Moentu and Ipule Phyic 6A For Capu Learning Aitance Serice at UCSB
Moentu any oing object will hae both oentu and kinetic energy We ue a lowercae p for oentu here i the forula p Notice that thi i a ector, o you will hae to break into coponent when adding up the oenta of eeral object. For Capu Learning Aitance Serice at UCSB
Moentu any oing object will hae both oentu and kinetic energy We ue a lowercae p for oentu here i the forula p Notice that thi i a ector, o you will hae to break into coponent when adding up the oenta of eeral object. Ipule if the oentu of an object change, then either it a or it elocity ut hae changed. In ot cae, we will conider the a to be contant, o a change in oentu will ean the object accelerated (elocity changed). So there ut hae been a force applied to it. Thi gie u a forula: p Fag t Thi i jut Newton 2 nd Law can you ee why? For Capu Learning Aitance Serice at UCSB
Moentu any oing object will hae both oentu and kinetic energy We ue a lowercae p for oentu here i the forula p Notice that thi i a ector, o you will hae to break into coponent when adding up the oenta of eeral object. Ipule if the oentu of an object change, then either it a or it elocity ut hae changed. In ot cae, we will conider the a to be contant, o a change in oentu will ean the object accelerated (elocity changed). So there ut hae been a force applied to it. Thi gie u a forula: p Fag t Sole thi for F ag to get F ag Thi i jut Newton 2 nd Law can you ee why? p t t a For Capu Learning Aitance Serice at UCSB
Typical Ipule Exaple: A golf ball (initially at ret) i truck by a club, and the ball i gien a elocity of 50 /. If the a of the ball i 46 gra and the club i in contact with the ball for 5, what i the aerage force applied to the ball by the club? For Capu Learning Aitance Serice at UCSB
Typical Ipule Exaple: A golf ball (initially at ret) i truck by a club, and the ball i gien a elocity of 50 /. If the a of the ball i 46 gra and the club i in contact with the ball for 5, what i the aerage force applied to the ball by the club? We can find the ipule (change in oentu) directly in thi proble: Take a inute and copute it for yourelf For Capu Learning Aitance Serice at UCSB
Typical Ipule Exaple: A golf ball (initially at ret) i truck by a club, and the ball i gien a elocity of 50 /. If the a of the ball i 46 gra and the club i in contact with the ball for 5, what i the aerage force applied to the ball by the club? We can find the ipule (change in oentu) directly in thi proble: The ball tart at ret, o the initial oentu i 0. After the club hit it, the ball ha oentu p final =(0.046kg)(50/)=2.3kg-/ So the ipule i Δp=2.3kg-/ For Capu Learning Aitance Serice at UCSB
Typical Ipule Exaple: A golf ball (initially at ret) i truck by a club, and the ball i gien a elocity of 50 /. If the a of the ball i 46 gra and the club i in contact with the ball for 5, what i the aerage force applied to the ball by the club? We can find the ipule (change in oentu) directly in thi proble: The ball tart at ret, o the initial oentu i 0. After the club hit it, the ball ha oentu p final =(0.046kg)(50/)=2.3kg-/ So the ipule i Δp=2.3kg-/ Now we can diide by Δt to find F ag =460N For Capu Learning Aitance Serice at UCSB
Note on Ipule - Ipule alway occur a action-reaction pair - Longer ipact tie ean aller force, and ice-era Real-Life Exaple: Autoobile afety: Dahboard Seatbelt and Airbag Cruple zone Product packaging Styrofoa pacer Egg carton Sport Baeball: Padded catcher itt Golf: Deforation of ball during brief ipact Boxing gloe: Padding ean aller ipact to the hand (and face, etc.) Cycling: Alway wear your helet! Sleep technology Head on a pillow ore cofortable than head on a concrete floor. For Capu Learning Aitance Serice at UCSB
Coneration of Moentu A long a there are no outide force, the total oentu of a yte of object will not change. We will ue thi idea ainly in colliion proble (but it i uch ore fundaental, and alway applie) For Capu Learning Aitance Serice at UCSB
