King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 18

Kinetics of a Particle: Impulse and Momentum Objective: To develop the principle of linear impulse and momentum for a particle. To solve problems involving force, time, and velocity.

Newton’s Second Law Impulse change in momentum Principle of linear impulse and momentum equation

Linear momentum L = mv Measure of impact effect Compare bullets with small mass and high velocity Ship with huge mass and slow velocity L is a vector -- points in same direction as v Unit: kg.m/s or slug.ft/s Components (rectangular coordinates): Lx=mvx, Ly=mvy, Lz=mvz

Linear Impulse Measure the effect of force during the time force acts. I is a vector quantity in the direction of force Unit N.s or Ib.s When F is constant

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

Principle of Linear Impulse and Momentum for a system of Particles

Scalar Equations

Free Body Diagram Select the particle Establish x, y frame Establish the direction of the particle initial and final velocities Drew the impulse and moment diagrams. Include all the forces acting on the particle’s FBD will create an impulse, even though some of these forces will do no work. Resolving the vectors along the x, y axis Apply

Example 15-1 m=100 kg At rest smooth t=10 s V2=? N=?

Example 15-3 W=50 Ib P=(20t) Ib V2=? T=2 sec. V1=3 ft/s mk=0.3

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

Problem 15-4 m=12 Mg Fy=150 kN V=? h=? t=6 s Start from rest

Problem 15-6 m = 28 Mg At rest V = ? t = 4 s F = 4 - 0.01 t2

Problem 15-19 m = 75 kg Start from rest v = 200 mm/s t = 0.4 s. mk= 0.5 Impulse = ?

Thank You