1 ME2100 Homework 1. Determine the gravitational force exerted by a. The moon on the earth, using the following data. Make sure that you show your work Mass of moon : m m = 7.35*10 22 kg Mass of earth : m e = 5.976*10 24 kg Radius of moon : r m = 1.738*10 6 m Radius of earth : r e = 6.731*10 6 m Distance between moon & earth : 3.844*10 8 m b. The sun on the earth, using the following data. Make sure that you show your work Mass of sun : m s = 1.990*10 30 kg Mass of earth : m e = 5.976*10 24 kg Radius of sun : r s = 6.960*10 8 m Radius of earth : r e = 6.731*10 6 m Distance between sun & earth : 1.496*10 11 m Goal: Given: Assume : Draw : Soln:
2 2. Determine the force of gravity acting on a satellite when it is in orbit 20.2 * 10 6 m above the surface of the earth. Its weight when on the surface of the earth is 8450 N. Use the data given in previous problem as needed. Goal: Given: Assume : Draw : Soln:
3 3. At what distance, in kilometers, from the surface of the earth on a line from center to center would the gravitational force of the earth on a body be exactly balanced by the gravitational force of the moon on the body? Use the data in problem as needed. (As a challenge first work out the problem using only symbols and then plug in the numbers at the end) Goal: Given: Assume : Draw : Soln:
4 4. Two forces are applied at point B of beam AB. Determine the magnitude and direction of the resultant using trigonometry. Challenge : use variables like P,Q for the forces and θ,φ for the angles and derive the solution for a whole class of problems. NOTE : the resultant will not be along line BC. GOAL : Given : P = 2kN, Q = 3kN, θ = 40,φ = 60 Find : R the resultant Solution : Draw the parallelogram with sides along P and Q. P C Hint : Use Sine and cosine law with parallelogram law of addition Q
5 5. The post is to be pulled out of the ground using two ropes A and B. Rope A is subjected to a force (tension) of 600 lb and is T lb directed at a known angle φ o from the vertical. If the resultant force acting on the post is to be always 1200 lb, vertically upward, B determine the force T in rope B and the corresponding angle θ o. Challenge : plot the value of T and θ as a function of φ. For students having difficulty use φ = 30 o θ φ A 600 lb
6 6. Using the figure shown a. Determine the magnitude and its direction of the resultant F r = F 1 + F 2 measured from the positive u- axis. b. Determine the components along the u and v axes of F 1 c. Determine the components along the u and v axes of F 2 F 1 = 150N
7 7. Three cables are attached to a tree as shown in figure. a. Represent the vectors AB, AC, and AD. b. Find the unit vector along u AB, u AC, and u AD c. Find the direction angles of each of the above vectors.
8 8. Three cables are attached to a block as shown in figure. a. Find the unit vector along u OA, u OB, and u OC b. Represent the vectors F 1, F 2, and F 3,. c. Find the direction angles of OA, OB, and OC
9 9. A cable is attached to B to the right angle pipe OAB in figure. The tension in the cable is 750 lb and a moment/torque of 10 lb.ft is applied at B as shown along line of action AB. a. Represent the tension in the cable as a vector F BC b. Find the unit vector u BC c. Find the direction angles of the vector F BC d. Represent the moment as a vector. M=10 lb.ft
10 10. Two forces F 1 and F 2 are applied to an eyelet as shown in figure. Determine the resultant F R = F 1 + F 2, and write in vector notation. Find the unit vector along the resultant and then use it to obtain the direction angles of the resultant.
11 11. The flex-headed ratchet wrench is subjected to a force P lb, applied perpendicular to the handle as shown. Find the moment or torque this imparts along the vertical axis of the bolt at A assuming θ as a given angle. θ
12 12. Determine a. Moment M 1 of F 1 about moment center A b. Moment M 2 of F 2 about moment center A c. Sum of M 1 and M 2 which we will call M 3 d. If F 1 and F 2 are parallel and opposite to each other will your answer in part c. Why OR why not? e. Find the scalar component of M 3 about the axis of the shaft AB. f. Would your answer in part e be different if M 1 and M 2 had been calculated for a moment center at B? (first reason your answer and than confirm by computing)
13 13. A 2 kn force acts on one end of the curved rod. Section AB of the rod lies in the xy plane and section BC lies in the zy plane. Determine the moment about moment center A and about moment center B Now find the magnitude about the line AB and then about line BC. Reason your answers. (For hints see on page 182)
14 14. For the beam pinned at A and acted by T BC, F B and M C, replace the loads by equivalent loading at A. Present your answers as vectors and also sketch the equivalent force and moment.
