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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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Question
Chapter 3.4, Problem 78P
To determine
The systems that is equivalent to a force
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Students have asked these similar questions
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.
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°
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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- Replace 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_forward2. Replace the force system acting on the frame by a resultant force (R) and couple moment (MA) at point A. Draw the equivalent force system F=30 kN 2 m 3 m F2=50 kN F= 25 kN 40° 3 m 5 m 30° Aarrow_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
- Calculate 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_forward1. 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_forward250 N 200 mm 20 mm E 40 mm 100 mm 50 N 160 mm 120 N 300 N Four forces are applied to the machine component ABDE as shown. Replace these forces with an equivalent force-couple system at A.arrow_forward
- Replace 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_forward2. Replace the force system acting on the frame by a resultant force (R) and couple moment (MA) at point A. Draw the equivalent force system F;=30 kN 2 m 3 m F2=50 kN F3= 25 kN 40° 3 m 5 m 30° Aarrow_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_forward
- Replace 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_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_forwardCalculate the magnitude of the moment about the base point O of the 600-N force. 2 m 40° 600 N 4 marrow_forward
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How to balance a see saw using moments example problem; Author: Engineer4Free;https://www.youtube.com/watch?v=d7tX37j-iHU;License: Standard Youtube License