Page 1. t F t m v. N s kg s. J F t SPH4U. From Newton Two New Concepts Impulse & Momentum. Agenda

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1 SPH4U Agenda Fro Newton Two New Concepts Ipulse & oentu Ipulse Collisions: you gotta consere oentu! elastic or inelastic (energy consering or not) Inelastic collisions in one diension and in two diensions Eplosions Coent on energy conseration Ballistic pendulu Fnet a Fnet t F t net Ipulse J F t net Change In oentu Ipulse = Change in oentu oentu; p oentu is ector in direction o elocity. Ipulse is ector in direction o orce. N s kg s SPH4U: Lecture 4, Pg SPH4U: Lecture 4, Pg Ipulse and Area under Force Tie graph Think Is it possible or a syste o two objects to hae zero total oentu while haing a non-zero total kinetic energy?. YES. NO correct yes, when two objects hae the sae ass and elocities and they push o each other..oentu is zero and kinetic energy is nonezero. J F t area under F s. t cure a balls traeling at the sae speed hit each other head-on. SPH4U: Lecture 4, Pg 3 SPH4U: Lecture 4, Pg 4 Page

2 Change in oentu Question y A 0 kg cart collides with a wall and changes its direction. What is its change in -oentu p? I the bear and the ball hae equal asses, which toy eperiences the greater change in oentu? Change in oentu: p = p ater - p beore Teddy Bear: p = 0-(-) = Bouncing Ball: p = -(-) = SPH4U: Lecture 4, Pg 5 a. -30 kg /s b. -0 kg /s c. 0 kg /s d. 0 kg /s e. 30 kg /s p - pi 0kg - 0kg - 30kg s s s SPH4U: Lecture 4, Pg 6 You drop an egg onto ) the loor ) a thick piece o oa rubber. In both cases, the egg does not bounce. In which case is the ipulse greater? A) Floor B) Foa C) the sae Question I = P Sae change in oentu sae ipulse In which case is the aerage orce greater A) Floor B) Foa C) the sae p = F t F = p/t Saller t = larger F SPH4U: Lecture 4, Pg 7 Pushing O Fred (75 kg) and Jane (50 kg) are at rest on skates acing each other. Jane then pushes Fred w/ a constant orce F = 45 N or a tie t=3 seconds. Who will be oing astest at the end o the push? A) Fred B) Sae C) Jane Fred F = +45 N (positie direct.) I = +45 (3) N-s = 35 N-s I = p = i I/ = - i = 35 N-s / 75 kg =.8 /s Note: P red + P jane = 75 (.8) + 50 (-.7) = 0! Jane F = -45 N Newton s 3 rd law I = -45 (3) N-s = -35 N-s I = p = i I/ = - i = -35 N-s / 50 kg = -.7 /s SPH4U: Lecture 4, Pg 8 Page

3 A 50 g baseball is thrown at a speed o 0 /s. It is hit straight back to the pitcher at a speed o 40 /s. The interaction orce is as shown here. What is the aiu orce F a that the bat eerts on the ball? What is the aerage orce F a that the bat eerts on the ball? Hitting a Baseball Use the ipulse approiation: Neglect all other orces on ball during the brie duration o the collision. p I (area under orce cure) F (6 s) F (.003 s) a Hitting a Baseball a p - ( - ) i i (0.5 kg)(40 /s + 0 /s) 9.0 kg /s Thereore, Fa (9.0 kg /s) / (.003 s) 3,000 N p (9.0 kg /s) F a = =,500 N t (.006 s) SPH4U: Lecture 4, Pg 9 SPH4U: Lecture 4, Pg 0 A Karate Collision With an epert karate blow, you shatter a concrete block. Consider that your hand has a ass o 0.70 kg, is initially oing downward at 5.0 /s, and stops 6.0 beyond the point o contact. (a) What ipulse does the block eert on your hand? (b) What is the approiate collision tie and aerage orce that the block eerts on your hand? 5.0 /s y t i J p (0.70 kg)(5.0 /s) 3.5 N s y (0.006 ) t s 5.0 /s i J (3.5 N s yˆ ) Fa =,500 N t ( s) SPH4U: Lecture 4, Pg dp FEXT dt oentu Conseration dp 0 FEXT 0 dt p The concept o oentu conseration is one o the ost undaental principles in physics. This is a coponent (ector) equation. We can apply it to any direction in which there is no eternal orce applied. You will see that we oten hae oentu conseration (F EXT =0) een when echanical energy is not consered. Elastic collisions don t lose echanical energy In inelastic collisions echanical energy is reduced We will show that linear oentu ust still be consered, F=a SPH4U: Lecture 4, Pg Page 3

4 Elastic s. Inelastic Collisions A collision is said to be elastic when kinetic energy as well as oentu is consered beore and ater the collision. K beore = K ater Carts colliding with a spring in between, billiard balls, etc. A collision is said to be inelastic when kinetic energy is not consered beore and ater the collision, but oentu is consered. K beore K ater Car crashes, collisions where objects stick together, etc. i Inelastic collision in -D: Eaple A block o ass is initially at rest on a rictionless horizontal surace. A bullet o ass is ired at the block with a uzzle elocity (speed). The bullet lodges in the block, and the block ends up with a speed. In ters o,, and : What is the initial speed o the bullet? What is the initial energy o the syste? What is the inal energy o the syste? Is kinetic energy consered? beore ater SPH4U: Lecture 4, Pg 3 SPH4U: Lecture 4, Pg 4 Eaple... Eaple... Consider the bullet & block as a syste. Ater the bullet is shot, there are no eternal orces acting on the syste in the -direction. oentu is consered in the direction! P, i = P, += + =(+) initial inal SPH4U: Lecture 4, Pg 5 Now consider the kinetic energy o the syste beore and ater: Beore: E B Ater: E A So E A E B Kinetic energy is NOT consered! (riction stopped the bullet) Howeer, oentu was consered, and this was useul. SPH4U: Lecture 4, Pg 6 Page 4

