Section 5.1: Momentum and Impulse Tutorial 1 Practice, page Given: m = 160 g = 0.16 kg;! v = 140 m/s [E] Required:! p ; E k
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1 Section 5.1: Momentum and Imulse Tutorial 1 Practice, age Gien: m 160 g 0.16 kg; 140 m/s [E] Required: ; E k Analysis: m ; E k 1 2 m2 Solution: m E k 1 2 m2 (0.16 kg(40.0 m/s [E] 6.4 kg m/s [E] 1 (0.16 kg(40.0 m/s2 2 E k 130 J Statement: The momentum of the uck is 6.4 kg m/s [E], and the kinetic energy is 130 J. 2. Gien: m kg; m/s [E]; m g 0.16 kg; m/s [E] Required: 2 1 Analysis: m Solution: 1 2 m 1 1 m 2 2 (6.2 kg(1.6 m/s [E] (0.16 kg(40.0 m/s [E] kg " m/s [E] Statement: The difference in the momenta is 3.5 kg m/s [E]. Tutorial 2 Practice, age (a Gien: F 250 N [forward]; t s Required: Analysis: Ft Solution: Ft (250 N [forward]( s 0.75 N " s [forward] Statement: The imulse imarted by the hockey stick is 0.75 N s [forward]. (b Gien: Ft 0.75 N " s ; m 180 g 0.18 kg; i 0 Required: f Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-1
![Analysis: Ft m( f " i Ft m( f " i Ft m f Ft f m + i Solution: Ft f m + i 0.75 kg " m/s [forward] + 0 m/s 0.18 kg f 4.2 m/s [forward] Statement: The final elocity is 4.2 m/s [forward]. 2.](/docs-images/79/78946739/images/2-0.jpg "Gien: aerage force 468 N; t 2.9 s Required: force time grah; Ft Analysis: The aerage force is 468 N, so the grah is a straight line at F 468. Calculate the area under the cure.")
2 Analysis: Ft m( f " i Ft m( f " i Ft m f Ft f m + i Solution: Ft f m + i 0.75 kg " m/s [forward] + 0 m/s 0.18 kg f 4.2 m/s [forward] Statement: The final elocity is 4.2 m/s [forward]. 2. Gien: aerage force 468 N; t 2.9 s Required: force time grah; Ft Analysis: The aerage force is 468 N, so the grah is a straight line at F 468. Calculate the area under the cure. Solution: Draw the grah. Ft bh (2.9 s(468 N Ft 1400 N "s Statement: The imulse of the collision is 1400 N s [away from the wall]. Section 5.1 Questions, age (a Gien: m kg; 6.9 m/s [N] Required: Analysis: m Solution: m ( kg(6.9 m/s [N] 2900 kg " m/s [N] Statement: The momentum of the moose is kg m/s [N]. (b Gien: m kg; 5 km/h [forward] Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-2
3 Required: Analysis: m Conert the elocity to metres er second. 5 km [forward] 1 h h 3600 s 1000 m 1 km 1.4 m/s [forward] Solution: m ( kg(1.4 m/s [forward] kg " m/s [forward] Statement: The momentum of the bus is kg m/s [forward]. (c Gien: m 995 g kg; 16 m/s [S] Required: Analysis: m Solution: m (0.995 kg(16 m/s [S] 16 N s [S] Statement: The momentum of the squirrel is 16 N s [S]. 2. Answers may ary. Samle answer: Imulse is the change in momentum of an object during a certain time. Its units are newton seconds (N s. 3. Gien: m 79.3 kg; kg " m/s [W] Required: Analysis: m m Solution: m kg " m/s [W] 79.3 kg 27.2 m/s [W] Statement: The elocity of the bicycle is 27.2 m/s [W]. 4. Gien: m/s [W] ; 4.5 kg m/s [W] Required: m Analysis: m m Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-3
4 Solution: m 4.5 kg m/s [W] 9.0 " 10 2 m/s [W] m 5.0 " 10 #3 kg Statement: The mass of the rojectile is "3 kg or 5.0 g. 5. Gien: 29.5 m/s [forward]; kg " m/s [forward] Required: m Analysis: m m Solution: m kg " m/s [forward] 29.5 m/s [forward] m 78.3 kg Statement: The mass of the skier is 78.3 kg. 6. Answers may ary. Samle answer: In lacrosse, when a layer follows through when striking a ball, this increases the time interal oer which the collision between the ball and lacrosse stick occurs and thus contributes to an increase in the elocity change of the ball. Following through, a hitter can hit the ball in such a way that it is moing faster when it leaes the stick. This can imroe erformance in lacrosse by making the ball trael farther in a gien amount of time and by making it harder for an oosing layer to catch u with or react to the ball in time. 7. Both balls will hit the floor with the same seed, and both will rebound with this same seed. Since the basketball has more mass, the same seed means it has more momentum. To reerse its larger momentum requires a larger imulse on the basketball. 