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Ch 13: Momentum and Impulse M Sittig AP Physics B Summer Course 2012 2012年AP物理B暑假班 Don’t forget Add Fnet=ma to Equation Wall One-Minute Drill (and graph) Momentum N3: Forces come in pairs, F12 = F21 (equal in magnitude, opposite in direction). When two objects interact for time Δt, we can write: F12·Δt = F21·Δt m1·a1·Δt = m1·(Δv1/ Δt) ·Δt = m1·Δv1 = m2·Δv2 Time of collision Momentum (it’s a vector) Momentum is defined as p = m·v. Momentum is conserved: if one object gains momentum from interacting with another object, the other object loses an equal amount of momentum. How much momentum is gained or lost in a collision? F12·Δt = m1·Δv1 Momentum p m v Momentum (kg ·m/s) Mass (kg) Velocity (m/s) Example Problem What is the total momentum of the system that includes spheres 1 and 2 only? Practice Problem What is the total momentum of the system that includes all three spheres? Practice Problem What is the total momentum of the system that includes all three spheres? Practice Problem An object of mass m drops from rest and falls for a time t. Ignore air resistance. After time t the magnitude of momentum is ___. Impulse F12·Δt = m1·Δv1 If the mass of an object doesn’t change in a collision, then m·Δv = Δp, so F·Δt = change in momentum. Let’s give this a name… impulse! Impulse J F t p Impulse (N·s) Force (N) Time (s) Change in momentum(k g·m/s) Practice Problem Two balls of equal mass swing down and hit identical bricks while traveling at identical speeds. Ball A bounces back, but ball B stops immediately upon hitting the brick. Which ball has a better chance of knocking the brick over? Practice Problem In the diagram, a 40-kg block is moving along a horizontal frictionless surface, acted upon by two horizontal forces as shown. What is the displacement of the block during a 5-second time interval? Practice Problem In the diagram, a 40-kg block is moving along a horizontal frictionless surface, acted upon by two horizontal forces as shown. What is the change in the momentum of the block during a 5-second time interval? Practice Problem In the diagram, a 40-kg block is moving along a horizontal frictionless surface, acted upon by two horizontal forces as shown. What is the net impulse delivered to the block during a 5-second time interval? Practice Problem The diagram shows an object in its initial state (on the left) and the final state on the right. Which of the following vectors best describes a possible direction of the impulse imparted on the object between the initial and the final moments? Conservation of Momentum Within a system, if there are no external forces acting, total momentum is conserved. Total Momentumbefore collision = Total Momentumafter collision Momentum is a vector, so it’s conserved in horizontal and vertical directions. You can resolve momentum into x- and ycomponents. Example Problem Practice Problem A family which includes a girl with a mass of 20 kg and her younger brother who has a mass of 15 kg is out playing on a pond covered with frictionless ice. The girl and her brother are standing next to each other at rest, when suddenly the boy reaches out and gives his sister a big shove. As a result of the push, the girl ends up moving off at a speed of 3.0 m/s. What is the boy's resulting motion? Practice Problem A ball of mass m, moving with speed v, collides with another ball of mass M, initially at rest. After the collision the balls stick together, moving with speed V. Find an expression for V in terms of m, M and v. Elastic and Inelastic Collisions Elastic Collisions Momentum is conserved. Kinetic energy is conserved. Perfectly elastic collisions: gas molecules, small particles. Inelastic Collisions Momentum is conserved. Kinetic energy is NOT conserved. Perfectly inelastic collision: the two objects stick together. Elastic and Inelastic Collisions In our daily life, most collisions are somewhere in between. Practice Problem What kind of collision was this?