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

2. 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:

3. 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:

4. 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.

5. Conservation of energyh
But at maximum height, we have
Principle of work & energy:

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