Mechanics1 Week1 Lecture1 - Fall 2024 PDF

Lecture 1 LECTURE 1 Fall 2024 ‫بسم هللا الرحمن الرحيم‬ ‫‪Mansoura National University‬‬ ‫‪Faculty of Engineering‬‬ ‫جامعة المنصورة االهلية‬ ‫كلية الهندسة‬  Mechanics 1 LECTURE 1 Fall 2024 Prepared by Dr. Neveen Abd E...

Lecture 1 LECTURE 1 Fall 2024 ‫بسم هللا الرحمن الرحيم‬ ‫‪Mansoura National University‬‬ ‫‪Faculty of Engineering‬‬ ‫جامعة المنصورة االهلية‬ ‫كلية الهندسة‬  Mechanics 1 LECTURE 1 Fall 2024 Prepared by Dr. Neveen Abd El-Fattah El-Shamy Assistant Professor Mathematical and Engineering Physics Dept. Faculty of Engineering Mansoura University Mansoura National Mansoura University National University Faculty of Engineering Faculty of Engineering FallFall 20242024 Mechanics 1 AIM Apply knowledge of mathematics to solve fundamental mechanical engineering problems. LECTURES SECTIONS R. C. Hibbeler, "Engineering Mechanics: Statics and Dynamics, Fourteenth Edition", Pearson Prentice Hall, New Jersey, 2016. Dr. Neveen Abd El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 (1/40) 2021/2022 Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 2023 20242024 Mechanics 1 Intended Learning Outcomes  Recognize the types of forces, moments and the Equilibrium of Rigid Body. Select appropriate solutions to simplify systems of forces and moments to equivalent systems.  Identify support reactions and subjects of centroids.  Evaluate the characteristics of complete free-body diagrams. Apply knowledge of mathematics to write appropriate equilibrium equations from the free-body diagram, including the support reactions on a structure.  Use computational facilities to analyze simple structures frames, and machines. Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 5/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Contents  Vectors in 3D  Equilibrium of Particle  Systems of Forces and Moments  Equilibrium of Rigid Body  Frames and Machines  Center of Gravity and Centroid  Friction Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 6/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Methods of Evaluation  Final exam 50 Marks  Mid-term exam 20 Marks  Semester work 30 Marks Quizzes [10 Marks], Scientific Day [10 Marks] Activities in Tutorials [5 Marks] and Attendance [5 Marks] Total 100 Marks Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 7/23 (1/40) Dr. Neveen Abd El-Fattah 2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 WEEK 1 Introduction (Vectors in 2D) 2-3 Vectors in 3D 4 Equilibrium of Particle in 3D Quiz 1 5-6 Systems of Forces and moments 7 Equilibrium of Rigid Body in 2D 8 Midterm Exam 9 Equilibrium of Rigid Body in 2D cont. 10 - 11 Frames and Machines Quiz 2 12 Center of Gravity and Centroid 13 Friction 14 Scientific Day Final Exam Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 8/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Force Vectors Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 7/23 (1/40) Dr. Neveen Abd El-Fattah 2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National v University 2022/2023 Faculty of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Mechanics A branch of the physical science which deals with the effects of forces on objects. Rigid-Body Mechanics Statics Dynamics Deformable-Body Mechanics, Fluid Mechanics. Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 9/23 (1/40) Dr. Neveen Abd El-Fattah 2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Statics deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity. Dynamics is concerned with the accelerated motion of bodies. Scalar is a quantity that is completely characterized by a single number, positive or negative. Vector is a quantity that has both size (or magnitude) and direction. For example, velocity, acceleration, force, and moment. Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 10/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Coordinate systems Two-dimensional coordinates system y x -coordinate A(x, y) y -coordinate x O(0, 0) 12 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 11/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Three dimensional coordinate system Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 12/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Three dimensional coordinate system z P(x, y, z) y -coordinate z -coordinate O (0, 0, 0) y Q(0, y, 0) x -coordinate D (x, 0, 0) y -coordinate H(x, y, 0) x 14 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 13/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Units of measurements U.S. Customary units and SI units System of units U.S. Customary SI Unit Symbol Unit Symbol Force Pound lb newton=kg.m/s2 N Mass slug=lb.s2/ft - Kilogram kg Length Foot Meter ft m Time Second Second s s 15 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 14/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Magnitude|V| Vector V: Direction 𝜽 Line of action of the vector V Graphically tip magnitude P sense tail 𝜽 O reference line direction Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 15/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Cartesian Rectangular Components of a Vector in Two Dimensions (2D) Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 16/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 𝐕𝑥 is the component of the vector 𝐕 along the x axis; x component of the vector 𝐕 𝐕𝑦 is the component of the vector 𝐕 along the y axis; y component of the vector 𝐕 y 𝐕𝑦 𝐕 V 𝐕 = 𝐕𝑥 + 𝐕𝑦 x 𝐕𝑥 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 17/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 𝐕 = 𝐕𝑥 + 𝐕𝑦 𝐕𝑦 𝐕 𝑉𝑥 = 𝑉 cos 𝜃 𝑉𝑦 = 𝑉 sin 𝜃 𝐕𝑥 The Cartesian vector form of the vector 𝐕 𝐕 = 𝑉𝑥 𝐢 + 𝑉𝑦 𝐣 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 18/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 Determine the x and y components of the forces shown in the Figure. Hence, Writ each vector in the Cartesian vector form. 𝐹1 = 400 N Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 19/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 𝐹1𝑥 = 400sin 45𝑜 𝐹1 = 400 N 𝐹1𝑥 = 282.8 N, 𝐴𝑛𝑠. 𝐹1𝑦 = 400cos 45𝑜 𝐹1𝑦 = 282.8 N, 𝐴𝑛𝑠. Cartesian vector form of the vector 𝐅1 𝐅1 = 282.8 𝐢 + 282.8 𝐣 N, Ans. Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 20/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 𝐹2𝑥 = −150cos 30𝑜 𝐹1 = 400 N 𝐹2𝑥 = −129.9 N, 𝐴𝑛𝑠. 𝐹2𝑦 = 150sin 30𝑜 𝐹2𝑦 = 75 N, 𝐴𝑛𝑠. Cartesian vector form of the vector 𝐅2 𝐅2 = −129.9 𝐢 + 75 𝐣 N, Ans. Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 21/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National Mansoura FEMNU University National University Spring Faculty 2023 of Engineering Faculty of Engineering FallFall Mechanics1 20232024 If the vector components of V are known; 𝐕𝑥 and 𝐕𝑦 y then its magnitude V will be 𝐕𝑦 V 𝑉= 𝑉𝑥2 + 𝑉𝑦2 V 𝑉𝑦 and the direction angle  𝜃 x 𝑉𝑥 𝐕𝑥 𝑉𝑦 𝜃= tan−1 𝑉𝑥 Dr. Neveen LectureAbd 1 El-Fattah Engineering El-Shamy Mechanics: Statics I Mechanics1 22/23 (1/40) Dr. Neveen Abd El-Fattah2021/2022 El-Shamy Lecture 1 Mansoura National University Faculty of Engineering