Chapter 9: Linear Momentum Momentum β’ Momentum of single mass m β’ Total Momentum of several masses β’ Conservation of momentum Momentum π β’ Start with πΉ = mπ = β¦ β’ Single particle , mass βmβ & velocity π£ π = mπ£ Units of p [=] Momentum is a vector, direction isβ¦ β’ Momentum of system of particles CQ1 (on board) Conservation of momentum (p-cons) β’ If Fnet = 0, then total momentum of system is unchanged a.k.a. CONSERVED ptotal before = ptotal after (on board) Impulse J Dp = Fnet ππ‘ β’ Fnet = dp/dt ο¨ β’ For finite Dt, Fnet,avg = Dp/Dt ο¨ J = Dp = Fnet,avg Dt β’ DK = Fnet ππ₯ ο Area under F-x curve (on board) β’ Dp = Fnet ππ‘ ο Area under F-t curve (on board) β’ CQs: 1,2,3,(4,5 demo),6,7,8,9 P-cons in 1D: gliders on air track ptotal before = ? Same speeds Oο ο ο ptotal after = ? and bounce off different speeds ----> <-Same speeds CQs: 1,2,3,4,5 ο ο and stick vafter=? Types of collisions-elastic, inelastic, perfectly inelastic Momentum, total energy conserved in ALL types of collisions. β’ KE conserved β’ KE NOT conserved ο ο Elastic Inelastic β’ KE NOT conserved ο Perfectly inelastic Maximum KE loss; objects stick ο¨same final v (air track, silly putty vs crazy ball) Examples of p-cons β’ Perfectly inelastic collision: vβ = ? (on board) β’ Recoil of gun(M=3kg, m=.01kg,vb=500 m/s) vG=? J=?, average force=? (on board) Elastic collisions (on board) p-cons ο¨ KE-cons ο¨ Messy algebraβ¦ Exercise: In perfectly inelastic collision, DKE=? E-cons AND p-cons β’ Speed of bullet β ballistic pendulum β’ p-cons then E-cons β’ M=5kg, m=10g, h=5cm CTP-10,14 v1=? 9-52 A 6.5 g bullet moving directly upward at 890 m/s strikes and passes through the center of mass of a 2.7 kg block initially at rest. The bullet emerges from the block moving directly upward at 470 m/s. To what maximum height does the block then rise above its initial position? 1D p-cons then E-cons P-cons in 2D β’ πΉπππ‘ = mπ ο¨βFnet=maβ along x-axis AND along y-axis ππ‘ππ‘ = m1π£1 + m2π£2 + m3π£3 + β¦ ο¨along x-axis AND along y-axis Problem 9-75 CQs: 11, 12, 13 9-75 A projectile proton with a speed of 740 m/s collides elastically with a target proton initially at rest. The two protons then move along perpendicular paths, with the projectile path at 33° from the original direction. After the collision, what are the speeds of (a) the target proton and (b) the projectile proton? DRAW A PICTURE, THEN WRITE 2D P-CONS EQS Center of mass (com) β’ 2 equal masses βmβ separated by distance βdβ β’ masses m1 and m2 separated by distance βdβ β’ masses m1 and m2 separated by distance βdβ, located at x1 and x2 com in 2D Center of mass (com) in 2D, 3D β’ M = m1 + m2 + + m3 β¦ β’ β’ π1π₯1+π2π₯2+π3π₯3+β― Xcom = π π1π¦1+π2π¦2+π3π¦3+β― Ycom = π Mπ = π ππ ππ 9-5 What is the x coordinate (in m) of the center of mass for the uniform plate shown in the figure if L = 13 cm? F=ma for com Mπ = d/dt ο¨ d/dt ο¨ π ππ ππ β’ πΉπππ‘ = π πΉπ = πΉππ₯π‘ + β’ Explosion of projectile πΉπππ‘ = πΉππ₯π‘ (on board) Explosion of projectile β’ External force = gravity causes trajectory β’ Internal forces cause explosion
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