB, which is used as a temporary...Ch. 3.1 - Prob. 19PCh. 3.1 - A small boat hangs from two davits, one of which...Ch. 3.1 - Prob. 21PCh. 3.1 - In Prob. 3.16, determine the perpendicular...Ch. 3.1 - In Prob. 3.16, determine the perpendicular...Ch. 3.1 - In Prob. 3.20, determine the perpendicular...Ch. 3.2 - Given the vectors P=3i-j+2k,Q=4i+5j-3k, and...Ch. 3.2 - Prob. 26PCh. 3.2 - Knowing that the tension in cable AC is 1260 N,...Ch. 3.2 - Knowing that the tension in cable AD is 405 N,...Ch. 3.2 - Three cables are used to support a container as...Ch. 3.2 - Three cables are used to support a container as...Ch. 3.2 - The 20-in. tube AB can slide along a horizontal...Ch. 3.2 - Solve Prob. 3.31 for the position corresponding to...Ch. 3.2 - Prob. 33PCh. 3.2 - Prob. 34PCh. 3.2 - Knowing that the tension in cable AB is 570 N,...Ch. 3.2 - Prob. 36PCh. 3.2 - A farmer uses cables and winch pullers B and E to...Ch. 3.2 - Solve Prob. 3.37 when the tension in cable AB is...Ch. 3.2 - To lift a heavy crate, a man uses a block and...Ch. 3.2 - Prob. 40PCh. 3.2 - Prob. 41PCh. 3.2 - Prob. 42PCh. 3.2 - Prob. 43PCh. 3.2 - A sign erected on uneven ground is guyed by cables...Ch. 3.2 - The frame ACD is hinged at and D and is supported...Ch. 3.2 - In Prob. 3.45, determine the moment about the...Ch. 3.2 - Prob. 47PCh. 3.2 - Prob. 48PCh. 3.3 - Two parallel 60-N forces are applied to a lever as...Ch. 3.3 - A plate in the shape of a parallelogram is acted...Ch. 3.3 - Prob. 51PCh. 3.3 - Prob. 52PCh. 3.3 - Four 112-in. -diameter pegs are attached to a...Ch. 3.3 - Prob. 54PCh. 3.3 - Prob. 55PCh. 3.3 - Prob. 56PCh. 3.3 - Replace the two couples shown with a single...Ch. 3.3 - Prob. 58PCh. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - Prob. 60PCh. 3.3 - Prob. 61PCh. 3.3 - The force P has a magnitude of 250 N and is...Ch. 3.3 - Prob. 63PCh. 3.3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3.3 - Prob. 65PCh. 3.3 - A force and couple act as shown on a square plate...Ch. 3.3 - Prob. 67PCh. 3.3 - Prob. 68PCh. 3.3 - Prob. 69PCh. 3.3 - Replace the 150-N force by an equivalent...Ch. 3.3 - Prob. 71PCh. 3.3 - Prob. 72PCh. 3.4 - A 4-m-long beam is subjected to a variety of...Ch. 3.4 - Prob. 74PCh. 3.4 - Determine the single equivalent force and the...Ch. 3.4 - The weights of two children sitting at ends A and...Ch. 3.4 - Prob. 77PCh. 3.4 - Prob. 78PCh. 3.4 - Four forces act on a 700375 -mm plate as shown....Ch. 3.4 - Prob. 80PCh. 3.4 - Prob. 81PCh. 3.4 - A truss supports the loading shown. Determine the...Ch. 3.4 - A machine component is subjected to the forces and...Ch. 3.4 - Solve Prob. 3.83, assuming that P=60N.Ch. 3.4 - Prob. 85PCh. 3.4 - Prob. 86PCh. 3.4 - Prob. 87PCh. 3.4 - Prob. 88PCh. 3.4 - Prob. 89PCh. 3.4 - Assuming e 600 in Prob. 3.89, replace the two...Ch. 3.4 - A blade held in a brace is used to tighten a screw...Ch. 3.4 - Prob. 92PCh. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 94PCh. 3.4 - Prob. 95PCh. 3.4 - Three children are standing on a 55-m raft. The...Ch. 3 - For the shift lever shown, determine the magnitude...Ch. 3 - Consider the volleyball net shown. Determine the...Ch. 3 - A crane is oriented so that the end of the 25-m...Ch. 3 - The 25-m crane boom AO lies in the yz plane....Ch. 3 - A single force P acts at C in a direction...Ch. 3 - While tapping a hole, a machinist applies the...Ch. 3 - A 500-N force is applied to a bent plate as shown....Ch. 3 - Prob. 104RPCh. 3 - Prob. 105RPCh. 3 - Prob. 106RPCh. 3 - Prob. 107RPCh. 3 - A regular tetrahedron has six edges of length a. A...
