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SC.CE.05.01 Collisions: Momentum and Impulse Momentum: The product of the mass of an object and its velocity Momentum = “p” p=mv If mass is constant, then a change of momentum equals mass times change in velocity: Δp=mΔv A vector quantity Vector means… Impulse: The average force multiplied by its time interval of action Impulse = FΔt A vector quantity Vector means… Simply stated: Impulse = change in momentum =Δp Impulse/momentum principle: The impulse acting on an object produces a change in momentum of the object that is equal both in magnitude and direction to the impulse For example: m=7kg v=2m/s p=14kg ×m/s m=0.07kg v=200m/s p=14 kg × m/s Conservation of Momentum: When the net external force acting on a system is zero, the total momentum of the system is conserved In other words: the momentum before a collision will equal the momentum after a collision When internal forces are equal (but opposite), momentum is conserved Example: A 100 kg fullback moving straight downfield with a velocity of 5 m/s collides head on with a 75 kg defensive back moving in the opposite direction with a velocity of -4m/s. The defensive back hangs on to the fullback, and the two players move together after the collision. a. What is the initial momentum of each player? b. What is the total momentum of the system? c. What is the velocity of the two players immediately after the collision? Example (cont’d) a: What is the initial momentum of each player? Fullback: m = 100 kg v = 5 m/s p=? p = mv p= Defensive back: m = 75 kg v = -4 m/s p=? p = mv p= b. What is the total momentum of the system? p total = p fullback + p defensive back p total = 500 kg x m/s + -300 kg x m/s p total = 200 kg x m/s c. What is the velocity of the two players immediately after the collision? v=? m= 100 kg + 75 kg =175 kg p=mv So: v=p/m v= 200 kg x m/s 175 kg Types of Collisions: Perfectly Inelastic to Perfectly Elastic Extend your knowledge of momentum and energy conservation! Perfectly Inelastic Collisions A collision in which the objects stick together after colliding No bounce If p is known before collision for both objects, we simply add them together to get final p A lot of the original kinetic energy is transformed Example: railroad car coupling, two balls of clay, a football tackle Partially Inelastic Some kinetic energy is transformed Elastic No kinetic energy is transformed Atoms collide without “spending” energy When pool balls collide: Most collisions are elastic: both momentum and kinetic energy are conserved Momentum is transferred from the cue ball to the target ball We can determine the velocity of both balls after collision It gets tricky when multiple pool balls are involved, but I know you can do it! Collisions at an Angle Oh geez, here we go… An Inelastic Two-Dimensional Collision: Remember that momentum is a vector quantity? Now our football players from Monday are running perpendicular to one another p2=300kg x m/s 31° p1=500kg x m/s Elastic Two-Dimensional Collisions Initial kinetic energy = 1/2mv2 must also equal the sum of the kinetic energies Collision Type Characteristics Examples Totally elastic KE Atomic Less elastic Less More inelastic Totally inelastic is conserved Usually involves collisions where objects can’t touch No damage to either object particles with similar charges Magnets with similar poles facing each other damage or heat Ball bearings created Well inflated Less sound created basketball More damage or A ball with very little heat bounce More sound created Objects` stick together and become one system Involves greatest loss of KE A ball of soft clay A bad car accident where cars stick together