PHY 101 1st Edition Lecture 17 Outline of Last Lecture I Comparison Impulse Momentum Theorem vs Work Energy Theorem II Relationship Between Kinetic Energy Momentum Outline of Current Lecture III 6 2 Conservation of Momentum IV More on Conservation of Momentum V 6 3 Collision in 1D VI Perfectly Inelastic in 1D Current Lecture 6 2 Conservation of Momentum Pi m1v1i m2v2i before condition Pf m1v1f m2v2f after condition Law of conservation of momentum total momentum of an isolated system is a constant The momenta of individual objects in the systems any changes after a condition but the vector summation of all momenta does not change This is a direct consequence of Newton s 3rd law Action and reaction forces are always equal in magnitude opposite in direction and act on different objects During the collision o Object 1 exerts a force F12 to object 2 o Object 2 exerts a force F21 to object 1 Suppose the collision is a t Apply the impulse momentum theorem to object 1 o F21 t p1 m1v1f m1v1i Apply the impulse momentum theorem to object 2 o F12 t p2 m2v2f m2v2i According to Newton s 3rd law o F21 F12 We have F21 t F12 t Therefore o M1v1f m1v1i m2v2f m2v2i These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Rearrange the equation o M1v1f m2v2f m1v1i m2v2i The total momentum remains unchanged Example o An archer of mass 60kg stands at rest on frictionless ice He fired a 0 5kg arrow horizontally at 50m s o What is the archer s speed after he fires the arrow o Solution both the archer and the arrow have no initial speeds Initial momentum of the system is zero M1v1f m2v2f 0 m1v1f m2v2f V1f m2v2f m1 0 5 50 60 0 42 m s Recoil kickback More on Conservation of Momentum M1v1f m2v2f m1v1i m2v2i After collision before collision The total momentum is constant doesn t change Conservation of momentum only applied to isolated systems A system is said to be isolated if there is no external force acting on it 6 3 Collision in 1D Collision 2 objects move closer to each other and interact They may or may not move apart after the collision For an isolate systems o The total momentum is conserved o The total KE may or may not stay the same Different types of collision o Elastic a collision in which both momentum and KE are conserved o Inelastic a collision in which only momentum is conserved When 2 objects collide stick together the collision is perfectly inelastic Momentum is always conserved for an isolated systems regardless of type of collision Example o Elastic collision billiard ball approximately o Inelastic collision most macroscopic collision are inelastic o Ex A head on collision of cars o Before the collision Assuming m1 m2 v1i v2i Total momentum pi 0 Total KE 0 o After the collision V1f v2f 0 total momentum pf 0 Total KE 0 not conserved o Where does the KE go Perfectly Inelastic in 1D Perfectly inelastic collision two colliding bodies stick together after collision The momentum is always conserved Before collision p1 m1v1 m2v2i After the collision they stick together have a common vf o Pf m1vf m2vf m1 m2 vf Momentum conservation pf pi o m1 m2 vf m1v1i m2v2i vf m1v1i m2v2i m1 m2
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