King Fahd University of Petroleum & Minerals

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

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

Impulse change in momentum Newton’s Second Law 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

King Fahd University of Petroleum & Minerals