Lecture no 17&18 Conservation of Momentum Prepared by Engr.Sarfaraz Khan Turk Lecturer at IBT LUMHS Jamshoro

Momentum In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg m/s, or equivalently, N s) is the product of the mass and velocity of an object. For example, a heavy truck moving fast has a large momentum—it takes a large and prolonged force to get the truck up to this speed, and it takes a large and prolonged force to bring it to a stop afterwards. If the truck were lighter, or moving more slowly, then it would have less momentum. Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude:p=mv

Momentum Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

Conservation of Momentum

Conservation on Momentum In the absence of an external force the momentum of a closed system is conserved.

Law of Conservation of Momentum In a closed system, the vector sum of the momenta before and after an impact must be equal. Before After m1v1 +m2v2 = m1v1’ + m2v2’

Closed System: A system that has no gain nor loss of mass.

Isolated System: A closed system with no net external force acting on it.

Internal and External Forces Internal Forces: act between objects within a system. External Forces: are exerted by objects outside the system.

A stationary firecracker explodes A stationary firecracker explodes. What is the total momentum of the pieces that it breaks into? Question Coyle ,4th of July 2009, Hudson River

Example: Recoiling Cannon

Example 1: Recoiling Cannon A cannon of mass 750kg shoots a cannon ball of mass 30kg with a velocity of 20m/s. Find the recoil velocity of the cannon. m1v1 +m2v2 = m1v1’ + m2v2’ Answer: -0.8m/s

Collisions Elastic (Kinetic Energy is conserved) Inelastic (Kinetic Energy is not conserved) Deformed objects Objects stick together Note: Momentum is conserved in both types of collisions.

Example 2: Inelastic Collision A bullet of mass 0.010kg is shot at a speed of 30m/s towards a 5kg stationary block. The bullet becomes embedded in the block an the two fly off together. Find the speed with which they fly off. Answer: 0.06m/s

Problem 3 A 45 kg student is riding on a 7kg scateboard with a velocity of +4m/s. The student jumps of the cart with a velocity of -1m/s. Find the velocity of the scateboard after the student jumped off. Answer: +36m/s