Momentum in 2 Dimensions. Unit 1B

Transcription

1 Momentum in 2 Dimensions Unit 1B

2 You were introduced to momentum and momentum calculations, including 1D collisions, in Physics In this part of unit 1 we will study: 2D collisions Explosions where one mass separates into three separate parts

3 We will start with practical examples of collisions from Physics 2204 and further extend this to 2D collisions.

4 Recall: Momentum The physics definition of momentum is mass times velocity. p mv p = momentum (kgm/s) m = mass (kg) v = velocity (m/s)

5 Conservation of Momentum Total momentum before a collision is equal to the total momentum after a collision. **Solving requires the SAME approach as in 2204: p p total before collision = total after collision The only difference is we will be dealing with 2 dimensions

6 Conservation of Momentum Quick review of 1D Example 1: Mass 1 (4.20 kg) is travelling m/s [E] when it hits and sticks to Mass 2 (9.50 kg) which is stationary. What velocity do they travel together? p before p after p p p 1i 2 i (1 2) f m v m v ( m m ) v 1 1i 2 2i 1 2 f 4.20 kg(12.00 m ) 9.50 kg(0 m ) (4.20kg 9.50 kg) v s s f 50.4kg 13.7kgv m s 50.4kg m s 13.7kg v vf f f 3.68 [ E] m s

7 Ex. 2 Mass 1(1.5 kg) is travelling 5.0 m/s [N] and hits Mass 2 (2.0 kg) travelling 1.0m/s [S]. After the collision Mass 2 travels 1.6 m/s [N] what is v 1? (Sketch a picture) p before p after p p p p 1i 2i 1f 2f m v m v m v m v 1 1i 2 2i 1 1f 2 2f

8 Explosions (Sketch a picture) Ex. 3 Mass 1 (1.5 kg) and Mass 2 (2.0 kg) are parked next to each other with a spring between them. When the spring is released Mass 1 travels 3.0 m/s [L]. What is v 2?

9 Applying the law of conservation of momentum to 2D collisions. As in 1D: Total momentum before a collision is equal to the total momentum after a collision. In 2 D: Information should be organized in two categories: momentum before collision and momentum after collision (horizontal and vertical) (horizontal and vertical) Solving 2D problems will require the use of components when analyzing collisions. In any collision: Σp X (before) = Σp X (after) Σp Y (before) = Σp Y (after) From there, you can identify the given quantities and the quantity you are required to find.

10 A graphic organizer such as the following could be used.

11 2D collisions will be limited to the following: OFF CENTRE An object colliding with a stationary object (in which both scatter) both angles after the collision will be given to students. You will be expected to determine: the final velocity of one particle, and the initial velocity of moving particle.

12 Sample Workings

13 Orthogonal Two moving objects colliding at 90 O (and both scatter). Angles after the collision will be given to start and then progress to where only one resultant angle is given. You will be expected to determine the following: final velocity of two particles moving together including the angle initial velocity of one of the particles.

14 Sample Workings

15 Explosions Treatment of explosions should include one mass separating into three separate parts in which: one part moves in either the horizontal (x) or vertical (y) frame, one part moves perpendicular to that frame, and the final element moves at some angle. Students will determine the velocity (magnitude and direction) of the final element.

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17 Examples: OFF CENTRE 1. A 19.2 kg curling stone (A) moving at 2.10 m/s [N] strikes another identical stone (B) off centre. Stone A moves off with a velocity of 1.82 m/s [11.0 o East of North]. What will be the velocity of stone B after the collision? (Ignore frictional and rotational effects) kg 2.10 m s 40.32kg m s 0

18 1. A 19.2 kg curling stone (A) moving at 2.10 m/s [N] strikes another identical stone (B) off centre. Stone A moves off with a velocity of 1.82 m/s [11.0 o East of North]. What will be the velocity of stone B after the collision? (Ignore frictional and rotational effects) px before px after sin11 o 6.668kg m s p Bx pbx 6.668kg m s cos11 o kg m s p py after Y before pby pby 6.018kg m s

19 6.668kg m 6.668kg m s s kg m s 6.018kg m s p B p kg 2 2 p m B s tan o o p kg [42.07 N of W] B B B B m s o m v kg [42.07 N of W] o kg m s [42.07 N of W] v m [42.07 o ] B s N of W 19.2kg m s

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21 2. Find the velocity of the cue ball. Mass: Cue ball 0.17 kg, 8 ball 0.15 kg

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23 What kind of collision were these last two examples? A) Highly Elastic B) Inelastic Collisions in which objects bounce freely from each other would be examples of highly elastic collisions. Collisions in which the bodies stick together after contact or are greatly deformed would be examples of inelastic collisions.

24 ORTROGONAL 3. A 92 kg quarter back moving at 7.0 m/s [S] is tackled by a 115 kg linebacker running at 8.0 m/s [E]. What will be the velocity of the centre of mass of the combination of the two players immediately after impact? This is an example of an inelastic collision. L Q

25 4. A 1000 kg car is moving eastward at 20 m/s. It collides inelastically with a 1500 kg van traveling northward at 30 m/s. What is the velocity of the two vehicles immediately after the collision?

26 5. Two billiard balls with identical mass collide (m=0.160 kg). Mass 1 is travelling 2.20 m/s [S], mass 2 is travelling 3.10 m/s [W]. After the collision v 1 is 2.56 m/s [14.0 O N of W]. Determine the velocity of mass 2 after the collision kg m s kg m s 0 p p X before X after cos14 o p x m 2 kg s sin14 o kg m s p m 2 x kg s py before py after pby p m 2 Y kg s p m 2 Y kg s p m 2 x kg s 2 2 p kg m 2 s tan o

27 p o p kg m [12.33 ] 2 s W of S m v o kg [12.33 W of S] m s v 2 o kg [12.33 W of S] m s 0.160kg o [12.33 W of N] m s o v 2.89 m [12.3 ] 2 s W of N

28 6. Two snowboarders collide together at the bottom of a ski lift. After the collision both snowboarders move together at a velocity of 2.32 m/s [24.0 o E of N]. Snowboarder J has a mass of 71.0 kg and was initially travelling with a velocity of 3.00 m/s [N]. Determine snowboarder D s initially velocity given D s mass was 29.5 kg and was originally travelling East.

29 Explosions Text page A 0.60-kg fireworks bundle is at rest just before it explodes into three fragments. A 0.20-kg fragment (A) flies at 14.6 m/s [W], and a 0.18-kg fragment (B) moves at 19.2 m/s [S]. What is the velocity of the third fragment (C) just after the explosion? Assume that no mass is lost, and that the motion of the fragments lies in a plane. Solution: i) Find the mass of C. ii) iii) What is the initial momentum? (before the explosion) What is the total momentum after the explosion?

30 iv) Find the momentum of parts A B v) Find momentum of C. vi) What is C s final velocity? V - 30

31 8. An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 ms 1 and 2 kg second part moving with a velocity of 8 ms 1. If the third part flies off with a velocity of 4 ms 1, determine its mass. (1) 7 kg (2) 17 kg (3) 3 kg (4) 5 kg

32 Text Questions: Page 499 # 6, 10 Page 505 #58, 59A) , 66A), 68, 72, 80, 82

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40 Physics meets Biology

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