Statics & Dynamics

1. Statics & Dynamics University of Ontario Institute of Technology ENGR 2020

2. Lecture Outline • Introductory details • Fundamentals • Definitions • Solution Style and Technique • Vectors

3. Contact Details • Dr. Jean-Claude (John) Stranart • 416-738-4403 (emergency or occasional evening) • jcstranart@hotmail.com ???@uoit.ca • Subject: UOIT: xxxxx • Web site / Web CT • fax: 416-978-5741

4. Dr. Jean-Claude (John) Stranart • Background • Ph.D. University of Toronto • M.A.Sc. University of Toronto • B.A.Sc. Waterloo • Research in mechanics, finite elements, fatigue/fracture, smart structures

5. Subject Matter/Overview • Statics • Equilibrium of a Particle • Force System Resultants • Equilibrium of a Rigid Body • Structural Analysis • Centre of Gravity/Centroid • Friction

6. Subject Matter/Overview • Dynamics • Kinematics of a Particle • Kinetics of a Particle • Force, Acceleration • Work, Energy • Impulse, Momentum • Kinematics of a Rigid Body • Kinetics of a Rigid Body • Force, Acceleration • Work, Energy • Impulse, Momentum

7. Textbook • Engineering Mechanics: Statics and Dynamics • R.C. Hibbler, 10th Edition • Work book/Study Pack

8. Lectures • 9:10 –11:00 Wednesday & Friday • Room UA 1240 • 10 minute break ~ 10:00 • Available for questions after class • If something is not clear, bring it up, don’t wait • Room change on May 13 (only) • UA 1120 or UA 1140

9. Tutorial • Wednesday • 12 – 2 pm • Room UA 2120 • Is everyone available ? (Midterms)

10. Office Hours • UA 3045 • To be determined

11. Marks/grading • Problem Sets (5) 25% • Project 5% • 10-15 hours, details to follow • Midterm Test 1 10% • June 1 • Midterm Test 2 20% • July 6 • Final Exam 40%

12. Problem Sets • Due at the beginning of class on: • May 20 • June 3 • June 17 • July 8 • July 22 • Assigned from Hibbler • ~ 20 questions, ONLY 2 marked • Est. 6 hours/set

13. Students • What is your background? • Why are you taking the course? • What do see as the biggest challenges? • What is your learning style? • What software do you know ? • Excel, MatLab, MathCad, Maple

14. Fundamentals • Mechanics • Rigid-body mechanics, deformable-body mechanics, fluid mechanics • Rigid body mechanics • Statics – equilibrium of bodies • ie at rest or constant velocity • Dynamics • Accelerated motion of bodies • Include turning, curving,

15. Fundamentals • Basic quantities • Length • Time • Mass • Force • SI • length [m], time [s], mass [kg] • force is derived [N = kg m s-2 ] • US customary • length [ft], time [s], force [lb, lbf] • mass is derived [m=W/g, 32.2 lb/ 32.2 ft/s2 = 1.0 slug]

16. Fundamentals

17. Fundamentals • Idealisations • Particle: has mass but size can be neglected • simplifies analysis • ie earth w.r.t. its orbit • Rigid body • Application of load does not change geometry of the body • Concentrated force • Loading is assumed to act on a point • Area over which load is applied is small w.r.t. size of body

18. Newton’s Three Laws of Motion • Basis of rigid body mechanics • Assumes non-accelerating frame of reference • 1) a particle at rest, or moving in a straight line with constant velocity, will remain in that state provided the particle is not subjected to an unbalanced force

19. Newton’s Three Laws of Motion • 2) a particle subjected to an unbalanced experiences an acceleration that has the same direction as the force and a magnitude that is proportional to the force*

20. Newton’s Three Laws of Motion • 3) for every force acting on a particle, the particle exerts an equal, opposite and colinear reaction

21. Analysis Procedure • Read problem carefully and relate the physical situation to the applicable theory • Draw necessary diagrams, tabulate problem data • Apply the relevant principles(mathematical expression) • Solve the equations • Check unit consistency • Check significant digits

22. Analysis Procedure (continued) • Evaluate the answer • Judgement, common sense • Is it reasonable • Can the solution be validated by another method?

23. Solution Style • Two aspects to any engineering solution • Technical solution that is correct • Communication of the solution to others • As essential as technical accuracy • Solution must be clearly presented and able to be followed

24. Solution Style • Statement of the problem • Free body diagram • Assumptions, relevant principles • Applicable equations • Solution • Concluding statement • Boxed/highlighted

25. Free Body Diagram • Sketch of the particle/body/system isolated from the surrounding system • ALL forces which the surroundings exert on the particle/body/system are sketched on the body

26. Free Body Diagram: Procedure • Draw/sketch the particle isolated from its surrounding • Include co-ordinate axes • Indicate ALL forces that act on the body • Active/applied forces – ie loads, weight, magnetic, electrostatic • Reactive forces – constraints, supports • Known forces are labeled with magnitudes and directions

27. Free Body Diagram: Procedure • Unknown forces represented by letters and arrows (assumed direction) • In solution, if ‘negative’ force is obtained, minus sign indicates that the force is in the opposite direction of that originally assumed • Examples