Coneration of Moentu A long a there are no outide force, the total oentu of a yte of object will not change. We will ue thi idea ainly in colliion proble (but it i uch ore fundaental, and alway applie) Colliion (2 ain categorie) Elatic Colliion KE i conered (no diipatie force) A good approxiation for thing like billiard ball Your textbook ha hortcut forula for head-on elatic colliion (page 266). Ue thee forula if you want to aoid oe poibly difficult algebra Inelatic Colliion oe KE i lot due to diipatie force during ipact Special Cae: When the object tick together, the colliion i perfectly inelatic. Thi will be the eaiet type of proble to ole, becaue there i only 1 object after the colliion. Moentu i conered in all colliion. Ue coneration of oentu firt in all colliion proble. For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =?? =3/ BEFORE AFTER For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =?? =3/ BEFORE AFTER Thi i a perfectly inelatic colliion (they tick together). So we only need coneration of oentu. Write down the initial and final oentu for the yte, then et the equal. For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =?? =3/ BEFORE AFTER Thi i a perfectly inelatic colliion (they tick together). So we only need coneration of oentu. Write down the initial and final oentu for the yte, then et the equal. p f p i (100kg 50kg)(3 ) (100kg)(5 ) (50kg)( boy ) For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =?? =3/ BEFORE AFTER Thi i a perfectly inelatic colliion (they tick together). So we only need coneration of oentu. Write down the initial and final oentu for the yte, then et the equal. p f p boy i (100kg 50kg)(3 1 ) (100kg)(5 ) (50kg)( boy ) For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =?? =3/ BEFORE AFTER Thi i a perfectly inelatic colliion (they tick together). So we only need coneration of oentu. Write down the initial and final oentu for the yte, then et the equal. p f p boy i (100kg 50kg)(3 1 ) (100kg)(5 ) (50kg)( boy Why i the anwer negatie? What doe that ean? ) For Capu Learning Aitance Serice at UCSB
Exaple: A 100kg an and a 50kg boy are at a father-on ice kating jaboree. The an kate toward hi on at a peed of 5 /, and pick the boy up and put hi on hi houlder. If their final peed i 3 /, find the initial elocity of the boy. =5/ boy =-1/ =3/ BEFORE AFTER Thi i a perfectly inelatic colliion (they tick together). So we only need coneration of oentu. Write down the initial and final oentu for the yte, then et the equal. p f p boy i (100kg 50kg)(3 1 ) (100kg)(5 ) (50kg)( boy The boy i initially oing toward hi father. ) For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the billiard ball i initially at ret. Find the final elocity of each ball. Aue the colliion i elatic. 10 / V=?? V=?? BEFORE AFTER For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the billiard ball i initially at ret. Find the final elocity of each ball. Aue the colliion i elatic. 10 / V=?? V=?? BEFORE AFTER Since the colliion i elatic we can ue the forula on page 266 of your book: A,f A,i A A B B B,f A,i 2A A B For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the billiard ball i initially at ret. Find the final elocity of each ball. Aue the colliion i elatic. 10 / a b Va=?? a b Vb=?? BEFORE AFTER Since the colliion i elatic we can ue the forula on page 266 of your book: A,f A,f A,f A,i 10 5 A A 45g 45g B B 135g 135g B,f B,f B,f A,i 10 5 2 A A B 2(45g) 45g 135g For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the billiard ball i initially at ret. Find the final elocity of each ball. Aue the colliion i elatic. 10 / a b Va=?? a b Vb=?? BEFORE AFTER Since the colliion i elatic we can ue the forula on page 266 of your book: A,f A,f A,f A,i 10 5 A A 45g 45g B B 135g 135g B,f B,f B,f A,i 10 5 2 A A B 2(45g) 45g 135g Iportant note: The relatie peed of the ball i the ae before and after the colliion. Thi will alway hold true for head-on elatic colliion. For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the 8-ball i oing toward the golf ball at 5 /. Find the final elocity of each ball. Aue the colliion i elatic. 