Physics 131: Lecture 15 Today s Agenda Impulse and Momentum (or the chapter where physicists run out of letters) Non-constant t forces Impulse-momentum thm Conservation of Linear momentum External/Internal forces Examples Physics 201: Lecture 1, Pg 1
Conservation of Momentum Newton s second law for a system F ext net dp dt The total momentum of an isolated system remains constant dp Isolated system = no external forces 0 dt When two objects interact, they transfer momentum from one to the other. If they are isolated no momentum is lost. Physics 201: Lecture 1, Pg 2
Clicker Question 1: Heading into a collision two cars slam on their brakes and skid into each other. During the collision i are the two cars technically an isolated system? A. No, the two cars are not technically an isolated system. B. Yes, the two cars are technically an isolated system. Physics 201: Lecture 1, Pg 3
x Conservation of Momentum B A FAB F BA F AB is the force of fa acting on B F avg t p AB B In the x-direction: i avg BA F avg BA F t p BA A F avg AB t p F A avg AB F avg AB t p A p p A B Physics 201: Lecture 1, Pg 4
Conservation of Linear Momentum The total momentum of an isolated system remains constant Velocity can be positive or negative!! p p f i mv mv mv mv f i mv mv mv f i f mv i object 1 object 2 object 1 object 2 mv f + mv f = mv i + mv i In y-direction in x-direction Physics 201: Lecture 1, Pg 5
Conservation of Linear Momentum Collisions Explosions v =?? 10 m/s 15 kg Physics 201: Lecture 1, Pg 6
Collisions Conservation of momentum is very useful for collisions and explosions In collisions/explosions forces are very complicated, momentum gives us a useful way to solve these problems. (treat colliding/exploding particles as system) Two kinds of collisions Inelastic- (perfectly = objects stick together) Elastic- next time Momentum is almost always conserved during an collision/explosion (external forces are generally small compared to collision/explosion forces) Physics 201: Lecture 1, Pg 7
Clicker Question 2: Two blocks are sliding to the right on a frictionless surface and collide as shown below. Before the collision, the block M on the left has a speed of 4 m/s, and block 3M has a speed of 1 m/s. After the collision the left block (M) is observed to travel to the left with speed 2 m/s. What is the velocity of the 3M-block after the collision? (a) 3m/s (b) 5/3 m/s (c) 9 m/s (d) 5 m/s (e) 2/3 m/s v=2 m/s v =?? Physics 201: Lecture 1, Pg 8
Clicker Question 2: v=2 m/s v =?? Physics 201: Lecture 1, Pg 9
Clicker Question 3: Pre-Class Quiz: Two particles collide, one of which was initially moving and the other initially at rest. Is it possible for one particle to be at rest after the collision? A. Yes B. No Physics 201: Lecture 1, Pg 10
Pre-Class Quiz: Two particles collide, one of which was initially moving and the other initially at rest. Is it possible for both particles to be at rest after the collision? A. Yes B. No Physics 201: Lecture 1, Pg 11
Clicker Question 4: Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck. Which box ends up moving faster? (a) Box 1 (b) Box 2 (c) same 1 2 Impulse delivered to box 1 is larger Physics 201: Lecture 1, Pg 12
Clicker Question 5a: Pre-Class Quiz: Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula. Which skater, if either, has the greater momentum after the push-off? A. Paula B. Ricardo C. Neither Physics 201: Lecture 1, Pg 13
Clicker Question 5b: Pre-Class Quiz: Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula. Which skater, if either, has the greater speed after the push-off? A. Paula B. Ricardo C. Neither Physics 201: Lecture 1, Pg 14
2D Conservation of Linear Momentum The total momentum of an isolated system remains constant. object 1 object 2 object 1 object 2 m 1 v f + m 2 v f = m 1 v i + m 2 v i in x-direction object 1 object 2 object 1 object 2 m 1v f + m 2v f = m 1v i + m 2v i In y-direction Velocity can be positive or negative!! Physics 201: Lecture 1, Pg 15
Pre-Class Quiz: A 30.0g ball of clay traveling east at 5.00m/s collides and sticks together with a 50.0g 0g ball of clay traveling north at 7.00m/s. What is the speed of the resulting ball of clay? Physics (4.76 201: Lecture m/s) 1, Pg 16
Clicker Question 6: Two identical disks slide on a horizontal frictionless surface. Disk 1 is initially iti traveling in the positive x-direction at a speed v 1. Disk 2 is initially traveling in the positive y-direction at a speed v 2. The disks collide and stick together as shown in the figure below. The final speed of the two disks is v f = 4 m/s, and they are traveling at an angle θ = 20. What is the initial speed v 1 of disk 1 before the collision? (a) (b) (c) v 1 = 7.5 m/s v 1 =91m/s 9.1 v 1 = 11.3 m/s Cos 20 = 0.94 Sin 20 = 0.34 Physics 201: Lecture 1, Pg 17
Clicker Question 7: Two dry ice pucks slide on a horizontal, frictionless surface. Puck A, which is 2 kg, moves at speed 7 m/s in the positive x direction and Puck B, which is 1 kg, moves at speed 8 m/s in the negative y direction as shown in the figure. The pucks collide near the star in the figure. After the collision Puck B is moving in the positive x direction, while Puck A is moving in the direction that makes 45 with the positive x-axis as illustrated. What is the speed of Puck A after the collision? (a) 1 m/s (b) 2 m/s () (c) 2 2 m/s (d) 4 m/s (e) 4 2 m/s Physics 201: Lecture 1, Pg 18