Flipping Physics Lecture Notes: You Can t Run from Momentum

Transcription

1 Flipping Phyic Lecture Nte: Yu Can t Run frm Mmentum Symbl fr mmentum i a lwercae p. p i fr the Latin wrd petere which mean t make fr, t travel t, t eek, r t purue. It pretty clear thi wrd i where the letter p fr mmentum cme frm. D nt cnfue lwercae p fr mmentum with: Uppercae P, which i fr Pwer. ρ which i fr denity. (The lwercae Greek ymbl ρ i called rh.) Equatin fr mmentum i p m v m i fr ma v i fr velcity Mmentum i a vectr. S mmentum ha bth magnitude and directin. Unit fr mmentum are kg m ( ) p m v kg kg m m kg m have n pecial name. Nt t be cnfued with kg m 2 which i a newtn. If the velcity f the bject i zer, then the mmentum f the bject i zer. p m v m 0 ( ) Lecture Nte - Yu Can't Run frm Mmentum.dcx page 1 f 1

2 Newtn Secnd Law i F m a. Flipping Phyic Lecture Nte: Frce f Impact Equatin Derivatin The equatin fr acceleratin i a Δ v v f v i And knwing the equatin fr mmentum i p m v. Therefre: F m a v m f v i m v f m v i p f p i which we can ubtitute int Newtn Secnd Law. Δ p F Δ p Thi i the equatin fr the frce f impact during a clliin. The net frce acting n an bject equal the change in mmentum f the bject divided by the change in time while that net frce i acting n the bject. Bth frce and mmentum are vectr. Thi get u cler t Newtn riginal ecnd law which i F d p dt. The net frce acting n an bject equal the derivative f the mmentum f that bject with repect t time. If yu ever take a calculu baed phyic cure, like AP Phyic C, yu will get an pprtunity t wrk with thi equatin. Nte: Thi equatin fr the frce f impact acting n an bject during a clliin mark a paradigm hift in ur phyic learning. Befre we had thi equatin, we nly lked at bject befre they ran int ne anther. Nw, uing thi equatin, we can determine frce during clliin. Which mean drpping the medicine ball nt the grund actually ha tw part. Part 1, when the medicine ball i in free fall and part 2, when the medicine ball trike the grund Lecture Nte - Frce f Impact Equatin Derivatin.dcx page 1 f 1

3 Flipping Phyic Lecture Nte: Calculating the Frce f Impact when Stepping ff a Wall Example: A 73 kg mr.p tep ff a 73.2 cm high wall. If mr.p bend hi knee uch that he tp hi dwnward mtin and the time during the clliin i 0.28 ecnd, what i the frce f impact caued by the grund n mr.p? With the exceptin f the ma, m 73 kg, the knwn value fr thi prblem need t be plit int tw part. Part 1 Free Fall: v 1iy 0; h 1i 73.2cm 1m 100cm 0.732m Part 2 Clliin: v 1fy 0; ec We are lving fr the Frce f Impact during part tw, therefre we can ue the Frce f Impact equatin F Δ p Part 2: during part tw. F 2 Δ p 2 p 2f p 2i 2 2 m v 2f m v 2i 2 73 ( )( 0) ( 73) ( v 2i ) 0.28 Therefre, we need the velcity fr part 2 initial. Becaue the beginning f part 2 i the ame a the end f part 1, v 1f v 2i, therefre, we need t find the final velcity fr part 1. Part 1 Cnervatin f Energy: Zer line at the grund, initial pint at the tart f part 1, final pint at the end f part 1. ME 1i ME 1f PE g1i KE 1f mgh 1i 1 2 m v 1f v 1f ( 2) ( 9.81) ( 0.732) ± m v 2i And nw back t part 2: ( ) 2 gh 1i 1 ( 2 v 1f ) 2 v 1f 2gh 1i F 2 m v 2f m v 2i ( 73 )( 0) ( 73) ( ) lb F N lb 4.448N N 0177 Lecture Nte - Calculating the Frce f Impact after Stepping f a Wall.dcx page 1 f 1

