Applied Physics I (Phys 182)

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1 Applied Physics I (Phys 182) Dr. Joseph J. Trout E-ail: Cell: (610) Office: Disque 902 1

2 Moentu Ipulse Conservation of Moentu Explosions Inelastic Collisions Elastic Collisions Rocket Propulsion 2

3 Ipulse -Force ties the tie the force is in contact with an object. F N I =F t =Area under curve. t s t i t f 3

4 Ipulse -Force ties the tie the force is in contact with an object. F N I avg =F avg t F ave t s t i t f 4

5 A baseball player uses a bat to apply an average force of 100 N on a baseball for twenty seconds. What is the ipulse? F N I avg =F avg t =100 N 20 s F ave =2000 kg s t s t i t f 5

6 Moentu -Mass of an object ties the velocity of the object. p= v v p= = p x i p y j p z k 6

7 A 5 kg object oves at a velocity of 10 /s. What is the oentu of the object? p= v=5kg 10 /s =50 kg s v Sae units as ipulse... 7

8 Reeber Newton's Second Law? F net = a Consider constant net force, therefore constant acceleration. Also, consider constant ass. 8

9 Reeber Newton's Second Law? F = a net Consider constant net force, therefore constant acceleration. This eans that: a= v t = v v f i t Also, consider constant ass. F = a net 9

10 Reeber Newton's Second Law? F = a net Consider constant net force, therefore constant acceleration. This eans that: a= v t = v v f i t Also, consider constant ass. F = a net = F v v f i net t 10

11 F = a net a= v t = v v f i t = F v v f i net t F t= v v net f i F t= v v net f i F t= p p net f i p v 11

12 Reeber Newton's Second Law? F t= p p net f i F t= p net I = p net a= v t = v v f i t p v I F t net net 12

13 Ipulse: I avg =F avg t=a t= v t t= v I avg =F avg t= v f v i = p f p i = p F avg = p t 13

14 v i = 20 / s =2 kg v f =30/s 14

15 v i = 20 / s =2 kg v f =30/s I avg =F avg t= p I avg = v f v i =2kg 30 /s 2kg 20 / s =100 kg /s 15

16 v i = 20 / s =2 kg v f =30/s I avg =F avg t= p I avg = v f v i =2 kg 30 /s 2 kg 20 /s =100 kg /s Ball is in contact with bat for 10 seconds. F avg t= p F avg = p t =100 kg /s 10 s =1000 N 16

17 F t= p net If F net =0 then: 0= p= p f p i p f = p i Moentu is conserved. 17

18 Explosions! 18

19 They push off one another. According to Newton's 3 rd Law, forces are equal and opposite. Therefore, net force is equal to zero! 1 =50 kg v 1i =0 /s 2 =60kg v 2i =0 / s Ice Rink 19

20 They push off one another. According to Newton's 3 rd Law, forces are equal and opposite. Therefore, net force is equal to zero! F 21 F 12 F = F F =0 net 1 =50kg v 1i =0 /s 2 =60kg v 2i =0 / s Ice Rink 20

21 They push off one another. According to Newton's 3 rd Law, forces are equal and opposite. Therefore, net force is equal to zero! Moentu is conserved! F net =0 p=0 p i = p f 0= 1 v 1 f 2 v 2 f 1 =50kg v 1i =0 /s 2 =60kg v 2i =0 / s Ice Rink 21

22 They push off one another. According to Newton's 3 rd Law, forces are equal and opposite. Therefore, net force is equal to zero! 0= 1 v 1 f 2 v 2 f v 2 f =? v 1 f = 2 1 v 2 f 60 kg v i f 3.6 /s= 50 kg 3 /s v 2 f = 3 /s 1 =50kg v 1i =0 /s 2 =60kg v 2i =0 / s Ice Rink 22

