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King Fahd University of Petroleum & Minerals

King Fahd University of Petroleum & Minerals. Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 11. Sir Isaac Newton 1642-1727. Proposed fundamental laws that are the basis of modern mechanics 3 laws of motion law of gravitation. Newton ’ s laws.

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King Fahd University of Petroleum & Minerals

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  1. King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 11

  2. Sir Isaac Newton 1642-1727 Proposed fundamental laws that are the basis of modern mechanics 3 laws of motion law of gravitation

  3. Newton’s laws Law of inertia a body in motion will stay in motion and a body at rest will stay at rest unless acted upon by a net external force. Law of force-acceleration A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force Law of action-reaction for every action, there is an equal and opposite reaction mg = FN Law of gravitation - all bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

  4. 13.2 The Equation of Motion • Free-Body diagram (Force Diagram) • Kinetic diagram (acceleration Diagram)

  5. 13.3 Equation of Motion for a System of Particles Internal forces cancel each other

  6. 13.4 Equations of Motion: Rectangular Coordinates • When the net force is projected to separate coordinate axes the Newton’s second law still holds

  7. Free Body Diagram Method • Draw each object separately • Draw all the forces acting on that object • Get x and y components of all the forces to calculate the net force • Apply Newton’s second law to get acceleration • Use the acceleration in any motion analysis and establish a Kinetic Diagram ma

  8. Normal & Frictional Force Action-Reaction forces - mg = FN F mg Ff FN

  9. Dynamic Ff = kFN Static Ff = sFN Friction Applied external force Static Friction ( ms ) • Static friction – parallel force on the surface when there is no relative motion between the 2 objects • Static friction force can vary from zero to Maximum • The coefficient of static friction • is material dependent.

  10. Dynamic Ff = kFN Static Ff = sFN Friction Applied external force Kinetic Friction ( mk ) • Kinetic friction – parallel force on the surface when there is relative motion between the 2 objects • Kinetic friction force is always the same • The coefficient of Kinetic friction • is material dependent.

  11. Spring Force • Spring force • k : spring stiffness (N/m) • s : stretched or compressed length s

  12. Example 13-4 • m = 2 kg • y = 1m • smooth • a = ?

  13. Problem a = ?

  14. Same Example 13-5 m A= 3 kg m B= 5 kg From rest vB= ? In 2 second Block B Sameٍshould be Block A

  15. Problem VA = ? 2Sc+ SA= L 0 = 2ac+ aA aA= -2ac

  16. Review • Example 13.1 • Example 13.2 • Example 13.3 • Example 13.4

  17. Thank You

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