4 Flipping Phyic Lecture Nte: Impule Intrductin r If Yu Dn't Bend Yur Knee When Stepping ff a Wall Thi vide i an extenin f Calculating the Frce f Impact when Stepping ff a Wall. The idea i t figure ut hw much frce wuld be exerted n mr.p bdy if he didn t bend hi knee. I am unwilling t demntrate thi; intead I drpped a tmat. The time f impact fr the tmat wa 6 frame in a vide filmed at 240 frame per ecnd: 6frame 1ec 240frame 0.025ec The idea i that we can apprximate the time during the clliin if I did nt bend my knee t be the ame a the clliin fr the tmat. D I knw thi t be true? N. Hwever, again, I am unwilling t demntrate tepping ff a wall and nt bending my knee, thi i a gd apprximatin. Becaue I fell 73.2 cm, we determined lat time my velcity right befre triking the grund i m/ dwn and my velcity after triking the grund i zer becaue I tp. My ma i 73 kg. That mean the frce f impact during the clliin i: Unbent knee: Bent knee: F Δ p F 73 m v f m v i ( )( 0) ( 73) ( ) 0.28 ( 73 )( 0) ( 73) ( ) (The time f impact when bending my knee wa 0.28 ecnd.) N 1lb lb 4.448N 1lb N lb 4.448N Nt bending my knee decreae the time f impact frm 0.28 ecnd t ecnd and: F nt bent F bent Make the frce f impact rughly 11 time what it i when I bend my knee. The key here i that the nly thing which i different between the tw example i the time during the clliin. The ma, final velcity and initial velcity are all the ame in bth example. In ther wrd, the change in mmentum during bth example i exactly the ame. Fr thi rean, the change in mmentum i given a pecific name, it i called Impule. The ymbl fr Impule i uually a capital J and metime a capital I; I will uually jut write ut the wrd Impule. Nte that we can rearrange Newtn ecnd law t lve fr impule. F Δ p F Δ p Impule Nte: Impule i a vectr The dimenin fr Impule are N kg m, which i the ame thing a N kg m 2 kg m becaue: Pint f cnfuin fr tudent: Impule i equal t the change in mmentum f an bject and it i al equal t the frce f impact time the change in time. Impule F ( )( 0.28) ( ) ( 0.025) N 280N Impule Δ p m v f m v i ( 73) ( 0) ( 73) ( ) kg m Lecture Nte - Impule Intrductin r If Yu Dn't Bend Yur Knee When Stepping ff a Wall.dcx page 1 f 1

5 Flipping Phyic Lecture Nte: Prving and Explaining Impule Apprximatin Thi vide i an extenin f Impule Intrductin r If Yu Dn't Bend Yur Knee When Stepping ff a Wall. We determined the frce f impact when tepping ff the wall fr tw different cae: Δp N 990N 1) Bent knee: F bent Δp N 11000N 2) Nt bent knee: Fnt bent In rder t ay the frce f impact during the clliin wa equal t the net frce during the clliin, we needed t ue the Impule Apprximatin. Impule Apprximatin: During the hrt time interval f a clliin, the frce f impact i much larger than all the ther frce, therefre we can cnider the ther frce t be negligible when cmpared t the impact frce and the net frce i apprximately equal t the frce f impact. Thi beg the quetin, wa thi actually true in thee tw example? Let find ut: In rder t determine the frce during impact we need t draw a free bdy diagram: The frce f impact i caued by the grund n my bdy and i the Frce Nrmal: F y FN Fg FN Fy + Fg Fy + mg We can lve fr the frce f impact (the frce nrmal) during bth intance. Bent knee: ( )( ) (73 ) ( 9.81) N FN N Nt bent knee: FN And hw far ff were thee frce f impact frm when we ued the Impule Apprximatin? O A % A O A % Nt bent knee: E r A Bent knee: Er In ther wrd, with a time interval f 0.28 ecnd when bending my knee, the Impule Apprximatin wa 42% ff, which i, in my pinin t much And we prbably huldn t have dne Al, the hrter the time interval, the larger the frce f impact relative t the net frce, and therefre the mre apprpriate it i t ue the Impule Apprximatin. If yu want t ee all f the number behind thi calculatin, pleae viit: If yu want t ee all f the number behind thi calculatin, pleae viit: Lecture Nte - Prving and Explaining Impule Apprximatin.dcx page 1 f 1