15 15. Find equivalent loading at A and represent as a vector and also as a diagram.
16 16. The wing of the jet aircraft is subjected to a thrust of T= 8,000N from its engine, and the moment of 6000 N*m due to the rotation and the resultant lift force L= 45,000N (This is normally a distributed force, but has been reduced to a concentrated force as shown). If the mass of the wing is 2,100 Kg and the mass center is at G, determine the components of reaction where the wing is fixed to the fuselage at A. GOAL: Given : Assume : Soln : Draw Free Body diagram The body of the aircraft provides a fixed support for the wing (meaning 6 components of reaction, 2 each in x,y,z co-ordinates) Write equations of equilibrium six equations and six unknowns M = 6kN-m
17 17. The pipe assembly supports the vertical loads shown. Determine the components of reaction at the ball and socket joint A and the tension in the supporting cables BC and BD. GOAL : Given : 100N/m Assume: Soln : Draw FBD. Reduce distributed load to conc. load and find its line of action (i.e. 3m*100N/m=300N force acting at the mid-point Already shown for you in FBD) A ball and socket joint does NOT allow translation in all directions, but lets free rotation in each direction. 300N 1.5m
18 18. Determine the reactions at the fixed wall A. The 150 N force is parallel to the z axis, the 200N force is parallel to the y axis and the 300N force is parallel to the x axis. The moment of a couple has a magnitude of 100 N-m and has direction angles of θ x =67.4ºand θ z =39.8º. GOAL : 100N-m 300N Given : Assume: Soln :
19 19. A 200-N force is applied to the handle of the hoist in the direction shown. The bearing at A is a thrust bearing, and the bearing at B is a journal bearing. If the hoist is in equilibrium, what forces act on the shaft at A? What forces acts on the shaft at B? What is the maximum mass m in kilogram that can be lifted? GOAL : Given : Find : m Soln : Draw FBD. A journal bearing does NOT permit translation and rotation in two axes. A thrust bearing does NOT permit translation in three directions and does NOT permit rotation in two axes. After showing the above we will have 10 unknowns which includes the mass. Now make the assumption that the bearings are perfectly aligned this will take care of 4 moment reactions, two each at the two bearings and leave you with six unknowns.
20 20. A shaft is loaded through a pulley and a lever that are fixed to the shown shown in figure. Friction between the belt and the pulley prevents the belt from slipping. The support at A is a journal bearing, and the support at B is thrust bearing. Determine a. the force P required for equilibrium b. the loads acting on the shaft at supports at A and at B. c. find the direction angles of the reaction at A and B d. It is known that the bearing at A fails if the force on it exceeds 1000N and bearing at B fails if force on it exceeds 400 N. Discuss the failure of this mechanism based on your answers in part b.