23 2 =60 kg 1 =10 kg v 1i =v 2i =0 / s p i =0 23

24 Man jups out of canoe. 2 =60 kg v f 1 =? 1 =10 kg v 1i =v 2i =0 / s p i =0 v f 2 =4 /s 24

25 Man jups out of canoe. 2 =60 kg v f 1 =? 1 =10 kg v 1i =v 2i =0 / s p i =0 v f 2 =4 /s p i = p f 0= 1 v 1 f 2 v 2 f 1 v 1 f = 2 v 2 f v 1 f = 2 60 kg v 2 f 1 = 4 / s= 24 / s 10 kg 25

26 Collisions Totally Inelastic Inelastic Perfectly Elastic 26

27 Collisions Totally Inelastic Moentu conserved. KE is NOT conserved. Stick together after Collision. Inelastic Moentu conserved. KE is NOT conserved. Perfectly Elastic Moentu conserved. KE is conserved 27

28 Totally Inelastic Moentu conserved. KE is NOT conserved. Stick together after Collision. v 1i 2 1 v 2i 28

29 Totally Inelastic Moentu conserved. KE is NOT conserved. Stick together after Collision. v 1i v v f 2i p i = p f p 1i p 2i = p 1 f p 2 f 1 v 1i 2 v 2i = 1 v 1 f 2 v 2 f 1 v 1i 2 v 2i = 1 2 v f v 1 f =v 2 f =v f v f = 1 v 1i 2 v 2i

30 Totally Inelastic Moentu conserved. KE is NOT conserved. Stick together after Collision. 1 = 10 kg v 1i = 10 / s 2 = 90 kg v 2i =0 /s 1 2 v f p i = p f p 1i p 2i = p 1 f p 2 f 1 v 1i 2 v 2i = 1 v 1 f 2 v 2 f 1 v 1i 2 v 2i = 1 2 v f v 1 f =v 2 f =v f v f = 1 v 1i 2 v 2i

31 1 v 1i 1 v 2i Elastic Collisions Moentu and Kinetic Energy are Conserved. p p = p p 1i 2i 1 f 2 f v v = v v 1 1i 2 2i 1 1 f 2 2 f v 1i KE 1i KE 2i =KE 1 f KE 2 f v 2i 2 = v 1 f v 2 2 f 31

32 p 1i p 2i = p 1 f p 2 f 1 v 1i 2 v 2i = 1 v 1 f 2 v 2 f 1 v 1i 1 v 1 f = 2 v 2 f 2 v 2i KE 1i KE 2i =KE 1 f KE 2 f v 2 1i v 2 2i = 1 2 1v 2 1 f v 2 f 1 v 2 1i 2 v 2 2i = 1 v f 2 v 2 f 1 v 2 1i 1 v 2 1 f = 2 v 2 f v 2i 32

33 p 1i p 2i = p 1 f p 2 f 1 v 1i 2 v 2i = 1 v 1 f 2 v 2 f 1 v 1i 1 v 1 f = 2 v 2 f 2 v 2i 1 v 1i v 1 f = 2 v 2 f v 2i KE 1i KE 2i =KE 1 f KE 2 f v 2 1i v 2 2i = v 2 1 f v 2 f 1 v 2 1i 2 v 2i 2 = 1 v 1 f v 2 f v 2i 1 v 2 1i 1 v 2 1 f = 2 v 2 f 1 v 2 2 1i v 1 f = 2 v f v 2i 33

34 1 p 1i p 2i = p 1 f p 2 f 1 v 1i 2 v 2i = 1 v 1 f 2 v 2 f 1 v 1i 1 v 1 f = 2 v 2 f 2 v 2i 1 v 1i v 1 f = 2 v 2 f v 2i 2 KE 1i KE 2i =KE 1 f KE 2 f 1 2 1v 2 1i v 2 2i = v 2 1 f v 2 f 1 v 2 1i 2 v 2i 1 v 2 1i 1 v 1 f 1 v 2 2 1i v 1 f 2 = 1 v 1 f 2 = 2 v 2 f = 2 v 2 f v 2 f v 2i 2 2 v 2i 1 v 1i v 1 f v 1i v 1 f = 2 v 2 f v 2i v 2 f v 2i v 1i v 1 f v 1i v 1 f = 2 v 2 f v 2i v 2 f v 2i 1 v 1i v 1 f 2 v 2 f v 2i 3 v 1i v 1 f = v 2i v 2 f 34