6 Flipping Phyic Lecture Nte: Hw t Wear a Helmet A Public Service Annuncement frm Flipping Phyic v f vi mv f mvi Δv Newtn 2 Law: F ma m & m nd Δp p f pi mv f mvi F Impule Apprximatin: during the hrt time interval f the clliin, the frce f impact i much larger than all f the ther frce, therefre we can cnider the ther frce t be negligible when cmpared t the impact frce and the net frce i apprximately equal t the frce f impact. mv f mvi Fimpact F Fimpact mv f mvi Lking at the variable n the right hand ide f the equatin. Ma, final velcity, and initial velcity f my head: nne f thee variable depend n whether the helmet i n my head r nt. In ther wrd the right hand ide f the equatin i cntant. Thi i the cncept f Impule and i al equal t the change in mmentum f my head. Fimpact mv f mvi Δp Impule Wearing a helmet during a clliin will increae the time it take fr my head t tp and therefre decreae the frce f impact n my head, even thugh the impule i cntant. That i why yu huld buckle yur helmet, that it tay n yur head, increae the change in time during the clliin and reduce the frce f impact n yur head Lecture Nte - Hw t Wear a Helmet A Public Service Annuncement frm Flipping Phyic.dcx page 1 f 1

7 Flipping Phyic Lecture Nte: Intrductin t Cnervatin f Mmentum Remember, the equatin fr mmentum i p m v. Mmentum i cnerved in an ilated ytem. A ytem i ilated when the net frce n the ytem equal zer. F ytem 0 Δ p ytem 0 Δ p ytem 0 Δ p ytem p f ytem p i ytem p i ytem p f ytem In an algebra baed cla thi mean mmentum i cnerved during all clliin and explin. Cnervatin f Mmentum mean the um f the initial mmentum f the ytem befre the clliin r explin equal the um f the final mmentum f the ytem after the clliin r explin. The equatin fr Cnervatin f Mmentum i p i p f The katebard example: The velcity f mr.p befre the explin i zer; therefre mr.p initial mmentum i zer. The velcity f the ball befre the explin i zer; therefre the ball initial mmentum i zer. The ttal mmentum f the ytem initial i zer. p i p f 0 p f p hf + p bf h i fr human becaue p fr mr.p wuld be t cnfuing. The ball ha a velcity t the right after the explin; therefre the ball ha a pitive mmentum after the explin. Becaue the ball ha pitive final mmentum and the ttal mmentum i zer, mr.p mut have negative mmentum after the explin. Thi i why he mve t the left. p bf > 0 p hf < Lecture Nte - Intrductin t Cnervatin f Mmentum.dcx page 1 f 1

8 Flipping Phyic Lecture Nte: Intrductry Cnervatin f Mmentum Explin Prblem Demntratin Knwn: m b 0.066kg; m n 1.791kg; Δx b x bf x bi 0.015m 0.451m 0.436m; b 0.11ec v bf Δx b b 0.436m 0.11ec m Cnervatin f mmentum: p i p f p bi + p ni p bf + p nf m b v bi + m n v ni m b v bf + m n v nf Nte: The initial velcity f everything i zer, therefre the initial mmentum f the ytem i zer. 0 m b v bf + m n v nf m n v nf m b v bf v nf m b v nf ( )( 3.963) ( berved ) v nf Δ x x x f i E r O A A v bf m n m 0.15 m ( predicted ) ( ) ( ) m 0.400m 0.11ec m % 0181 Lecture Nte - Intrductry Cnervatin f Mmentum Explin Prblem Demntratin.dcx page 1 f 1

