ENGR 214 Chapter 14 Systems of Particles

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Presentation transcript:

ENGR 214 Chapter 14 Systems of Particles All figures taken from Vector Mechanics for Engineers: Dynamics, Beer and Johnston, 2004

Methods of analysis Newton’s law: If we have “n” particles: Linear momentum For a system of particles, the total linear momentum is Angular momentum: For a system of particles, the total angular momentum is:

Methods of Analysis Kinetic energy of a system of particles: Principle of work & energy: - can be applied to each particle - can be applied to entire system Principle of conservation of energy: Principle of impulse & momentum: For a system of particles:

Sample Problem 14.4 l Ball B, of mass mB, is suspended from a cord, of length l, attached to cart A, of mass mA, which can roll freely on a frictionless horizontal tract. While the cart is at rest, the ball is given an initial velocity v0. Determine (a) the velocity of B as it reaches its maximum elevation, and (b) the maximum vertical distance h through which B will rise.

Conservation of energy h But at maximum height, we have Principle of work & energy:

Together with Solve for h: Apply principle of impulse & momentum: Along horizontal direction: Together with Solve for h:

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