Physics 201: Lecture 14, Pg 1

Transcription

1 Physics 201: Lecture 14, Pg 1

2 Physics 131: Lecture 15 Today s Agenda Impulse and Momentum (or the chapter where physicists run out of letters) Non-constant forces Impulse-momentum thm Conservation of Linear momentum External/Internal forces Examples Physics 201: Lecture 14, Pg 2

3 Physics 201: Lecture 14, Pg 3

4 Things that stay the same So far we have focused on things that change Velocity Position Now we will explore some things that stay the same We say they are conserved Collisions! Physics 201: Lecture 14, Pg 4

5 Linear Momentum Moving object has linear momentum such that: p mv Vector quantity in same direction as velocity Units: kg m/s or N s px mv x p mv y mv y What makes change in motion difficult? Momentum gives a sense of how hard it is to stop an object Student, I really don't understand what exactly momentum is interms of a quantity. Physics 201: Lecture 14, Pg 5

6 Newton s Second law Newton s second law was originally written in terms of momentum F net d( mv) F net dt F F net dp dt dv m dt (1) ma (2) m a Equation (1) and (2) are equivalent if the mass is not allowed to change. Physics 201: Lecture 14, Pg 6

7 Newton s Second law From this we may define the impulse F net dp dt F F avg F avg t p J pp p tt J F avg t Impulse gives a measure of how much an object s momentum will be affected by a particular force Impulse is the cause, change in momentum is the effect Physics 201: Lecture 14, Pg 7

8 Impulse-Momentum Theorem An impulse on an object leads to a change in the objects momentum. (This is a vector) J p x f x J x p x p p fx i x p J ix x Student, Why in the textbook the formula J = pf - pi is written in scalars (not in vectors)? The momentum after an interaction, like a collision or explosion, equals the momentum before the interaction plus the impulse that arises from the interaction. Momentum can be positive or negative!! Physics 201: Lecture 14, Pg 8

9 Student Questions What is the difference between momentum and impulse? How to decide the sign of the momentum if the positive direction is not explicitly given? Is that same in the process of deciding the positive direction of velocity? Why is there no adequate, "official" definition for impulse? In one of the book's example questions, it says that the rebound speed is less than the impact speed, and that that is supposed to make sense. Then in another question, it says that the rebound speed is equal but in the opposite direction as the initial speed. Is one right over the other, or does it just depend d on the question/situation? it Physics 201: Lecture 14, Pg 9

10 Clicker Question 1: You drop an egg onto A) the floor B) a thick piece of foam rubber. In both cases, the egg does not bounce (assume the egg hits each surface with the same speed v). In which h case is the magnitude of the impulse greater? A) Floor B) Foam C) It s the same Physics 201: Lecture 14, Pg 10

11 Clicker Question 1: You drop an egg onto A) the floor B) a thick piece of foam rubber. In both cases, the egg does not bounce (assume the egg hits each surface with the same speed v). J J y F y p fy 0 m J y mv avg y t p iy mv F v avg y Smaller t = larger F mv tt Physics 201: Lecture 14, Pg 11

12 Impulse as an Area Under the Curve Physics 201: Lecture 14, Pg 12

13 Pre-Class Quiz This is why cars have crumple zones, to increase t and decrease the force. Student: Do Same Area = Impulse airbags and seatbelts do F similar things F as the crumple zones on cars? t t Student: Do we need to be able to do integral questions now? Physics 201: Lecture 14, Pg 13

14 Clicker Question 2: Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the impulse given to the ball by the floor the biggest? (a) Case 1 (b) Case 2 ()Bth (c) Both are the same Physics 201: Lecture 14, Pg 14

15 Clicker Question 2: Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the impulse given to the ball by the floor the biggest? Case 1: J y J y p f y p mv m J y 2mv i y v Case 2: J y p fy J y 0 m J y mv p iy v Physics 201: Lecture 14, Pg 15

16 Clicker Question 3: A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. A. greater than B. equal lto C. less than D. Can t say. It depends on how big the force is. Physics 201: Lecture 14, Pg 16

17 Clicker Question 3: A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. Same force, same time same impulse Same impulse same change of momentum Correct: Both of the carts have the same impulse seeing as they have the same force acting on them for the same amount of time and they both start with no momentum which results in an equal momentum for both. Incorrect: p=mv, lead has greater mass so greater momentum Incorrect: Since momentum is a product of mass and velocity, it fits that a 20 kg cart will have greater momentum when pushed will equal force compared to an object with lighter mass. Which has the greatest velocity? Physics 201: Lecture 14, Pg 17

18 Announcements Pre-class Quiz Test level questions and more writing If you do one or the other I prefer you watch the Prelecture Videos (just my opinion) Student: This was much more writing than I expected to do Student: I won't watch anyway. Student: I accidentally pressed "No" to the question "Have you completed the pre-class quiz?" Is there anyway to get back that point? It was a silly mistake. Physics 201: Lecture 14, Pg 18

19 Pig Activity Physics 201: Lecture 14, Pg 19

20 Clicker Question 4: A small car and a large truck collide head-on and stick together. Which one feels the larger impulse? a) the car b) the truck c) they both feel the same impulse d) can t tell without knowing the final velocities Physics 201: Lecture 14, Pg 20

21 Clicker Question 4: A small car and a large truck collide head-on and stick together. Which one feels the larger impulse? J x F x t Follow-up: Which one feels the larger acceleration? Physics 201: Lecture 14, Pg 21

22 Clicker Question 5: You drive down a one-way street at 30 km/hr when you see an identical car heading straight toward you at 30 km/hr, relative to the ground. You have two options: hit the car head-on or swerve into a massive concrete wall (also head- on). What should you do?(assume the collision time is approx. the same in both cases) a) hit the other car b) hit the wall c) makes no difference d) call your physics prof!! e) get insurance! Physics 201: Lecture 14, Pg 22

23 Clicker Question: Car feels same force whether it is stopped by an immovable wall or another car. It s the change in momentum that matters. F vf x v aavg x t t avg x F In terms of acceleration: ix mv fx t 0 mv x t mv avg x mvi x F avg ix ix vi aavg x t x F avg x ma avg x Physics 201: Lecture 14, Pg 23

24 B F AB External/Internal t l Forces F BA A F ext net dp F net dt dp F int net dt dp net 0 dt dp F ext net dt F ext Physics 201: Lecture 14, Pg 24

25 Conservation of Momentum Newton s second law for a system F ext net dp dt The total momentum of an isolated system remains constant Isolated system = no external forces Physics 201: Lecture 14, Pg 25