9 Flipping Phyic Lecture Nte: Intrductin t Elatic and Inelatic Clliin Let begin with tw different type f clliin: Elatic The tw bject bunce ff f ne anther. Ttal mmentum i cnerved. Remember mmentum i cnerved in all clliin and explin. Ttal kinetic energy i cnerved. Example: Billiard ball, air hckey puck. Inelatic Ttal mmentum i cnerved. Why? Ttal kinetic energy i nt cnerved. Kinetic energy i cnverted t heat and und. When the bject cllide, they defrm. That defrmatin caue frictin inide the bject t increae the internal energy f the bject. (Internal frictin increae the bject temperature.) Perfectly Inelatic: The tw bject tick tgether after the clliin. Example: Clay bject ticking t anther bject, tw ftball player clliding (and hlding ne anther cle), tw railrad car cupling. Inelatic Example: All real wrld bunce clliin. At the atmic level clliin are ften elatic, hwever, in the macrcpic wrld we live in, elatic clliin are an ideal cae which i never quite achieved. There i alway me defrmatin f the bject and therefre me kinetic energy cnverted t internal energy f the bject. Sadly, even billiard ball d nt cllide elatically thugh phyicit d apprximate the clliin a elatic and d we, fr the ake f thi cla. Type f Clliin I Mmentum Cnerved? I Kinetic Energy Cnerved? Elatic Ye Ye Inelatic Ye N Jut yu knw, clliin between hard phere are nearly elatic and therefre are generally cnidered t be elatic in phyic clae. Al, metime Perfectly Inelatic Clliin are called Cmpletely Inelatic r Ttally Inelatic. Thee term all mean the ame thing Lecture Nte - Intrductin t Elatic and Inelatic Clliin.dcx page 1 f 1

10 Flipping Phyic Lecture Nte: Intrductry Perfectly Inelatic Clliin Prblem Demntratin Knwn: m c 0.599kg; m b 0.066kg; b 0.16ec; v bi Δ x b b x x f i m b 0.16 Cnervatin f mmentum: p i p f p bi + p ci p bf + p cf m b v bi + m c v ci m b v bf + m c v cf m b v bi ( m b + m c ) v f Nte: v ci 0 & v cf v bf v f v f m v b bi m b + m c ( berved ) v f Δ x c c E r O A A ( )( ) m 0.16 m ( predicted ) x x cf ci m c 0.25 ( ( )) % 0183 Lecture Nte - Intrductry Perfectly Inelatic Clliin Prblem Demntratin.dcx page 1 f 1

11 Flipping Phyic Lecture Nte: Intrductry Elatic Clliin Prblem Demntratin Example: Cart 1 ha a ma f 2m and cart 2 ha a ma f m. Cart 2 i initially at ret. Cart 1 i mving at 40.9 cm/ when it cllide elatically with cart 2. If the peed f cart 1 after the clliin i 13.4 cm/, what i the peed cart 2 after the clliin? Knwn: m 1 2m; m 2 m; v 1i 40.9 cm ; v 1f 13.4 cm ; v 2i 0; v 2f? Mmentum i cnerved during all clliin : p i p f m 1 v1i + m 2 v2i m 1 v1f + m 2 v2f ( 2m) ( 40.9) + ( m) ( 0) ( 2m) ( 13.4) + ( m) v 2f ( 2) ( 40.9) ( 2) ( 13.4) + v 2f v 2f ( 2) ( 40.9) ( 2) ( 13.4) 55 cm v 55.0 cm (predicted) 2f Meaured i the lpe f the line: v 2f 52.8 cm (meaured) Relative errr fr ur velcity meaurement: E r O A A I Kinetic Energy cnerved? In ther wrd: KE i KE f KE f KE 1 i KE i 1 2 m v 1( 1i ) m v 2 ( 2i ) 2 1 ( 2 2m )( 40.9) ( 2 m ) 0 KE f 1 2 m v 1( 1f ) m v 2 ( 2f ) m ( ) m ( )( 13.4) ( 2 m )( 52.8) m KE f KE m % f the Kinetic Energy remain. i m % 0184 Lecture Nte - Intrductry Elatic Clliin Prblem Demntratin.dcx page 1 f 2

12 Mr. Becke Pint: With the ma f the cart in bae SI unit f kilgram: m 517g 1kg 1000kg 0.517kg When we ubtitute that int the equatin I gave fr kinetic energy initial, we get trange unit which are nt jule: KE i m ( ) ( 0.517) J cm2 Remember jule are J N m kg m 2 m ( ) kg m kg ( ) Mr.p pint ut it de nt matter in thi particular cae becaue the dimenin cancel ut: KE f KE m kg cm 2 i m 2 % kg cm Hwever, Mr. Becke i crrect that it i better t get in t the habit f cnverting t bae SI unit when dealing with energy Lecture Nte - Intrductry Elatic Clliin Prblem Demntratin.dcx page 2 f 2