21 21. Determine the location of the centroid of the beam s crosssectional area. Neglect the size of the corner welds at A and B for the calculation. GOAL: Given : Assume:: Draw: Solution:
22 22. The gravity wall is made of concrete. Determine the location of the center of gravity G for the wall. GOAL: Given : Assume:: Draw: Solution :
23 23. Determine the location of the centroid C of the area. GOAL: Given : Assume:: Draw: Solution :
24 24. Determine the location of the center of gravity of the three-wheeler. The location of the center of gravity of each component and its weight are tabulated in the figure. If the three-wheeler is symmetrical with respect to the x-y plane, determine the normal reactions each of its wheels exerts on the ground. GOAL: Given : Assume:: Draw: Solution :
25 25. Replace the distributed loading by an equivalent resultant force and specify where its line of action intersects a. member AB, measured from A. b. member BC, measured from C. GOAL: Given : Assume:: Draw: Solution :
26 26. The beam is subjected to the distributed loading. Determine the length b of the uniform load and its position a on beam such that the resultant force and couple moment acting on the beam are zero. GOAL: Given : Assume:: Draw: Solution :
27 27. Replace the distributed loading by an equivalent resultant force, and specify its location on the beam, measured from the pin at C. GOAL: Given : Assume:: Draw: Solution :
28 28. The truss is made from five members, each having a length of 4m and a mass of 7kg/m. If the mass of the gusset plates at the joints and the thickness of the members can be neglected, determine the distance d to where the hoisting cable must be attached, so that the truss does not tip (not rotate) when it is lifted. GOAL: Given : Assume:: Draw: Solution :
29 29. The wall crane supports a load of 1000lb as shown. Determine the horizontal and vertical components of reaction at the pins A and D. Also what is the force in the cable at the winch? The jib ABC has a weight of 100lb and member BD has a weight of 40lb. Each member is uniform and has a center of gravity at its center. Outline : First consider the pulley at E as shown below and find the tension in the cable. Use this tension and find the reactions at C as shown in the diagram below. Equivalent system of forces Similarly reduce the pulley at B into an equivalent system of forces. Now consider the structure with pulleys removed and equivalent forces shown for their point of attachment. (Remember Newton s third law). Do not forget the weight of the members. Now draw the FBD of structure which will now consist of ABC and BD. Write equilibrium equations Next break it into members ABC and BD. Again do not forget the weight of the members 4 3 P=1000lb T E T T 3 P=1000lb 4 Pulley E R CX T T 3 4 Pulley C R CY T R B1 Pulley B T R B2
30 30. Determine the reactions at the supports of the frame shown. The pin attached to member BCD, passes through a smooth slot in member AB. (Hint : Frame has two members AB and BD. Draw their FBD and apply equilibrium conditions. You will need to reduce distributed load to concentrated load) Outline Determine support reactions (FBD of whole structure, Eqm equations) Breakup structure and draw FBD, Eqm equations. Do not forget that pin attached to BCD behaves like a roller reactions are normal to surface of contact. Do not forget external moment at A when drawing FBD of AB or FBD of structure. 100 lb-ft
31 31. The two-bar mechanism consists of a lever arm AB and smooth link CD, which has a fixed collar at its end C and a roller at the other end D. a) Determine the force P needed to hold the lever in the position θ. The spring has a stiffness k and unstretched length 2L. Assume that the roller contacts either the top or bottom portion of the horizontal guide at D. b) Using any software of your choice (Matlab, Mathcad), draw a graph of θ vs P. (θ = 30 to 60). From the graph determine the maximum P required and at what angle does this occur. For part b, assume L = 1m, k = 100N/m. Challenge : Assume that P is acting at an angle β from the horizontal measured in clockwise direction instead of as shown in figure.
32 32. Determine the force in each member of the truss. First solve using P 1 and P 2 as the forces and the given length. Then substitute values a) P 1 = 240lb, P 2 = 100lb. state if the members are in tension OR compression. b) Determine the largest permissible load P 2 if P 1 = 0lb. No member should exceed 500lb in tension and 350 lb in compression.
33 33. Determine the force in each member of the truss in terms of the load P and state if the members are in tension OR compression. Challenge Use the result to solve P a. Members AB and BC can each support a maximum compressive force of 800lb, and members AD, DC, and BD can support a maximum tensile force of 1500lb. If a = 10ft, determine the greatest load P the truss can support. b. Members AB and BC can each support a maximum compressive force of 800lb, and members AD, DC, and BD can support a maximum tensile force of 2000lb. If a = 6ft, determine the greatest load P the truss can support.
34 34. Determine the force in a) members GF, GD and CD b) members BG, BC, and HG using the method of sections. c) using method of joints now solve for forces in AB, AH, BH, CG, DF, FE, DE. In all cases state if the members are in tension OR compression.
35 35. Draw the axial force, shear force and bending moment for the structure shown. OUTLINE : First obtain the support reactions R Ax, R Ay and R By by drawing R By Fx = 0 R Ax = 0N r M A = i 2000 j i = Fy = i 4000 j + + 8i R By j 2000 j i 2000 j i the FBD of whole structure and using equilibrium equations j i 4000 j + Now recognize that we have seven regions in the beam so you will have to draw seven FBD and write 7*3=21 equilibrium equations to obtain axial force, shear force and bending moments.