35 1 v 1i v 1 f = 2 v 2 f v 2i 1 3 v 1i v 1 f = v 2i v 2 f v 2 f = v 1i v 1 f v 2i v 2 f = v 1i v 1 f v 2i 35

36 3 v 1i v 1 f = v 2i v 2 f v 2 f = v 1i v 1 f v 2i v 2 f = v 1i v 1 f v 2i 1 1 v 1i v 1 f = 2 v 2 f v 2i 1 v 1i v 1 f = 2 v 1i v 1 f v 2i v 2i 1 v 1i 1 v 1 f = 2 v 1i 2 v 1 f 2 v 2i 2 v 2i 1 v 1i 2 v 2i 2 v 2i 2 v 1i = 2 v 1 f 1 v 1 f 1 2 v 1i 2 2 v 2i = 2 1 v 1 f v 1 f = v 1 i v 2 i 36

37 1 1 v 1i v 1 f = 2 v 2 f v 2i 1 v 1i v 2i v 2 f v 1i = 2 v 2 f v 2i 1 2v 1i v 2i v 2 f = 2 v 2 f v 2i 3 v 1i v 1 f = v 2i v 2 f v 1 f = v 2i v 2 f v 1i v 1 f = v 2i v 2 f v 1i 2 1 v 1i 1 v 2i 1 v 2 f = 2 v 2 f 2 v 2i 2 1 v 1i 1 v 2i 2 v 2i = 1 v 2 f 2 v 2 f 2 1 v 1i 2 1 v 2i = 1 2 v 2 f 1 2 v 2 f =2 1 v 1i 2 1 v 2i v 2 f = v 1 i v 2 i 37

38 Totally Elastic Collisions v 1 f = v 1 i v 2 i v 2 f = v 1 i v 2 i 38

39 1 = 10 kg v 1i =2/ s 2 = 10 kg v 2i =0 / s v 1 f = v 1 i v 2 i =0 0=0 v 2 f = v 1 i v 2 i =2/s 0=2 / s 39

40 1 = 10 kg v 1i =2/s 2 = 10 kg v 2i =0 /s 1 = 10 kg v 1 f =0 2 = 10 kg v 2 f =2/s v 1 f = v 1 i v 2 i =0 0=0 v 2 f = v 1 i v 2 i =2/s 0=2/s 40

41 h i v i =? M 41

42 P i =P f v i = M v f v f = M v i h i v i =? M v f Totally Inelastic Collision v f = M v i 42

43 h i v i =? M v f Totally Inelastic Collision v f = M v i 43

44 h f h i v i =? M v f Totally Inelastic Collision v f = M v i 44

45 1 2 M v f = M g h f h i h f v i =? M v f h i Totally Inelastic Collision v f = M v i 45

46 1 2 M v f = M g h f h i v f = 2 g h f h i = 2 g h h f v i =? M v f h i Totally Inelastic Collision v f = M v i 46

47 1 2 M v f = M g h f h i v f = 2 g h f h i = 2 g h h f h i v i =? M Totally Inelastic Collision v f = M v i v f v i = v f = 2 g h M v i= 2 g h M 2 g h 47

48 v i = M 2 g h h f h i v i =? M v f Totally Inelastic Collision v f = M v i 48

49 L L cos h f h i 49

50 L L cos h f h i h f h i = h=l L cos =L 1 cos 50

51 h=l 1 cos v i = = v M i 2 g h M 2 g L 1 cos h f h i v i =? M v f Totally Inelastic Collision v f = M v i 51