13 Flipping Phyic Lecture Nte: Demntrating Impule i Area Under the Curve Previuly we derived Impule frm the frce f impact equatin: Δp F Δp F Impule Nw we need t d mething imilar, nly uing calculu: pf t t dp f f F dt dp F dt dp F dt Δp F dt Impule p t t i i i And the integral i the Area Under the Curve. In ther wrd, if we drp a ball nt a frce plate, we get a frce curve that lk like thi: On a Frce v. Time graph, the area between the curve and the time axi i Impule. In thi particular cae the impule i 0.81 N Nte the frce change a a functin f time. In an algebra baed phyic cla like thi ne, we ue the average frce and the change in time t create a rectangle with the ame area a under the curve. Impule Favg N ( )( ) Nte: The tw value fr the Impule, Area under Curve and Faverage time, huld be the ame. Hwever, the PASCO Frce Platfrm de nt quite hw that crrectly. Δp Favg Impule (area under the frce v. time curve) 0187 Lecture Nte - Demntrating Impule i Area Under the Curve.dcx page 1 f 1

14 Flipping Phyic Lecture Nte: Demntrating Hw Helmet Affect Impule and Impact Frce A medicine ball i drpped n t a frce platfrm twice frm the ame height. (a) Withut a helmet and (b) with a helmet. FYI: The helmet i a clth diaper, which erve the exact ame functin a a helmet fr ur medicine ball. Δp Favg Impule Remember, a helmet will increae the time during the clliin t decreae the average frce during the clliin, hwever, it huld nt affect Impule Lecture Nte - Demntrating Hw Helmet Affect Impule and Impact Frce.dcx page 1 f 2

15 0188 Lecture Nte - Demntrating Hw Helmet Affect Impule and Impact Frce.dcx page 2 f 2

16 Flipping Phyic Lecture Nte: Review f Mmentum, Impact Frce, and Impule Cnervatin f Mmentum: p i p f Remember t write ut the full equatin befre yu ue it. m v1i 1 + m v2i 2 m v1f 1 + m v2f 2 Mmentum i cnerved when all frce are internal. In ther wrd, during all clliin and explin. An explin i a clliin mving backward in time. A minimum f tw bject in thi equatin Frce f Impact: F Δ p m v f m v i Clearly we ue thi equatin when we are lving fr the frce f impact during a clliin. Thi equatin nly deal with the frce acting n 1 bject Impule: F Δ p Impule Δ p F avg Impule i the area under the curve. Again, thi equatin nly deal with the impule acting n 1 bject Impule equal three thing: Δ p and and Area under the Frce v. Time curve. F avg 0189 Lecture Nte - Review f Mmentum, Impact Frce and Impule.dcx page 1 f 1

17 Flipping Phyic Lecture Nte: Uing Impule t Calculate Initial Height Example Prblem: A 66 g beanbag i drpped and tp upn impact with the grund. If the impule meaured during the clliin i 0.33 N, frm what height abve the grund wa the beanbag drpped? It i imprtant t recgnize there are tw part t thi prblem: Part 1, when the beanbag i in free fall. Part 2, when the beanbag i clliding with the grund. Knwn: Part 2: ma 66g 1kg 0.066kg; Impule 0.33N ; v 2f 0; v1f v 2i ; h1i? 1000g Impule m Impule2 Δp2 mv 2f mv 2i 0 mv 2i v 2i 5 v1f m Part 1: Ue cnervatin f mechanical energy. Set the initial pint where the beanbag i drpped, the final pint where the beanbag trike the grund and the zer line at the final pint. ( ) ( )( ) 2 5 v ME1i ME1f mgh1i mv1f 2 gh1i v1f 2 h1i 1f m 2 2 2g But the actual meaured height wa 0.50 m. Therefre ur predictin i way, way ff. Er O A % A 0.50 We can undertand thi errr if we lk at the data frm the frce enr after the clliin. Yu can ee the frce meaured ha a damped cillatin arund zer. It ge negative, then pitive and cntinue that pattern, leening in magnitude each time until it ettle dwn t zer. A negative frce meaurement n the frce platfrm make n ene becaue the beanbag de nt pull upward n the frce platfrm. My bet gue i the clliin between the beanbag and the frce platfrm caue the frce platfrm itelf t enter int imple harmnic mtin and therefre caue the frce platfrm t regiter a larger impule than it huld. I dn t think the frce platfrm i intended fr uch dynamic meaurement; it i intead intended fr mre tatic meaurement Lecture Nte - Uing Impule t Calculate Initial Height.dcx page 1 f 1