36 36. Draw the axial force, shear force and bending moment diagrams. (Even though not asked you will have to find the support reactions before proceeding) OUTLINE : First obtain the support reactions R Ax, R Ay and R By by drawing the FBD of whole structure and using equilibrium equations. Remember to reduce distributed load to concentrated load which will be area under curve area of R By Fx = 0 R Ax = 30 lb r M A = 0 6i 225 j + 9i R By j 200 k = Fy = 0 triangle. 225lb acting at 6ft from A. Now realize that the beam has two regions. So you will write 3*2 = 6 equations to obtain the axial force, shear force and bending moment. Be sure to consider the area of triangle as we did in ICE lb
37 37. Draw the shear force and bending moment OUTLINE : Find support reactions. Identify regions we did this in class for this problem. Write eqm. equations for each section. (There are five regions in this beam most often people will make a mistake of not identifying point E where a concentrated moment is applied). E
38 700lb 38. The beam consists of two segments pinconnected at B. Draw the axial force, shear force and bending moment diagrams for the E D 300lb beam. Assume that the moment is applied at point E for the analysis. (HINT : We have solved 300lb*ft a similar problem in class) CLUE : once you A find the reaction in pin B, you can actually look at 8ft 4ft the two members independently for the axial force, shear force and bending moment diagrams. 200lb/ft B 6ft C
IEC College of Engineering & Technology Greater Noida Department of Mechanical Engineering Engineering Mechanics Question Bank Prepared By: Prof (Dr) SS Chauhan Short Question Tutorial No 1 Parallelogram
Chap. 4 Equilibrium of Rigid Bodies For a rigid body, the condition of static equilibrium means that the body under study does not translate or rotate under the given loads that act on the body The necessary
Equilibrium of Force System The body is said to be in equilibrium if the resultant of all forces acting on it is zero. There are two major types of static equilibrium, namely, translational equilibrium
Today s Objective: Students will be able to RIGID BODY EQUILIBRIUM IN 3-D a) Identify support reactions in 3-D and draw a free body diagram, and, b) apply the equations of equilibrium. In-Class Activities:
Chap. 5 Equilibrium of a Rigid Body Chapter Outline Conditions for Rigid-Body Equilibrium Free-Body Diagrams Equations of Equilibrium Two and Three-Force Members Constraints and Statical Determinacy 5-2
Free ody iagram xercises F- 1 xample: Free ody iagrams The roller-band device consists of two rollers, each of radius, r, encircled by a flexible band of negligible thickness and subjected to the two tensions
CHAPTER Engineering Mechanics: Statics College of Engineering Department of Mechanical Engineering Tenth Edition EQUILIBRIUM OF A RIGID BODY 5c by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics Department
ENGR-1100 Introduction to Engineering Analysis Lecture 15 3-D FREE-BODY DIAGRAMS, EQUILIBRIUM EQUATIONS, CONSTRAINTS AND STATICAL DETERMINACY Today s Objective: Students will be able to: a) Identify support
Section 4 page 1 4. Equilibrium of Rigid Bodies SECTION OBJECTIVES: By the end of this section, you will be able to: a. Draw a free-body diagram of a rigid body; b. Solve 2-D static equilibrium problems.
Mechanics 1 Revision Notes July 2012 MECHANICS 1... 2 1. Mathematical Models in Mechanics... 2 Assumptions and approximations often used to simplify the mathematics involved:... 2 2. Vectors in Mechanics....
Q/1 Determine the magnitude F S of the tensile spring force in order that the resultant of F S and F is a vertical force. Determine the magnitude R of this vertical resultant force. Ams: F S = 60 Ib Q/2
Forces are analyzed in a number of ways; it is common approach to establish a coordinate system to quantify the forces and their effects in a system or body. Since it is customary to assign the axes, the
STATICS: CE201 Chapter 5 Equilibrium of a Rigid Body Notes are prepared based on: Engineering Mechanics, Statics by R. C. Hibbeler, 12E Pearson Dr M. Touahmia & Dr M. Boukendakdji Civil Engineering Department,
Problems Based on Force Concept (SEM. I) EXAMINATION. 2005-06 (ME) 1- Principal of transmissibility of a force. 2- Necessary and sufficient conditions of equilibrium of a system of coplanar force system.
