Collision and Explosion PHYSICS 220 Lecture 12 Collision and Explosion Lecture 12

Example m2 m1 v02 v01 initial m2 m1 vf final A freight train is being assembled in switching yard. Car 1 has a mass of m1=65 103kg and moves at a velocity v01=0.80 m/s. Car 2 has a mass of m2=92 103kg and moves at a velocity v02=1.3 m/s and couples to Car 1. Neglecting friction, find the common velocity vf of the cars after they become coupled. m2 m1 v02 v01 initial m2 m1 vf final Lecture 12

Example A fright train is being assembled in switching yard. Car 1 has a mass of m1=65 103kg and moves at a velocity v01=0.80 m/s. Car 2 has a mass of m2=92 103kg and moves at a velocity v02=1.3 m/s and couples to it. Neglecting friction, find the common velocity vf of the cars after they become coupled. Apply conservation of momentum: Pi=m1vo1+m2v02 Pf=(m1+m2)vf (m1+m2)vf = m1v01+m2v02 Lecture 12

iClicker S Pinitial = S Pfinal M v = M vf + M vf v = 2vf vf = v/2 A railroad car is coasting along a horizontal track with speed v when it runs into and connects with a second identical railroad car, initially at rest. Assuming there is no friction between the cars and the rails, what is the speed of the two coupled cars after the collision? A) v B) v/2 C) v/4 D) 2v S Pinitial = S Pfinal M v = M vf + M vf v = 2vf vf = v/2 Lecture 12

Center of Mass Center of Mass L m Example 1: xCM = (0 + mL)/2m = L/2 L X=L Lecture 12

Lecture 12

Center of Mass For symmetric objects that have uniform density the CM will simply be at the geometrical center! + CM Lecture 12

Exercise The disk shown below (1) clearly has its CM at the center. Suppose the disk is cut in half and the pieces arranged as shown in (2): Where is the CM of (2) as compared to (1)? A) higher B) lower C) same X CM (1) (2) Lecture 12

Exercise The CM of each half-disk will be closer to the fat end than to the thin end (think of where it would balance). The CM of the compound object will be halfway between the CMs of the two halves. X X CM This is higher than the CM of the disk X X (1) (2) Lecture 12

Dynamics of Many Particles ptot = mtotVcm FextDt = Dptot = mtotDVcm or Fext = mtotacm So if Fext = 0 then Vcm is constant Center of Mass of a system behaves in a SIMPLE way - moves like a point particle! - velocity of CM is unaffected by collision if Fext = 0 Lecture 12

Astronauts & Rope Two astronauts at rest in outer space are connected by a light rope. They are at a distance L and they begin to pull towards each other. Where do they meet? A) L/2 B) 2L/5 C) 1/5 L M = 1.5m m L Lecture 12

Astronauts & Rope... They start at rest, so VCM = 0. VCM remains zero because there are no external forces. So, the CM does not move! They will meet at the CM. M = 1.5m m CM L x=0 x=L Finding the CM: If we take the astronaut on the left to be at x = 0: Lecture 12

Explosion “before” M Example: m1 = M/3 m2 = 2M/3 v1 v2 “after” m1 m2 Which block has larger |momentum|? Each has same |momentum| Which block has larger speed? mv same for each  smaller mass has larger velocity Which block has larger kinetic energy? K = mv2/2 = m2v2/2m = p2/2m  smaller mass has larger kinetic energy Is mechanical (kinetic) energy conserved? NO Lecture 12

Explosion and Collision Procedure “before” “after” M m1 m2 Draw “before” and “after” Define system so that Fext = 0 Set up a coordinate system Compute ptotal “before” Compute ptotal “after” Set them equal to each other Collision “before” “after” m1 m2 Lecture 12 1

Type of Collision Elastic Collisions: Inelastic Collisions: collisions that conserve mechanical energy Inelastic Collisions: collisions that do not conserve mechanical energy Completely Inelastic Collisions: objects stick together Completely Inelastic Elastic Inelastic Lecture 12 1

2-D Problems Ptotal,x and Ptotal,y independently conserved after before Ptotal,x and Ptotal,y independently conserved Ptotal,x,before = Ptotal,x,after Ptotal,y,before = Ptotal,y,after Lecture 12

Elastic Collision Assuming Collision is elastic (KE is conserved) Balls have the same mass One ball starts out at rest pf pi vcm F Pf before after Lecture 12

Playing Pool According to what you have learned so far, you would want think twice before attempting the shot because … Lecture 12

Conservation of momentum Conservation of energy vc,i Vp,f vc,f 900 Lecture 12

Completely Inelastic Collision Lecture 12

Completely Inelastic Collision x before m2 v2 m1 v1 after m1+m2 vf  Work on overhead -- symbols only. Find vf and  Lecture 12

Completely Inelastic Collision in Two Dimensions Find vf and  x after m1+m2 vf  y Work on overhead -- symbols only. Lecture 12

iClicker Which of these is possible? (Ignore friction and gravity) A B M “before” “after” A B Which of these is possible? (Ignore friction and gravity) A B C = both D = neither Lecture 12