Example - Elastic Collision Suppose I have 2 identical bumper cars. One is motionless and the other is approaching it with velocity vi. If they collide elastically, what is the final velocity of each car? Note that this means m=m2= m =0 Physics 121: Lecture 16, Pg 11
Physics 121: Lecture 16, Pg 11 Example - Elastic Collision Suppose I have 2 identical bumper cars. One is motionless and the other is approaching it with velocity v1 . If they collide elastically, what is the final velocity of each car ? Note that this means, m1 = m2 = m v2B = 0
Example - Elastic Collision Let's start with the equations for conserving momentum and energy, mvi.B=mvl.A + mv2.A m 1.B 21A+12m2A(2) (v4+2)2=v2+ 2v 0 V1AO, V2A=O or both Both: contradicts(2 If v2A=0: V1A= V1B from(1)or(2) no collision Initially, v2=0. After the collision, V,=0 To satisfy equation (1),V2A=V18 Physics 121: Lecture 16, Pg 12
Physics 121: Lecture 16, Pg 12 Example - Elastic Collision Let’s start with the equations for conserving momentum and energy, mv1,B = mv1,A + mv2,A (1) 1 /2 mv2 1,B = 1 /2 mv2 1,A + 1 /2 mv2 2,A (2) Initially, v2 = 0. After the collision, v1 = 0. To satisfy equation (1), v2A = v1B. 2 2 2 1 2 1 2 ( ) A A A A v + v = v + v 2v1A v2 A = 0 v1A=0 , v2A=0 or both Both: contradicts (2) If v2A=0 : v1A= v1B from (1) or (2) no collision !
Lecture 16. ACT 1 Elastic Collisions have a line of 3 bumper cars all touching. A fourth car smashes into the others from behind Is it possible to satisfy both conservation of energy and momentum if two cars are moving after the collision All masses are identical. elastic collision A)Yes B) No Before After Physics 121: Lecture 16, Pg 13
Physics 121: Lecture 16, Pg 13 Lecture 16, ACT 1 Elastic Collisions I have a line of 3 bumper cars all touching. A fourth car smashes into the others from behind. Is it possible to satisfy both conservation of energy and momentum if two cars are moving after the collision? All masses are identical, elastic collision. A) Yes B) No Before After?
Glancing Collisions X component: m,vi+0=m,V1 CoS O+m,v2r cos p y component KE m,vi=2m,if t2m2v25 If 6 m Physics 121:Lecture 16, Pg 14
Physics 121: Lecture 16, Pg 14 Glancing Collisions x component: y component: KE: m1 m2 x y v1i v1f v2f m1 v1i + 0 = m1 v1 f cos + m2 v2 f cos 2 2 2 2 2 1 2 1 1 2 1 2 1 1 1 f f m v = m v + m v
Example of 2-d elastic collisions: Billiards If all we know is the initial velocity of the cue ball, we dont have enough information to solve for the exact paths after the collision. But we can learn some useful things Physics 121: Lecture 16, Pg 15
Physics 121: Lecture 16, Pg 15 Example of 2-D elastic collisions: Billiards If all we know is the initial velocity of the cue ball, we don’t have enough information to solve for the exact paths after the collision. But we can learn some useful things