18 Flipping Phyic Lecture Nte: Impule Cmparin f Three Different Demntratin Example Prblem: A racquetball i drpped n t three different ubtance frm the ame height abve each: water, il, and wd. Rank the during the clliin with each ubtance in rder frm leat t mt. (a) Impule. (b) Average Frce f Impact. (Aume the racquetball tp during the clliin with the water and il.) Let plit the demntratin up in t part: Part 1 i the free fall prtin. Becaue the racquetball i drpped frm the ame height in all three example, the velcity at the end f part 1 i the ame fr all three ubtance. Part 2 i the clliin. The initial velcity fr part 2 i the final velcity fr part 1 all three ubtance have the ame initial velcity fr part 2. We are auming the racquetball tp after clliding with the water and il, therefre the velcity fr part 2 final fr each i zer. Hwever, after clliding with the wd, the ball rebund t abut 2/3rd it riginal height, therefre the racquetball ha a pitive final velcity fr part 2. The ma f the racquetball i the ame fr all three ubtance. Part (a) fr the water and the il: Impule 2 Δ p 2 m v 2f m v 2i m( 0) m v 2i m v 2i S the impule fr the water and the il i the ame. Nte: Thi impule i actually pitive becaue the velcity fr part 2 initial i dwn and therefre negative, which make the impule fr the clliin with bth the water and the il, pitive. Fr the wd Impule 2 m v 2f m v 2i and we knw velcity fr part 2 final i pitive, the impule fr the wd i greater than the impule fr the water and the il. Anwer: Impule water Impule il < Impule wd Water Sil Wd v 1f v 2i Same Same Same v 2f 0 0 Pitive m racquetball Same Same Same Part (b) becaue they bth have the ame impule, cmparing frce f impact fr water and il i rather traightfrward. We knw impule equal the average frce f impact multiplied by the change in time during the clliin. Frm the vide, yu can ee the time f impact during the clliin with the water i much greater than the time f impact with the il, therefre the average frce f impact during the clliin with the water mut be le than the average frce f impact with the il. Impule F avg : Impule i the ame, water > il F water < F il We already knw Impule il < Impule wd, hwever, in rder t cmpare the average frce f impact between the il and the wd, we need t be able t cmpare the change in time during each clliin. Bth f the clliin appear t lat fr rughly 1 frame. Therefre we can etimate that the time during the clliin i the ame. Becaue the impule fr the il i le than the impule fr the wd and the tw change in time are the ame, then the frce f impact fr the il mut be le than the frce f impact fr the wd. Anwer: F water < F il < F wd 0191 Lecture Nte - Impule Cmparin f Three Different Demntratin.dcx page 1 f 1

19 Mechanical Energy Equatin: Flipping Phyic Lecture Nte: Review f Mechanical Energy and Mmentum Equatin and When T Ue Them Cnervatin f Mechanical Energy: ME i ME f Ue when W frictin 0 & W Fa 0 Wrk due t frictin equatin: W frictin ΔME Ue when W frictin 0 & W Fa 0 Net Wrk and Kinetic Energy equatin: W net ΔKE Thi equatin i alway true D nt cnfue with W frictin ΔME even thugh they lk imilar. Whenever yu ue thee equatin yu mut firt identify: Initial Pint, Final Pint, and Zer Line The fllwing i frm my vide Review f Mmentum, Impact Frce, and Impule. flippingphyic.cm/impule-review.html Cnervatin f Mmentum: p i Remember t write ut the full equatin befre yu ue it. p f m 1 v1i + m 2 v2i m 1 v1f + m 2 v2f Mmentum i cnerved when all frce are internal. In ther wrd, during all clliin and explin. An explin i a clliin mving backward in time. A minimum f tw bject in thi equatin Frce f Impact: F Δ p m v f m v i Clearly we ue thi equatin when we are lving fr the frce f impact during a clliin. Thi equatin nly deal with the frce acting n 1 bject Impule: F Δ p Impule Δ p F avg Impule i the area under the curve. Again, thi equatin nly deal with the impule acting n 1 bject Impule equal three thing: Δ p and and Area under the Frce v. Time curve. F avg Three imprtant additin: 1. Student ften tell me the wrk due t frictin need t be zer fr Cnervatin f Mmentum t be true. Thi i nt crrect and i prbably becaue they cnfue Cnervatin f Mmentum with Cnervatin f Energy. Cnervatin f Mmentum i true when all the frce are internal r balanced. We tranlate that t mean during all clliin and explin. 2. Yu d nt need t identify initial and final pint becaue they are alway aumed a: a. Initial pint i right befre the clliin/explin. b. Final pint i right after the clliin/explin. 3. Impule and Impact frce bth tart with the letter I and ften get cnfued by tudent. a. Dn t let thi happen t yu 0192 Lecture Nte - Review f Mechanical Energy and Mmentum Equatin and When T Ue Them.dcx page 1 f 1

