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 =?? Velocity is still a vector. When you confine your interest to a particular direction the velocity can be positive or negative. (Just like Newton s second law) Physics 201: Lecture 14, 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 Correct: It is possible that the moving particle transfers all of its momentum to another particle and becomes at rest. Example: billiard balls 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 Correct: The initial momentum must equal the final momentum. The initial momentum is nonzero. Therefore, if both particles are at rest after the collision, the final momentum will equal zero. This is not possible. Incorrect: it is possible for the 2nd particle at rest to absorb all of the momentum that the first particle had. If that is the case, then after the collision both particles can be at rest. Although, usually that is an extreme case (e.g. a mosquito ramming into a transport truck) Question: It says two particles collide, one of which was initially moving and the other initially at rest and asks if it is possible for both of them to be at rest after the collision. I understand that momentum must be conserved for both elastic and inelastic collisions however what if the object is sticky like gum? Wouldn t both objects (let s say the gum and the floor) both be at rest after the collision? i How is momentum conserved there? Physics 201: Lecture 1, Pg 11
Where to get help Office hours: Meyertholen M 2-3 F 12-2 2 Make appt. or just stop by Office hours: Harlow T 12-1 1 F 10-1111 Your TAs The Drop In Help Centre is in MP125 (TA has red lanyard): Monday to Thursday - 12:00 to 3:00 pm Friday 11:00 am to 2:00 pm Undergrad tutors (LM 204A) Thursdays 10 am - 12 pm Fridays 3 pm - 4 pm Wednesday 11-1 pm (technically a time for phy 151) Physics 201: Lecture 1, Pg 12
Test 2 Scheduling conflicts with test 2 in PHY131F The second term test in PHY131F will be written on November 11, from 18:10 to 19:30. If you have the same scheduling conflict with this test as you may have had for test 1, please answer the email that Ms. Seeley will send you, indicating whether or not you wish to register for the alternate sitting. If your conflict is new, you must submit the online form available from the link on the PHY131F course menu on the Portal to register for the alternate sitting, which will be held at 16:30 on November 11. The (firm!) deadline for registration is Thursday, November 6, at 16:00. Physics 201: Lecture 1, Pg 13
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 14
Clicker Question 4: Initially ball has certain momentum, box has none 1 2 p p p f p i p f pi p ball p p ball p 1 f ball i 2 f ball i p ball p 1 i ball f 2 i ball f p p p ball p Box 1 is faster!!! Physics 201: Lecture 1, Pg 15
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 Correct:The answer is that the total momentum of the system is conserved. How much momentum was their initially if both Paula and Ricardo were standing still? 0 total t momentum. Thus, after they push off ffthey must thave opposite and equal momenta in order for the total momentum to remain 0. Correct: They give the same force and same time. Incorrect: Ricardo has more mass. Momentum is mass multiplied by the velocity. Therefore, Ricardo should have more momentum. Question: Still having trouble figuring out when momentum is the same and when it is different (like in the skater question) can you please break it down more simply in class? Physics 201: Lecture 1, Pg 16
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 17
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 18
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) 14, Pg 19
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 20
Clicker Question 6: 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. Physics 201: Lecture 14, Pg 21
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 22