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

Sir Isaac Newton Proposed fundamental laws that are the basis of modern mechanics 3 laws of motion law of gravitation

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 = F N 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.

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

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

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

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

Normal & Frictional Force F FfFf FNFN Action-Reaction forces - mg = F N mg

Static Friction (  s ) 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. Static F f =  s F N Dynamic F f =  k F N Applied external force Friction

Kinetic Friction (  k ) 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. Static F f =  s F N Dynamic F f =  k F N Applied external force Friction

Friction (con.) When to use static friction or kinetic friction ? 1.If the 2 objects have relative motion – always use kinetic friction 2.If the calculated friction force to keep the 2 objects to stay together is greater than the maximum static friction – use kinetic friction 3.Otherwise: no relative motion, friction force is smaller than F max – use static friction

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

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

Problem a = ?

Example 13-5 m A = 3 kg m B = 5 kg From rest v B = ? In 2 second Block A Block B Same Same ٍ should be

V A = ? 2S c + S A = L 0 = 2a c + a A a A = -2a c Problem

Review Example 13.1 Example 13.2 Example 13.3 Example 13.4