ENGR0135 - Statics and Mechanics of Materials 1 (161) Homework # Solution Set 1. Summing forces in the y-direction allows one to determine the magnitude of F : Fy 1000 sin 60 800 sin 37 F sin 45 0 F 543.8689
ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body
9 Problem : The toggle switch consists of a cocking lever that is pinned to a fied frame at A and held in place b the spring which has an unstretched length of 00 mm. Determine the magnitude of the resultant
STRESS! Stress! verage Normal Stress in an xially Loaded ar! verage Shear Stress! llowable Stress! Design of Simple onnections 1 Equilibrium of a Deformable ody ody Force w F R x w(s). D s y Support Reaction
ENGR-1100 Introduction to Engineering Analysis Lecture 19 SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: a) Define a simple truss. b) Determine
EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body diagram. READING QUIZ 1. If a support prevents translation
STATICS Assist. Prof. Dr. Cenk Üstündağ 4 Force System Resultants Chapter Objectives Method for finding the moment of a force about a specified axis. Define the moment of a couple. Determine the resultants
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
ME 101: Engineering Mechanics Rajib Kumar Bhattacharjya Department of Civil Engineering Indian Institute of Technology Guwahati M Block : Room No 005 : Tel: 2428 www.iitg.ernet.in/rkbc Equilibrium of rigid
Tutorial 1 FORCE SYSTEM 1 Find out the magnitude and direction of the resultant with reference to horizontal axis for the system shown in fig. The forces F1,F and F3 all of which act on a point A of the
(Updated: 5/30/08) MEEG 2003 Meeting #1 Prior Basic Mathematics and Fundamental Concepts 1. Review the prior basic mathematics in App. B. 2. Solve and choose the correct answer to each of the 50 multiple-choice
7.1 SIMPLE TRUSSES STRUCTURAL ANALYSIS A truss is a structure composed of slender members joined together at their end points. The members commonly used in construction consist of wooden struts or metal
Engineering Mechanics Prof. Manoj Harbola Indian Institute of Technology, Kanpur Module - 01 Lecture - 03 Equilibrium II (Refer Slide Time: 00:24) We have been learning about the moment of a force or many
STATICS: CE201 Chapter 7 Internal Forces Notes are prepared based on: Engineering Mechanics, Statics by R. C. Hibbeler, 12E Pearson Dr M. Touahmia & Dr M. Boukendakdji Civil Engineering Department, University
Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none
Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Module 1 Lecture 2 Equations of Equilibrium Now we will discuss the equations of equilibrium;
Physics 107 HOMEORK ASSIGMET #8 Cutnell & Johnson, 7 th edition Chapter 9: Problems 16, 22, 24, 66, 68 16 A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself
CE297-FA09-Ch4 Page 1 Friday, September 18, 2009 12:11 AM Chapter 4: Equilibrium of Rigid Bodies A (rigid) body is said to in equilibrium if the vector sum of ALL forces and all their moments taken about
Equilibrium of bodies II In the previous lecture we have defined a couple moment. With this definition, we can now represent a force applied on a body pivoted at a point as the sum of the same force on
EQUIVALENT FORCE SYSTEMS 1. Replace the force and couple system by an equivalent single force and couple acting at point P. Ans: (a) 0.086i-1.184 kn, 21.6 kn m (b) 270 N, 6885 kn m 2. Determine the magnitude
09 Solutions 46060 6/8/10 3:13 PM Page 619 010 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 9 1. Prove that
Cables, Springs and Pulleys ME 202 Ideal Cable Neglect weight (massless) Neglect bending stiffness Force parallel to cable Force only tensile (cable taut) Neglect stretching (inextensible) 1 2 Sketch a
Chapter 1: Statics 1. The subject of mechanics deals with what happens to a body when is / are applied to it. A) magnetic field B) heat C ) forces D) neutrons E) lasers 2. still remains the basis of most
SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: a) Define a simple truss. b) Determine the forces in members of a simple truss. c) Identify zero-force
MECHANICS OF SOLIDS PRELIMINARY LEVEL TUTORIAL 3 PIN JOINTED FRAMES This tutorial is essential for anyone studying the group of tutorials on beams. o Essential pre-requisite knowledge for Edexcel HNC Mechanical
Physics 107 HOMEWORK ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapter 9: Problems 16, 22, 24, 60, 68 16 A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself
MINISTRY OF EDUCATION AND SCIENCE, YOUTH AND SPORTS OF UKRAINE STATE HIGHER EDUCATIONAL INSTITUTION «NATIONAL MINING UNIVERSITY» A.M. Dolgov THEORETICAL MECHANICS STATICS Tutorial DNIPROPETROVS K NMU 2013
