King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 20

Objective To analyze the mechanics of impact and introduce the coefficient of restitution

Conservation of Linear Momentum for a system of Particles Conservation of linear momentum equation

Impact Impact occurs when two bodies collide with each other during a very short period of time. Types of impact: –Central impact –Oblique impact Line of impact Plane of impact

Central Impact Mechanics of impact 1- Collision occur when 2- Deformation period

3- Maximum deformation period 4- Restitution period 5- Separation period

Coefficient of restitution “e” Coefficient of restitution “e” is defined as the ratio of the restitution impulse to the deformation impulse. Coefficient of restitution “e” is defined as the ratio of relative velocity after impact to the relative velocity before impact Coefficient of restitution “e” is a function of the impact velocity, material, size and shape of the colliding body, Coefficient of restitution “e” range between 0-1 Elastic impact e = 1 (re-bounce with same velocity) Plastic impact e = 0 (couple or stick together and move with common velocity)

Procedure for Analysis Identify the intial velocity “ “you may use” T 1 + V 1 = T 2 + V 2 Apply the conservation of momentum along the line of impact, you will get one equation with two unknown velocity Use the coefficient of restitution to obtain a second equation Solve both equation for final velocities after the impact

Example 15-9

Oblique Impact Central Impact : in one Dimension Oblique Impact : in two Dimension Four unknowns

Procedure for Analysis Establish x-axis as line of impact Establish y-axis as plane of impact Resolve the velocity components along x, and y as Apply the conservation of momentum along the line of impact Use the coefficient of restitution to obtain a second equation Solve both equation for final velocities along the line of the impact The momentum is conserved along the plane of impact; so

Summary for Analysis Along the line of the impact only Along the Plane of the impact only

Example 15-11

Momentum of particle A,B is conserved along the y axis, since no impulse acts on particle A,B