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- For the system of forces shown, find the equivalent force-couple system at A. If a single equivalent force were to act at D, determine the length from B to D. Note that based on the figure, since there is no given angle for the 150 N force, the manner of 120 N 100 N 60 N B 1m 270 N-m 150 N 120 N D 1 m 0.5 m 0.5 m 2 m which the distance is indicated in the figure suggests that the 150 N force is perpendicular to the 30° arm of the bar system. A 30°arrow_forwardReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. 100 N 560 mm 560 mm 560 mm 260 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R= i N M = Single resultant force. d = i 120 N N•m mmarrow_forwardCalculate the moment MB of the 605-N force about the bolt at B. Simplify your work by first replacing the force by its equivalent force- couple system at A. The moment is positive if counterclockwise, negative if clockwise. Assume F = 605 N, r = 215 mm, h = 705 mm, 0 = 33°, = 38° Answer: MB = i Ꮎ h N.marrow_forward
- A rigid body is acted upon by four forces and a couple as shown. (A) Replace the given system by a single force R. Show/locate R on the body indicating its magnitude, direction and position. (8) Find its equivalent system consisting of a single force acting at O and a couple. Draw this equivalent systemarrow_forwardA solid cylindrical shaft anchored to the wall at point O is subjected to 70 N and 85 N couples and a concentrated moment at point E. Determine the resultant couple moment. Hint: You can do this in either of two ways by applying (1) a "scalar" approach by evaluating the individual moments of the x, y, and z components of the 70N and 85N forces, taking positive moments to be in the positive coordinate directions according to the right-hand rule., or (2) the "vector approach" utilizing 3D position vectors using the general cross product definition for the force moment. 70 N 0.8 m 1.2 m 2 6 70 N 1.2 m 0.8 m 9 85 N 12 9 12 -1.2m 1.5m 8 D 85 N C 8 E 200 N·m Xarrow_forwardThe 6.4-kN force F is applied at point A. (a) Compute the moment of F about point O, expressing it both as a scalar (positive if CCW, negative if CW) and as a vector quantity. (b) Determine the coordinates of the points on the x- and y-axes about which the moment of F is zero. Assume XA = 0.8 m, yд = 1.2 m, a = 7, b = 11. y, m I 1 A (x, y) F b a -x, marrow_forward
- 1. Given the two forces and a couple M₁ shown, find the equivalent force-couple system acting at O. Then, replace the force-couple system with a wrench resultant, by writing the force and the moment associated with the wrench in a Cartesian vector form. You can assume that the point P through which the line of action of the wrench passes is already known and do not need to be calculated. M₁ 7m = 100 N·m 3 m 3 m 400 N 3 m SOTER 600 Narrow_forwardReplace the system of two forces and one couple by a wrench. Determine the magnitude of the moment M of the wrench, the magnitude of the force R of the wrench, and the coordinates of the point P in the x-y plane through which the wrench passes. 47 kN-m 1.1 m 1.1 m 20 kN 1.1 m -y 1.1 m 42 kN 3.1 m Answers: M = kN-m 4.68 R = kN 45.2 (xy) i m 0.146 1.70 ALarrow_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_forward
- 4. For the force-couple system as shown, determine the following: Magnitude of the couple moment Mc so that the equivalent system is a single force acting at point P b. a. Point of application of the single equivalent force along line AB if MC is equal to 180 lb-ft counterclockwise. 85 lb 40 ° 100 16 30 lb 15° Mc 35 lb 400 P 1 ft A 85 lb B 1 ft 200 lbarrow_forwardReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. 160 N 730 mm 730 mm 260 N 730 mm 280 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R = i M = i N.m Single resultant force. d = i mmarrow_forwardReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. 110 N 710 mm 710 mm 710 mm 185 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R= i N M= i Single resultant force. d= 100 N N-m mmarrow_forward
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