5 Inelastic Collision in -D: Eaple = 0 + ice (no riction) Eaple... Use conseration o oentu to ind ater the collision. Beore the collision: Ater the collision: Pi ( 0 ) P ( ) Pi P Conseration o oentu: ( ) =? ( ) ector equation SPH4U: Lecture 4, Pg 7 SPH4U: Lecture 4, Pg 8 ( ) Eaple... Now consider the K.E. o the syste beore and ater: Beore: E BUS Ater: So E A E A E B Kinetic energy is NOT consered in an inelastic collision! Lecture 4, Act oentu Conseration Two balls o equal ass are thrown horizontally with the sae initial elocity. They hit identical stationary boes resting on a rictionless horizontal surace. The ball hitting bo bounces back, while the ball hitting bo gets stuck. Which bo ends up oing aster? (a) Bo (b) Bo (c) sae SPH4U: Lecture 4, Pg 9 SPH4U: Lecture 4, Pg 0 Page 5

6 Lecture 4, Act oentu Conseration Since the total eternal orce in the -direction is zero, oentu is consered along the -ais. In both cases the initial oentu is the sae ( o ball). In case the ball has negatie oentu ater the collision, hence the bo ust hae ore positie oentu i the total is to be consered. The speed o the bo in case is biggest! Lecture 4, Act oentu Conseration init = - in = ( init + in ) / init = (+) = init / (+) nuerator is bigger and its denoinator is saller than that o. > SPH4U: Lecture 4, Pg SPH4U: Lecture 4, Pg Inelastic collision in -D Inelastic collision in -D... Consider a collision in -D (cars crashing at a slippery intersection...no riction). X: There are no net eternal orces acting. Use oentu conseration or both coponents. P, i P, + y: Py, i Py, y y beore ater = (, y ) + SPH4U: Lecture 4, Pg 3 SPH4U: Lecture 4, Pg 4 Page 6

7 Inelastic collision in -D... So we know all about the otion ater the collision! Inelastic collision in -D... We can see the sae thing using oentu ectors: = (, y ) y y P p p P p p y p tan p tan p p SPH4U: Lecture 4, Pg 5 SPH4U: Lecture 4, Pg 6 Eplosion (inelastic un-collision) Eplosion... No eternal orces, so P is consered. Beore the eplosion: Initially: P = 0 Finally: P = + = 0 Ater the eplosion: = - SPH4U: Lecture 4, Pg 7 SPH4U: Lecture 4, Pg 8 Page 7

8 Lecture 4, Act 3 Center o ass A bob eplodes into 3 identical pieces. Which o the ollowing conigurations o elocities is possible? (a) (b) (c) both Lecture 4, Act 3 Center o ass No eternal orces, so P ust be consered. Initially: P = 0 In eplosion () there is nothing to balance the upward oentu o the top piece so P inal 0. () () () SPH4U: Lecture 4, Pg 9 SPH4U: Lecture 4, Pg 30 Lecture 4, Act 3 Center o ass Coent on Energy Conseration No eternal orces, so P ust be consered. All the oenta cancel out. P inal = 0. We hae seen that the total kinetic energy o a syste undergoing an inelastic collision is not consered. echanical Energy is lost: Where does it go??» Heat (bob)» Bending o etal (crashing cars) Kinetic energy is not consered since work is done during the collision! oentu along a certain direction is consered when there are no eternal orces acting in this direction. In general, oentu conseration is easier to satisy than energy conseration. () SPH4U: Lecture 4, Pg 3 SPH4U: Lecture 4, Pg 3 Page 8

9 Question A 4.0 kg ass is oing to the right at.0 /s. It collides with a 0.0 kg ass sitting still. Gien that the collision is perectly elastic, deterine the inal elocities o each o the asses. Solutions Question A 4.0 kg ass is oing to the right at.0 /s. It collides with a 0.0 kg ass sitting still. Gien that the collision is perectly elastic, deterine the inal elocities o each o the asses. Conseration o oentu p p i i i 4.0kg kg 0kg s kg kg 0kg s Conseration o Energy Oh No, we Khae i K unknowns. I only there i was another i equation. 4.0kg kg 0kg s 6.0J 4.0kg 0kg Question A 4.0 kg ass is oing to the right at.0 /s. It collides with a 0.0 kg ass sitting still. Gien that the collision is perectly elastic, deterine the inal elocities o each o the asses. L Ballistic Pendulu L L L =0 kg kg s 0kg 6.0J 4.0kg 0kg kg kg 0kg s kg 8.0-0kg s 4. 0kg kg 8.0-0kg s J kg 0kg 4. 0kg s kg 8.0-0kg.4 s s 4. 0kg -0.8 A projectile o ass oing horizontally with speed strikes a stationary ass suspended by strings o length L. Subsequently, + rise to a height o H. Gien H, what is the initial speed o the projectile? H + SPH4U: Lecture 4, Pg 36 Page 9

10 Two stage process: Ballistic Pendulu.... collides with, inelastically. Both and then oe together with a elocity (beore haing risen signiicantly).. and rise a height H, consering K+U energy E. (no non-conseratie orces acting ater collision) Ballistic Pendulu... Stage : oentu is consered in -direction: ( ) Stage : K+U Energy is consered ( EI EF ) ( ) ( ) gh gh Eliinating gies: gh SPH4U: Lecture 4, Pg 37 SPH4U: Lecture 4, Pg 38 Page 0