PHYSICS 220 Lecture 12 Collision and Explosion Lecture

PHYSICS 220 Lecture 12 Collision and Explosion Lecture 12 1

Example • A freight train is being assembled in switching yard. Car 1 has a mass of m 1=65 103 kg and moves at a velocity v 01=0. 80 m/s. Car 2 has a mass of m 2=92 103 kg and moves at a velocity v 02=1. 3 m/s and couples to Car 1. Neglecting friction, find the common velocity vf of the cars after they become coupled. m 2 Lecture 12 v 02 m 1 vf v 01 initial final 2

Example • A fright train is being assembled in switching yard. Car 1 has a mass of m 1=65 103 kg and moves at a velocity v 01=0. 80 m/s. Car 2 has a mass of m 2=92 103 kg and moves at a velocity v 02=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=m 1 vo 1+m 2 v 02 Pf=(m 1+m 2)vf = m 1 v 01+m 2 v 02 Lecture 12 3

Center of Mass L Example 1: m m x. CM = (0 + m. L)/2 m = L/2 L Example 2: Lecture 12 m 5 m X=0 X=L x. CM = (0 + 5 m. L)/6 m = 5 L/6 4

Center of Mass • For symmetric objects that have uniform density the CM will simply be at the geometrical center! + CM + Lecture 12 + + 5

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 Lecture 12 (1) (2) 6

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). l The CM of the compound object will be halfway between the CMs of the two halves. l This is higher than the CM of the disk X X CM (1) Lecture 12 X X (2) 7

Dynamics of Many Particles ptot = mtot. Vcm Fext. Dt = Dptot = mtot. DVcm 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 8

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) 2 L/5 C) 1/5 L m M = 1. 5 m L Lecture 12 9

Astronauts & Rope. . . l l 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 M = 1. 5 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 10

Explosion How much further does the stage go? Lecture 12 11

Explosion Example: m 1 = M/3 m 2 = 2 M/3 v 1 “before” M m 1 m 2 v 2 “after” • 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 = mv 2/2 = m 2 v 2/2 m = p 2/2 m * smaller mass has larger kinetic energy • Is mechanical (kinetic) energy conserved? * NO Lecture 12 12

Explosion and Collision Explosion M m 1 m 2 Procedure “before” • Draw “before” and “after” • Define system so that Fext = 0 • Set up a coordinate system Collision m 1 Lecture 12 m 2 “before” “after” • Compute ptotal “before” • Compute ptotal “after” • Set them equal to each other 13

Type of Collision • Elastic Collisions: – collisions that conserve mechanical energy • Inelastic Collisions: – collisions that do not conserve mechanical energy • Completely Inelastic Collisions: – objects stick together Elastic Lecture 12 Inelastic Completely Inelastic 14

2 -D Problems y x before after • Ptotal, x and Ptotal, y independently conserved Ptotal, x, before = Ptotal, x, after Ptotal, y, before = Ptotal, y, after Lecture 12 15

Elastic Collision • Assuming – Collision is elastic (KE is conserved) – Balls have the same mass – One ball starts out at rest pf pi vcm Pf F before Lecture 12 after 16

Playing Pool • According to what you have learned so far, you would want think twice before attempting the shot because … Lecture 12 17

• Conservation of momentum vc, f 900 Vp, f vc, i • Conservation of energy Lecture 12 18

Completely Inelastic Collision y m 1 x v 1 v 2 m 2 • Find vf and Lecture 12 before m 1+m 2 vf after 19

Completely Inelastic Collision in Two Dimensions x • Find vf and y Lecture 12 m 1+m 2 vf after 20