Friction is the contact resistance exerted by one body when the second body moves or tends to move past the first body. Friction is a retarding force that always acts opposite to the motion or to the tendency
Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics
Recitation #6 October 14, 2003 TORSION OF CIRCULAR SECTIONS Assumptions 1) This analysis can only be applied to solid or hollow circular sections 2) The material must be homogeneous 3) Torque is constant
NGR0135 - Statics and Mechanics of Materials 1 (2161) Homework #8 Solution Set 1. One should begin by drawing a free-body diagram for the beam, as shown below. here are horizontal and vertical reaction
COURSE: CE 201 (STATICS) LECTURE NO.: 28 to 30 FACULTY: DR. SHAMSHAD AHMAD DEPARTMENT: CIVIL ENGINEERING UNIVERSITY: KING FAHD UNIVERSITY OF PETROLEUM & MINERALS, DHAHRAN, SAUDI ARABIA TEXT BOOK: ENGINEERING
EQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS Today s Objectives: Students will be able to: 1. Analyze the planar kinetics In-Class Activities: of a rigid body undergoing rotational motion. Check Homework
1 MUKAVEMET EĞİLME 2 3 4 5 6 7 8 9 Topic 8.1: Special Topics I - Combined Stress Up to this point we have considered only or mainly one type of applied stress acting on a structure, member of a structure,
Two-Force Members, Three-Force Members, Distributed Loads Two-Force Members - Examples ME 202 2 Two-Force Members Only two forces act on the body. The line of action (LOA) of forces at both A and B must
Name: Skill Sheet 7.A Adding Displacement Vectors A displacement vector is a quantity that contains two separate pieces of information: () magnitude or size, and () direction. When you add displacement
7 Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are usually applied transverse (perpendicular) to its longitudinal axis. These transverse
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1-1958 Physics, Chapter 3: The Equilibrium of a Particle
In the figure, two blocks, of mass g and g, are connected with a cord around a uniform disk of mass gand radius cm. The disk can rotate without friction about a fixed horizontal axis through its center;
Three-Dimensional Force Systems Many problems in real-life involve 3-Dimensional Space. How will you represent each of the cable forces in Cartesian vector form? Applications Given the forces in the cables,
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Planar kinetics of a rigid body: Force and acceleration Chapter 17 Chapter objectives Introduce
STATICS UNIT I FORCES INTRODUCTION Mechanics: Mechanics is the science which deals with the effects of forces on material bodies. Under the influence of forces, a body may be in motion or in rest. Statics:
Torque and Equilibrium In the notes bodies in Equilibrium, it was stated that static equilibrium can only truly exist if the net force is zero and if there is no net torque. In particular, if no rotation
Chapter 4 - Forces and Newton s Laws of Motion w./ QuickCheck Questions 2015 Pearson Education, Inc. Anastasia Ierides Department of Physics and Astronomy University of New Mexico September 8, 2015 Review
Eighth E CHAPTER VECTOR MECHANICS FOR ENGINEERS: 8 STATICS Ferdinand P. Beer Friction E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Contents Introduction Laws of Dry Friction.
Structural Axial, Shear and Bending Moments Positive Internal Forces Acting on a Portal Frame 1 Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent
ASSIGNED 1) Knowing that α = 40, determine the resultant of the three forces shown: 2) Two cables, AC and BC, are tied together at C and pulled by a force P, as shown. Knowing that P = 500 N, α = 60, and
EQUILIBRIUM OF A PARTICLE, THE FREE-BODY DIAGRAM & COPLANAR FORCE SYSTEMS Today s Objectives: Students will be able to : a) Draw a free body diagram (FBD), and, b) Apply equations of equilibrium to solve
Lecture 32. TORSION EXAMPLES HAVING MORE THAN ONE DEGREE OF FREEDOM Figure 5.40 (a) Two-disk, torsional vibration example, (b) coordinates and free-body diagram for Torsional Vibration Examples We worked
Static Equilibrium Equilibrium implies the object is at rest (static) or its center of mass moves with a constant velocity (dynamic) Static equilibrium is a common situation in engineering Principles involved
Announcements 2-D Vector Addition Today s Objectives Understand the difference between scalars and vectors Resolve a 2-D vector into components Perform vector operations Class Activities Applications Scalar
Chapter 5 The Laws of Motion The Laws of Motion The description of an object in motion included its position, velocity, and acceleration. There was no consideration of what might influence that motion.