20 Flipping Phyic Lecture Nte: 2D Cnervatin f Mmentum Example uing Air Hckey Dic Example: A 28.8 g yellw air hckey dic elatically trike a 26.9 g tatinary red air hckey dic. If the velcity f the yellw dic befre the clliin i 33.6 cm/ in the x directin and after the clliin it i 10.7 cm/ at an angle 63.4 S f E, what i the velcity f the red dic after the clliin? Knwn: m g; m g; v 2i 0; v 1iy 0; v 1ix 33.6 cm ; v 1f 10.7 S f E; v 2f? Remember mmentum i a vectr we need t break velcitie int cmpnent in the x & y directin: c A H v 1fx v v 1fx v 1f c ( 10.7)c( 63.4) cm 1f inθ O H v 1fy v v 1fy v 1f inθ ( 10.7)in( 63.4) cm 1f (negative becaue it i Suth) Nw we can ue cnervatin f mmentum in bth the x and y directin: x-directin: p ix p fx m 1 v 1ix + m 2 v 2ix m 1 v 1fx + m 2 v 2fx m 1 v 1ix m 1 v 1fx + m 2 v 2fx (becaue v 2ix 0 ) m 1 v 1ix m 1 v 1fx m 2 v 2fx v 2fx m v m v ( 1 1ix 1 1fx 28.8 )( 33.6) ( 28.8) ( ) m v 2fx cm y-directin: ( g) nte: v 2fx cm ( ) g g cm cm p iy p fy m 1 v 1iy + m 2 v 2iy m 1 v 1fy + m 2 v 2fy 0 m 1 v 1fy + m 2 v 2fy m 1 v 1fy m 2 v 2fy v 2fy m 1 v 1fy m ( )( ) 26.9 (becaue v 1iy v 2iy 0 ) cm a 2 + b 2 c 2 v 2f 2 v 2fx 2 + v 2fy 2 v 2f v 2fx 2 + v 2fy cm tanθ 2f O A v 2fy θ v 2f tan 1 2fx v 2f 32.5 cm v 2fy v N f E (predicted) tan Lecture Nte - 2D Cnervatin f Mmentum Example uing Air Hckey Puck.dcx page 1 f 2

21 Meaured final velcity f the red air hckey dic i v 2f 32.0 N f E (pretty cle, eh) We cnider thi an elatic clliin, wa kinetic energy cnerved? Firt, in rder t wrk with energy, cnvert everything t bae SI unit m g 1kg 1000g kg; m 1kg 26.9g g kg v 1i 33.6 cm 1m 100cm m ; v 10.7 cm 1f 1m 100cm m ; v 32.5 cm 2f 1m 100cm m 1 KE i 2 m v i 2 m v i ( )( 0.336) J (becaue v 2i 0 ) KE i J 1000mJ 1J mJ KE f 1 2 m v f 2 m v f ( )( 0.107) ( )( 0.320) J KE f J 1000mJ 1J mJ E r O A % A In ther wrd, 5.14% f the kinetic energy wa cnverted t heat and und during the elatic clliin Lecture Nte - 2D Cnervatin f Mmentum Example uing Air Hckey Puck.dcx page 2 f 2