10 / a 5 / BEFORE b Va=?? a AFTER b Vb=?? Now let ee what happen if BOTH object are oing before the colliion. The hortcut forula will only work if one of the object i at ret, o we hae to witch our point of iew before we can plug in the nuber. We need to ubtract the elocity of one of the object fro both initial elocitie, then ue the forula, then add back the elocity to get the final anwer. In thi cae, let ay the 8-Ball i at ret. That gie a new initial elocity for the golf ball of 10 / (-5 /) = 15 /. For Capu Learning Aitance Serice at UCSB
Exaple: A golf ball (45 gra) roll toward a billiard ball (135 gra). The initial peed of the golf ball i 10 /, and the 8-ball i oing toward the golf ball at 5 /. Find the final elocity of each ball. Aue the colliion i elatic. 10 / a 5 / BEFORE b Va=?? a AFTER b Vb=?? A,f A,f A,f A,f A,i 15 7.5 7.5 A A B B 45g 135g 45g 135g ( 5 ) 12.5 B,f B,f B,f B,f A,i 15 7.5 7.5 2 A A ( 5 B 2(45g) 45g 135g ) 2.5 Notice that the relatie peed of the ball i till the ae before and after the colliion. Thi will alway hold true for head-on elatic collion. For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). final =? Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? We hould tart by writing down the coponent of each player initial elocity: Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x a,y (6 ) co(40 ) 4.6 (6 ) in(40 ) 3.9 b,x 0 b,y 4 40 Player B Player A Ma 80kg Ma 90kg =4 / =6 / For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x a,y (6 ) co(40 ) 4.6 (6 ) in(40 ) 3.9 b,x b,y 0 4 40 Player B Next we can write down the forula for coneration of oentu in each direction: Player A Ma 90kg =6 / Ma 80kg =4 / For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x a,y (6 ) co(40 ) 4.6 (6 ) in(40 ) 3.9 b,x b,y 0 4 40 Player B Coneration of oentu in each direction: Player A Ma 90kg Ma 80kg =4 / x direction =6 / (90kg) (4.6 ) (80kg) (0 ) (170kg) f,x Total a = 90kg + 80kg y direction (90kg) (3.9 ) (80kg) (4 ) (170kg) f,y For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x a,y (6 ) co(40 ) 4.6 (6 ) in(40 ) 3.9 b,x b,y 0 4 40 Player B Coneration of oentu in each direction: Player A Ma 90kg Ma 80kg =4 / x direction =6 / (90kg) (4.6 f,x 2.4 ) (80kg) (0 ) (170kg) f,x y direction (90kg) (3.9 f,y 3.9 ) (80kg) (4 ) (170kg) f,y For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x (6 ) co(40 ) 4.6 b,x 0 a,y (6 ) in(40 ) 3.9 b,y 4 Coneration of oentu in each direction: x direction (90kg) (4.6 f,x f,y 2.4 y direction (90kg) (3.9 3.9 ) (80kg) (0 ) (80kg) (4 ) (170kg) ) (170kg) f,x f,y Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / Cobine the coponent to find the agnitude and direction of the final elocity: For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x (6 ) co(40 ) 4.6 b,x 0 a,y (6 ) in(40 ) 3.9 b,y 4 Coneration of oentu in each direction: x direction (90kg) (4.6 f,x f,y 2.4 y direction (90kg) (3.9 3.9 ) (80kg) (0 ) (80kg) (4 ) (170kg) ) (170kg) f,x f,y Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / Cobine the coponent to find the agnitude and direction of the final elocity: 2 2 f (2.4 ) (3.9 ) 4. 6 For Capu Learning Aitance Serice at UCSB
Exaple: Thi one will be 2-dienional. Two hockey player are initially kating a hown in the figure. They collide, and tick together. Find their final elocity (agnitude and direction). Thi i a perfectly inelatic colliion, o we hould ue coneration of oentu. We need to hae eparate forula for x- and for y-direction final =? Coponent of each player initial elocity: a,x (6 ) co(40 ) 4.6 b,x 0 a,y (6 ) in(40 ) 3.9 b,y 4 Coneration of oentu in each direction: x direction (90kg) (4.6 f,x f,y 2.4 y direction (90kg) (3.9 3.9 ) (80kg) (0 ) (80kg) (4 ) (170kg) ) (170kg) f,x f,y Player A Ma 90kg =6 / 40 Player B Ma 80kg =4 / Cobine the coponent to find the agnitude and direction of the final elocity: 2 2 f (2.4 ) (3.9 ) 4. 6 tan( ) 3.9 2.4 58 For Capu Learning Aitance Serice at UCSB