Explanation Concept used: Write the coordinate of point A as ( 0 , − 30 , 75 ) mm . Write the coordinate of point B as ( 0 , 90 , 75 ) mm . Write the expression for position vector of point B with respect to point A. r → B = ( 0 − 0 ) i ^ + ( 90 − ( − 30 ) ) j ^ + ( 75 − 75 ) k ^ = 120 j ^ mm Here, r → B is the position vector of point B with respect to point A. Write the coordinate of point C as ( 60 , 0 , 0 ) mm . Write the expression for position vector of point C with respect to point A. r → C = ( 60 − 0 ) i ^ + ( 0 − ( − 30 ) ) j ^ + ( 0 − 75 ) k ^ = ( 60 i ^ + 30 j ^ − 75 k ^ ) mm Here, r → C is the position vector of point C with respect to point A Write the coordinate of point D as ( 60 , 50 , 0 ) mm . Write the expression for position vector of point D with respect to point A. r → D = ( 60 − 0 ) i ^ + ( 50 − ( − 30 ) ) j ^ + ( 0 − 75 ) k ^ = ( 60 i ^ + 80 j ^ − 75 k ^ ) mm Here, r → D is the position vector of point D with respect to point A. Write the expression for force in vector form at point B. F → B = ( − 240 j ^ − 125 k ^ ) N Here, F → B is the force in vector form at point B. Write the expression for force in vector form at point C. F → C = − 300 i ^ N Here, F → C is the force in vector form at point C. Write the expression for force in vector form at point D. F → D = 150 k ^ N Here, F → D is the force in vector form at point D. Write the expression for resultant force in vector form. R → = F → B + F → C + F → D …… (1) Here, R → is the resultant force in vector form. Write the expression for moment due to force F → B about point A. M → B = r → B × F → B …… (2) Here, M → B is the moment due to force F → B about point A. Write the expression for moment due to force F → C about point A. M → C = r → C × F → C …… (3) Here, M → C is the moment due to force F → C about point A. Write the expression for moment due to force F → D about point A. M → D = r → D × F → D …… (4) Here, M → D is the moment due to force F → D about point A. Write the expression for net moment about point A. M → = M → B + M → C + M → D …… (5) Here, M → is the net moment about point A

2nd Edition

ISBN: 9780073398167

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

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its enviro…

Videos

Question

Chapter 3.4, Problem 87P

To determine

The equivalent force and couple at point A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.4, Problem 86P

Chapter 3.4, Problem 88P

Students have asked these similar questions

A machine component is subjected to the forces shown, each of which is parallel to one of the coordinate axes. Replace these forces with an equivalent force-couple system at A.

A 260-lb force is applied at A to the rolled-steel section shown.Replace that force with an equivalent force-couple system at the center C of the section.

Three cables are attached to a bracket as shown. Replace the forces exerted by the cables with an equivalent force-couple system at A

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. 12P Ch. 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. 15P Ch. 3.1 - Prob. 16P Ch. 3.1 - Prob. 17P Ch. 3.1 - A wooden board AB, which is used as a temporary...Ch. 3.1 - Prob. 19P Ch. 3.1 - A small boat hangs from two davits, one of which...Ch. 3.1 - Prob. 21P Ch. 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. 26P Ch. 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. 33P Ch. 3.2 - Prob. 34P Ch. 3.2 - Knowing that the tension in cable AB is 570 N,...Ch. 3.2 - Prob. 36P Ch. 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. 40P Ch. 3.2 - Prob. 41P Ch. 3.2 - Prob. 42P Ch. 3.2 - Prob. 43P Ch. 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. 47P Ch. 3.2 - Prob. 48P Ch. 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. 51P Ch. 3.3 - Prob. 52P Ch. 3.3 - Four 112-in. -diameter pegs are attached to a...Ch. 3.3 - Prob. 54P Ch. 3.3 - Prob. 55P Ch. 3.3 - Prob. 56P Ch. 3.3 - Replace the two couples shown with a single...Ch. 3.3 - Prob. 58P Ch. 3.3 - Shafts A and B connect the gear box to the wheel...Ch. 3.3 - Prob. 60P Ch. 3.3 - Prob. 61P Ch. 3.3 - The force P has a magnitude of 250 N and is...Ch. 3.3 - Prob. 63P Ch. 3.3 - A 260-lb force is applied at A to the rolled-steel...Ch. 3.3 - Prob. 65P Ch. 3.3 - A force and couple act as shown on a square plate...Ch. 3.3 - Prob. 67P Ch. 3.3 - Prob. 68P Ch. 3.3 - Prob. 69P Ch. 3.3 - Replace the 150-N force by an equivalent...Ch. 3.3 - Prob. 71P Ch. 3.3 - Prob. 72P Ch. 3.4 - A 4-m-long beam is subjected to a variety of...Ch. 3.4 - Prob. 74P Ch. 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. 77P Ch. 3.4 - Prob. 78P Ch. 3.4 - Four forces act on a 700375 -mm plate as shown....Ch. 3.4 - Prob. 80P Ch. 3.4 - Prob. 81P Ch. 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. 85P Ch. 3.4 - Prob. 86P Ch. 3.4 - Prob. 87P Ch. 3.4 - Prob. 88P Ch. 3.4 - Prob. 89P Ch. 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. 92P Ch. 3.4 - Four signs are mounted on a frame spanning a...Ch. 3.4 - Prob. 94P Ch. 3.4 - Prob. 95P Ch. 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. 104RP Ch. 3 - Prob. 105RP Ch. 3 - Prob. 106RP Ch. 3 - Prob. 107RP Ch. 3 - A regular tetrahedron has six edges of length a. A...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The equivalent force and couple at point A.

Solution Summary: The author explains the equivalent force and couple at point A, and the expression for position vector of point B.

Concept explainers

Videos

The equivalent force and couple at point A.

Want to see the full answer?

Chapter 3 Solutions