p250c2:19: Linear Momentum and CollisionsMomentum: a measure of motionForce: a cause of change in motionWhat changes when a force is applied?Linear Momentum: p ≡ mv (vector!!!!!)the tendency of an object to pursue straight line motionExample:What is the magnitude of the momentum of a 1180 kg car traveling at 30.0 mph (13.4 m/s)? What is the magnitude of the momentum of a .142 kg baseball thrown with a speed of 101 mpg (45.1 m/s)? with timechanges;changenot does massbut ;vmtvmFtvmamF∆∆=∆∆==p250c2:2Impulse: the change in motionExample: A .144 kg baseball moving towards home plate with a speed of 43.0 m/s is bunted by a bat which exerts an average force of 6.50E3 N on the ball in the direction of the pitcher for 1.30 ms. What is the impulse on the ball and what is its final speed?vmptFJamFtavvmpJ∆=∆=∆==∆=∆∆=∆= and sincep250c2:3Conservation of momentumtwo (or more) bodies + action/reaction + no external forcesFAB = − FBA → equal but opposite impulses→ ∆pA + ∆pB = 0When the net external force on a system is zero, the total momentum of that system is constant.p1 + p2 + p3 + ... is constantCollisions, explosions etc: m1v1 + m2v2 =m1v’1 + m1v’2p250c2:4Example: Two canoes meet in the middle of a lake, whereupon a person in one canoe pushes on the other canoe with a force of 46 N to separate the canoes. If the first canoe and occupants have a total mass of 30 kg and the second canoe and occupants have a mass of 250 kg, determine the momentum and speed of each canoe after 1.20 s of pushing. (What is the TOTAL initial and final momentum of the two canoe system?)p250c2:5Collisions (in the absence of external forces)Elastic Collisionsconserve KE (total KE is the same before and after collision)this is a “springy” collisionInelastic Collisionssome KE is lost during collision (heat, sound, etc.)this is a somewhat “sticky” collisionCompletely Inelastic Collisionsobjects stick togethermaximum possible loss of KEIn all collisions, the total momentum is conserved!p250c2:6Example: A 1200 kg car moving at 2.5 m/s is struck in the rear by a 2600 kg truck moving at 6.2 m/s. If the vehicles stick together after the collision, what is the speed of the wreckage just after the collision?p250c2:7Example: A 95.0 kg running back moving at3.75 m/s collides head on with a 111 kg linebacker moving in the opposite direction at 4.10 m/s who makes a successful tackle. What is the speed of the players just after the collision? What is their total initial and final kinetic energies?p250c2:8Elastic collisionsconservation of KE + conservation of momentumin one dimension. impactor (m1) hits target (m2) at rest1211,202121,12,222,11201,22,11012:algebra212121vmmmvvmmmmvvmvmvmvmvmvmffffff+=+−=++=+=Chapter 8: Applying Conservation Lawstrack demo's!!!!!p250c2:9Example: A 96 kg bumper car moving 1.24 m/s bounces (elastically) off a stationary 135 kg bumper car at rest. What are the final velocities of the cars?p250c2:10Center of Mass aka Center of Inertia“average” location of mass of a system of particlesthe center of mass of a system is also the balance point where the system can be balanced (in a uniform gravitational field)→ aka the center of gravitythe center of mass of an object does NOT need to be located in the physical body.horseshoe, egExternal forces and the motion of center of massiiicmcmcmiiicmmmmmmmzysimilarlymxmmmxmxmxΣΣ=++++=ΣΣ=++++=rrrr212211212211),(dtMddtdMMsincedtdMreactionactionmmMcmcmcmextcmintintextcm)(02211vvaPFaFFFFaaa===Σ==Σ−Σ+Σ=Σ=++=p250c2:11Example: Suppose two masses are separated by a distance of .500 m. One of the masses is .260 kg and the other is .170 kg. How far from the first mass is the center of mass of this