# LN_Sec_15-1_15-3 - PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM...

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PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (Section 15.1) Today’s Objectives : Students will be able to: a) Calculate the linear momentum of a particle and linear impulse of a force. b) Apply the principle of linear impulse and momentum. c) Apply the principle of linear impulse and momentum to a system of particles. d) Understand the conditions for conservation of momentum.

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LINEAR MOMENTUM AND IMPULSE The impulse may be determined by direct integration . Graphically, it can be represented by the area under the force versus time curve . If F is constant, then I = F (t 2 –t 1 ) . Linear impulse : The integral F dt is the linear impulse, denoted I . It is a vector quantity measuring the effect of a force during its time interval of action. I acts in the same direction as F and has units of N·s or lb·s. Linear momentum : The vector m v is called the linear momentum, denoted as L . This vector has the same direction as v . The linear momentum vector has units of (kg·m)/s or (slug·ft)/s.
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM This equation represents the principle of linear impulse and momentum. It relates the particle’s final velocity, v 2 , and initial velocity ( v 1 ) and the forces acting on the particle as a function of time. The principle of linear impulse and momentum is obtained by integrating the equation of motion with respect to time. The equation of motion can be written F = m a = m (d v /dt) Separating variables and integrating between the limits v = v 1 at t = t 1 and v = v 2 at t = t 2 results in m v 2 –m v 1 d v m F dt v 2 v 1 t 2 t 1 = =

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PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM The two momentum diagrams indicate direction and magnitude of the particle’s initial and final momenta, m v 1 and m v 2 . The impulse diagram is similar to a free body diagram, but includes the time duration of the forces acting on the particle. The particle’s initial momentum plus the sum of all the impulses applied over [t 1 t 2 ] is equal to the particle’s final momentum. The principle of linear impulse and momentum in vector form is written as m v 1 + = m v 2 F dt t 2 t 1
IMPULSE AND MOMENTUM: SCALAR EQUATIONS The scalar equations provide a convenient means for applying the principle of linear impulse and momentum once the velocity and force vectors have been resolved into x, y, z components.

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## This note was uploaded on 04/25/2009 for the course 222 AND 34 dynamics a taught by Professor Ibrahim during the Spring '09 term at American University of Sharjah.

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LN_Sec_15-1_15-3 - PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM...

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