1.5 Extra Practice and Attached Solutions

Physics 30 Workbook – Summer (Online) Unit 1: Momentum and Impulse p.28 HOMEWORK (2-D Conservation: Tail-to-Tip) 1. A 7.0 kg object, moving East at 13.0 m/s, collides with an 11.0 kg object moving South at 6.0 m/s. If they stick together, what is the final velocity of the combined mass? 2. A mass M , moving West at 4.0 m/s, collides with a mass 5 M moving South at 2.0 m/s. If they stick together upon collision, determine the direction they travel after the collision. 3. Mass 1, moving East, collides with Mass 2 which is at rest. After the collision, Mass 2 is moving at an angle of 22 q S of E. Sketch the tail-to-tip diagram showing conservation of momentum. © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020

Physics 30 Workbook – Summer (Online) Unit 1: Momentum and Impulse p.29 4. A 120 kg bomb, initially at rest, explodes into three pieces. The first piece has a mass of 46.0 kg and is moving at 50.0 m/s East, while the second piece has a mass of 27.0 kg and is moving at 140 m/s South. Determine the final velocity of the third piece. 5. A bomb that is moving East explodes into two pieces. The 38.0 kg piece is moving at 140 m/s North, while the 55.0 kg piece is moving at 111 m/s. Determine a) the initial speed of the bomb b) the angle of the 55.0 kg mass’s final velocity SOLUTIONS 1. 6.2 m/s at 36 q S of E (54 q E of S) 3. 2. 68 q S of W (22 q W of S) 4. 94.1 m/s at 58.7 q N of W (31.3 q W of N) 5. a) 32.2 m/s b) 60.6 q S of E (29.4 q E of S) © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020

Physics 30 Workbook – Summer (Online) Unit 1: Momentum and Impulse p.32 2. A bomb, initially at rest, explodes into 3 pieces. Piece 1 has a momentum of 194.4 kg m/s directed 40.0 q N of E, while piece 2 has a momentum of 187.2 kg m/s directed at 11.0 q N of W. Determine the momentum of the third piece just after the explosion. SOLUTIONS 1. x 2 c = 31.73 kgm/s ; y 2 c = ± 35.03 kgm/s ; v 2 c = 4.7 m/s at 48 q S of E (42 q E of S , 312 q ) 2. x 3 c = 34.841 kgm/s ; y 3 c = ± 160.678 kgm/s ; p = 164 kg m/s ; T = 77.8 q S of E (12.2 q E of S) © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020

Physics 30 Workbook ± Summer Online Unit 1 Solutions - 15 - LESSON 6: 2D CONSERVATION OF MOMENTUM (Tail-to-Tip) 1. 1 1 1 v m p = (7) (13) = 91 kg m/s ; 2 2 2 v m p = (11) (6) = 66 kg m/s Conservation of Momentum (Collision) T T p p c & & 12 2 1 p p p c ± & & & 2 2 12 66 91 ± c p = 112.4 kg m/s v m p c c 12 12 18 4 . 112 12 12 c c m p v = 6.2 m/s 91 66 tan T T = 36 q S of E (54 q E of S) 2. 1 1 1 v m p = ( M ) (4.0) = 4 M ; 2 2 2 v m p = (5 M ) (2.0) = 10 M Conservation of Momentum (Collision) T T p p c & & 12 2 1 p p p c ± & & & M M 4 10 tan T ¸ ¹ · ¨ © § ² 4 10 tan 1 T T = 68 q S of W (22 q W of S) 3. Conservation of Momentum (Collision) T T p p c & & 2 1 1 p p p c ± c & & & p 1 = 91 p 2 = 66 12 p c T p 1 = 4 M p 2 = 10 M 12 p c T p 1 p 2 c p 1 c 22 q T 1 c T 1 c © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020

Physics 30 Workbook ± Summer Online Unit 1 Solutions - 17 - LESSON 7: 2D CONSERVATION OF MOMENTUM (Components) 1. 1 1 1 v m p = (40) (6.5) = 260 kg m/s x p 1 & = 260 cos 20 q = 244.32 kg m/s y p 1 & = ² 260 sin 20 q = ² 88.93 kg m/s 2 2 2 v m p = (10) (9) = 90 kg m/s x p 2 & = ² 90 cos 80 q = ² 15.63 kg m/s y p 2 & = 90 sin 80 q = 88.63 kg m/s 1 1 1 v m p c c = (40) (5) = 200 kg m/s x p 1 c & = 200 cos 10 q = 196.96 kg m/s y p 1 c & = 200 sin 10 q = 34.73 kg m/s Conservation of momentum Tx Tx p p c & & x x x x p p p p 2 1 2 1 c ± c ± & & & & x p 2 96 . 196 63 . 15 32 . 244 c ± ² & x p 2 c & = 31.73 kg m/s Ty Ty p p c & & y y y y p p p p 2 1 2 1 c ± c ± & & & & y p 2 73 . 34 63 . 88 93 . 88 c ± ± ² & y p 2 c & = ² 35.03 kg m/s 2 2 2 03 . 35 73 . 31 ± c p = 47.264 kg m/s 2 2 2 v m p c c 10 264 . 47 2 2 2 c c m p v = 4.7 m/s 73 . 31 03 . 35 tan T T = 48 q S of E (42 q E of S) y x 10 q y p 1 c x p 1 c 1 p c = 200 p 1 =260 y x 20 q p 1x p 1y y x 80 q p 2 = 90 p 2y p 2x 31.73 35.03 2 p c T © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020

Physics 30 Workbook ± Summer Online Unit 1 Solutions - 18 - Lesson 7 Homework (2-D Conservation of Momentum: Components) 2. Let m 1 = 2.7 kg piece ; m 2 = 3.6 kg piece ; m 3 = 1.7 kg piece x p 1 c & = 194.4 cos 40 q = 148.92 kg m/s y p 1 c & = 194.4 sin 40 q = 124.96 kg m/s x p 2 c & = ² 187.2 cos 11 q = ² 183.76 kg m/s y p 2 c & = 187.2 sin 11 q = 35.72 kg m/s Conservation of momentum Tx Tx p p c & & x x x p p p 3 2 1 0 c ± c ± c & & & x p 3 76 . 183 92 . 148 0 c ± ² & x p 3 c & = 34.84 kg m/s Ty Ty p p c & & y y y p p p 3 2 1 0 c ± c ± c & & & x p 3 72 . 35 96 . 124 0 c ± ± & y p 3 c & = ² 160.68 kg m/s 2 2 3 68 . 160 84 . 34 ± c p = 164 kg m/s 84 . 34 68 . 160 tan T T = 77.8 q y x 11 q y p 2 c x p 2 c 2 p c = 187.2 34.84 160.68 3 p c T y x 40 q y p 1 c x p 1 c 1 p c = 194.4 © 2020 Edmonton Public Schools DRAFT SUMMER SCHOOL 2020 October 2020