King Fahd University of Petroleum Minerals Mechanical Engineering

King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 22

Principle of Linear Impulse and Momentum Initial momentum + Sum of all Impulse = Final momentum

Conservation of Linear Momentum for a system of Particles 0 Conservation of linear momentum equation

Impulse & Average Force Impulse

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

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 according to the impact velocity, material, size and shape of the colliding body, Coefficient of restitution e: range between 0 -1 Coefficient of restitution e: is defined along the line of impact only 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

Oblique Impact Central Impact : one Dimension Oblique Impact : 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 x-axis after the impact • The momentum is conserved along the plane of impact; so

ANGULAR MOMENTUM • For a point object the angular momentum is v m Units - kg. m 2/s or sl. ft 2/s It is a vector. Here the vector is pointing toward you. Using right-hand rule r

Angular Impulse and Momentum Principles

Conservation of Angular Momentum

Example 15 -3 W=50 Ib P=(20 t) Ib v 2=? t=2 sec. v 1=3 ft/s mk=0. 3

Example 15 -3 From rest v. B=? t=6 sec. Block A Block B

Problem m=12 Mg Fy=150 k. N V=? h=? t=6 s Start from rest

Problem m = 28 Mg At rest V=? t=4 s F = 4 - 0. 01 t 2

Example 15 -4 m. A=15 Mg m. B=12 Mg Couple together V 2=? After coupling Favg = ? In 0. 8 s

Example 15 -5 m. C =1200 -Ib mp = 8 -Ib vp=1500 ft/s t = 0. 03 s. vc 2= ? Favg= ? Favg

Example 15 -7 mp = 800 kg m. H = 300 kg From rest Impulse = ? Couple together Impulse =

Example 15 -9

Example 15 -11

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

Example 15 -13

Problem m = 400 g v 1= 2 m/s M = 0. 6 N. m v 2=? t=3 s