Linear Momentum and Collisions 9.1 Linear Momentum and Its Conservation9.2 Impulse and Momentum9.3 Collisions9.4 Elastic and Inelastic Collisions in One Dimension9.5 Two-Dimensional Collisions9.6 The Center of Mass9.7 Motion of a System of Particles9.8 (Optional) Rocket Propulsion
9.1 Linear Momentum and Its Conservation The linear momentum of a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle:
Conservation of Momentum for a Two-Particle System Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.
9.2 Impulse and Momentum The impulse of the force F acting on a particle equals the change in the momentum of the particle caused by that force.
EXAMPLE : How Good Are the Bumpers
Solution
9.3 Collisions
9.4 Elastic and Inelastic Collisions in One Dimension An elastic collision between two objects is one in which total kinetic energy (as well as total momentum) is the same before and after the collision. An inelastic collision is one in which total kinetic energy is not the same before and after the collision (even though momentum is constant). – perfectly inelastic collision – inelastic collision
Elastic Collisions
EXAMPLE : A Two-Body Collision with a Spring
Solution
9.5 Two-Dimensional Collisions
EXAMPLE : Billiard Ball Collision
Solution
9.6 The Center of Mass
The center of mass of any symmetric object lies on an axis of symmetry and on any plane of symmetry.
EXAMPLE : The Center of Mass of Three Particles
Solution
EXAMPLE : The Center of Mass of a Rod
Solution
9.7 Motion of a System of Particles The center of mass of a system of particles of combined mass M moves like an equivalent particle of mass M would move under the influence of the resultant external force on the system.
EXAMPLE : The Exploding Rocket
Solution
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Homework.4
9.8 Rocket Propulsion