8. (a Gien: F N [forward] ; t 5.0 ms s Required: Analysis: Ft Solution: Ft ( N [forward](5.0 " 10 #3 s 5.5 N $s [forward] Statement: The imulse is 5.5 N s [forward]. Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-4
5 (b Gien: m 0.12 kg; i 0 m/s; Ft 5.5 N " s [forward] Required: f Analysis: Ft m( f " i Ft m( f " i f Ft m + i Solution: f Ft m + i 5.5 N "s 0.12 kg + 0 m/s f 46 m/s Statement: The seed of the uck just after it leaes the stick is 46 m/s. 9. (a Gien: m 225 g kg; y 74 cm 0.74 m Required: Analysis: The otential energy as you dro the hone is equal to the kinetic energy when it hits the ground. Use E k E g, E k 1 2 m2 and E g mgy to obtain 1 2 m2 mgy. Isolate in this equation: 2gy. Calculate the seed, and then use m to calculate the momentum. Solution: Calculate the seed when the hone hits the ground. 2gy 2(9.8 m/s 2 (0.74 m 3.81 m/s (one extra digit carried Calculate the momentum. m (0.225 kg(3.81 m/s [down] 0.86 kg m/s [down] Statement: The cellhone s momentum at the moment of imact is 0.86 kg m/s [down]. (b The surface of the imact makes no difference to the momentum. The seed and mass do not change, so the momentum does not change. 10. (a Gien: m 0.25 kg; y 1.5 m; f 4.0 m/s [u] Required: imulse of the ball, Analysis: The otential energy as you dro the ball is equal to the kinetic energy when it hits the ground. Use E k E g, E k 1 2 m2 and E g mgy to obtain 1 2 m2 mgy. Isolate in this equation: 2gy. Calculate the elocity, and then use m( f " i to calculate the imulse imarted by the floor to the ball. Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-5
6 Solution: Calculate the elocity of the ball just before it hits the ground. 2gy 2(9.8 m/s 2 (1.5 m 5.42 m/s (one extra digit carried The elocity is downward, so i 5.42 m/s [down]. m( f " i (0.25 kg(4.0 m/s [u]" 5.42 m/s [down] (0.25 kg(4.0 m/s [u] m/s [u] 2.36 N #s [u] (one extra digit carried 2.4 N #s [u] Statement: The imulse imarted by the floor to the ball is 2.4 N s [u]. (b Gien: 2.36 N " s [u] ; F 18 N [u] Required: t Analysis: Ft, so t F. Solution: t F 2.36 N " s 18 N t 0.13 s Statement: The ball is in contact with the floor for 0.13 s. 11. (a Gien: m kg; 88 m/s [forward] Required: Analysis: The initial elocity of the arrow is 0 m/s. Use m. Solution: m (0.030 kg(88 m/s [forward] 2.64 N "s [forward] (one extra digit carried 2.6 N "s [forward] Statement: The imulse is 2.6 N s [forward]. (b Gien: t s; 2.64 N "s [forward] Required: F Analysis: Ft, so F t. Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-6
7 Solution: F t 2.64 kg " m/s [forward] s F 1.8 # 10 2 N [forward] Statement: The aerage force of the bowstring on the arrow is N [forward]. 12. (a Gien: i 63 m/s [W] ; m kg; f 41 m/s [E] Required: Analysis: m( f " i Solution: m( f " i (0.057 kg(41 m/s [E] " 63 m/s [W] (0.057 kg(41 m/s [E] + 63 m/s [E] 5.93 N #s [E] (one extra digit carried Statement: The magnitude of the imulse is 5.9 N s. (b Gien: 5.93 N " s [E] ; t s Required: F Analysis: Ft, so F t. Solution: F t 5.93 N " s [E] s F 2.6 # 10 2 N [E] Statement: The aerage force is N [E]. Coyright 2012 Nelson Education Ltd. Chater 5: Momentum and Collisions 5.1-7
, remembering that! v i 2
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