Chapter 1 : Balancing 1 of Rotating Masses l 833 Features 1. Introduction.. Balancing of Rotating Masses. 3. Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane. 4. Balancing
5 Chapter Objectives To show how to determine the forces in the members of a truss using the method of joints and the method of sections. To analyze the forces acting on the members of frames and machines
7.2 Wedges 7.2 Wedges Example 1, page 1 of 4 1. If the coefficient of static friction equals 0.3 for all surfaces of contact, determine the smallest value of force P necessary to raise the block. Neglect
Introduction to Statics.PDF Edition Version 0.95 Unit 18 Trusses: Method of Joints Helen Margaret Lester Plants Late Professor Emerita Wallace Starr Venable Emeritus Associate Professor West Virginia University,
Chapter 17 Planar Kinetics of a Rigid Body: Force and Acceleration 17.1 Moment of Inertia I 2 2 = r dm, 單位 : kg m 或 slug m ft 2 M = Iα resistance to angular acceleration dm = ρdv I = ρ V r 2 dv 17-2 MOMENT
ENGR-1100 Introduction to Engineering Analysis Lecture 11 MOMENT OF A COUPLE Today s Objectives: Students will be able to a) define a couple, and, In-Class activities: b) determine the moment of a couple.
Chapter 3 THE STATIC ASPECT OF SOLICITATION 3.1. ACTIONS Construction elements interact between them and with the environment. The consequence of this interaction defines the system of actions that subject
ENGR0135 - Statics and Mechanics of Materials 1 (2161) Homework #11 Solution Set 1. (a) The torques transmitted by cross sections in intervals AB, BC, CD, and DE are T AB 25 kip ft, T BC 75 kip ft, T CD
Forces & Newton 1 What Is a Force? A Force is an interaction between two bodies. Convention: F a,b means the force acting on a due to b. A Force is a push or a pull. A Force has magnitude & direction (vector).
Chapter 8: Rotational Equilibrium and Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Definition of Torque Torque,, is the tendency of a force to rotate an object
CHAPTER 6 Space Trusses INTRODUCTION A space truss consists of members joined together at their ends to form a stable threedimensional structures A stable simple space truss can be built from the basic
PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY (Sections 18.1-18.4) Today s Objectives: Students will be able to: a) Define the various ways a force and couple do work. b) Apply the principle of work
10 Space Truss and Space Frame Analysis 10.1 Introduction One dimensional models can be very accurate and very cost effective in the proper applications. For example, a hollow tube may require many thousands
EXMPLES Ex- 1 Example: oplanar Forces etermine the x and y components of F 1 and F 2 acting on the boom. Express each force as a artesian vector. y F 1 = 200 N 30 o 5 12 13 F 2 = 260 N x Ex- 2 Example:
ANGULAR MOMENTUM, MOMENT OF A FORCE AND PRINCIPLE OF ANGULAR IMPULSE AND MOMENTUM Today s Objectives: Students will be able to: 1. Determine the angular momentum of a particle and apply the principle of
Structural Analysis: Space Truss Space Truss - 6 bars joined at their ends to form the edges of a tetrahedron as the basic non-collapsible unit - 3 additional concurrent bars whose ends are attached to
Introduction to Statics.PDF Edition Version 1.0 Notebook Helen Margaret Lester Plants Late Professor Emerita Wallace Starr Venable Emeritus Associate Professor West Virginia University, Morgantown, West
5 1. Draw the free-body diagram of the dumpster D of the truck, which has a weight of 5000 lb and a center of gravity at G. It is supported by a pin at and a pin-connected hydraulic cylinder C (short link).