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Lecture no 17&18 Conservation of Momentum

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

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Lecture no 17&18 Conservation of Momentum

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

  2. Momentum • In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kgm/s, or equivalently, Ns) 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

  3. 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.

  4. Conservation of Momentum

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

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

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

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

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

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

  11. Example: Recoiling Cannon

  12. 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

  13. 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.

  14. 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

  15. 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

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