Chapter 9 - Momentum w./ QuickCheck Questions
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1 Chapter 9 - Momentum w./ QuickCheck Questions 2015 Pearson Education, Inc. Anastasia Ierides Department of Physics and Astronomy University of New Mexico October 15, 2015
2 Review of Last Time Torque - rotational equivalent to force Static equilibrium - net torque and net force have to both be zero Center of gravity & natural axis of rotation Hooke s law, Young s modulus, tensile stress and strain Elasticity of material; spring-like behavior
3 In Chapter 4-7 Learned about Newton s 3 rd law
4 In Chapter 4-7 Learned about Newton s 3 rd law Learned that when objects interact, the applied force from one object on another is equal in magnitude, but opposite in direction
5 In Chapter 4-7 Learned about Newton s 3 rd law Learned that when objects interact, the applied force from one object on another is equal in magnitude, but opposite in direction Here we apply this logic to understand how interacting objects affect each other s motion
6 In Chapter 4-7 Learned about Newton s 3 rd law Learned that when objects interact, the applied force from one object on another is equal in magnitude, but opposite in direction Here we apply this logic to understand how interacting objects affect each other s motion In particular, their momentum
7 Stop To Think A hammer hits a nail. The force of the nail on the hammer is A. Greater than the force of the hammer on the nail. B. Less than the force of the hammer on the nail. C. Equal to the force of the hammer on the nail. D. Zero.
8 Stop To Think A hammer hits a nail. The force of the nail on the hammer is A. Greater than the force of the hammer on the nail. B. Less than the force of the hammer on the nail. C. Equal to the force of the hammer on the nail. D. Zero. The force of the hammer on the nail and the force of the nail on the hammer are the two members of the action/ reaction pair of Newton s 3rd law. They must have the same magnitude.
9 Stop To Think A hammer hits a nail. The force of the nail on the hammer is A. Greater than the force of the hammer on the nail. B. Less than the force of the hammer on the nail. C. Equal to the force of the hammer on the nail. D. Zero. The force of the hammer on the nail and the force of the nail on the hammer are the two members of the action/ reaction pair of Newton s 3rd law. They must have the same magnitude.
10 Collisions and Elasticity A collision is a short-duration interaction between two objects
11 Collisions and Elasticity A collision is a short-duration interaction between two objects Objects are compressed during a collision, requiring time to re-expand
12 Collisions and Elasticity A collision is a short-duration interaction between two objects Objects are compressed during a collision, requiring time to re-expand The duration of a collision depends on the material the objects are made from
13 Collisions and Elasticity A collision is a short-duration interaction between two objects Objects are compressed during a collision, requiring time to re-expand The duration of a collision depends on the material the objects are made from The amount of compression is a measure of the magnitude of the force exerted on the object
14 Impulse - Kicking a Ball
15 Impulse - Kicking a Ball Compression occurs during contact due to the force between the two objects
16 Impulse - Kicking a Ball Compression occurs during contact due to the force between the two objects This force is called the impulse force - large force exerted over a small time interval
17 Impulse - Kicking a Ball The effect of an impulsive force is proportional to the area under the forceversus-time curve
18 Impulse - Kicking a Ball The area is called the impulse J of the force.
19 Impulse - Kicking a Ball The area is called the impulse J of the force. To simplify, look at the average force
20 Impulse It is useful to think of the collision in terms of an average force F avg
21 Impulse It is useful to think of the collision in terms of an average force F avg F avg is defined as the constant force that has the same duration Δt yielding the same area under the curve
22 Impulse
23 Impulse Impulse has units of N s or kg m/s (preferred)
24 Impulse Impulse has units of N s or kg m/s (preferred) It is a vector quantity pointing in the same direction as the average force, F avg,
25 Impulse Impulse has units of N s or kg m/s (preferred) It is a vector quantity pointing in the same direction as the average force, F avg,
26 Example 9.1: Finding the impulse on a bouncing ball A rubber ball experiences the force shown in the figure as it bounces off the floor. a. What is the impulse on the ball? b. What is the average force on the ball?
27 Example 9.1: Finding the impulse on a bouncing ball A rubber ball experiences the force shown in the figure as it bounces off the floor. a. What is the impulse on the ball? b. What is the average force on the ball? PREPARE The impulse is the area under the force curve. Here the shape of the graph is triangular, so we ll need to use the fact that the area of a triangle is 1/2 height base.
28 Example 9.1: Finding the impulse on a bouncing ball SOLVE a. The impulse is
29 Example 9.1: Finding the impulse on a bouncing ball SOLVE a. The impulse is b. From J = F avg t, we can find the average force that would give this same impulse:
30 Example 9.1: Finding the impulse on a bouncing ball SOLVE a. The impulse is b. From J = F avg t, we can find the average force that would give this same impulse:
31 Example 9.1: Finding the impulse on a bouncing ball SOLVE a. The impulse is b. From J = F avg t, we can find the average force that would give this same impulse: ASSESS The average value of the force is half the max value, not surprising for a triangular force.
32 Stop To Think 9.1 Graph A is the force-versus-time graph for a hockey stick hitting a 160 g puck. Graph B is the force-versus-time graph for a golf club hitting a 46 g golf ball. Which force delivers the greater impulse? A. Force A B. Force B C. Both forces deliver the same impulse.
33 Stop To Think 9.1 Graph A is the force-versus-time graph for a hockey stick hitting a 160 g puck. Graph B is the force-versus-time graph for a golf club hitting a 46 g golf ball. Which force delivers the greater impulse? A. Force A B. Force B C. Both forces deliver the same impulse.
34 Stop To Think 9.1 Graph A is the force-versus-time graph for a hockey stick hitting a 160 g puck. Graph B is the force-versus-time graph for a golf club hitting a 46 g golf ball. Which force delivers the greater impulse? JA = (300 N) (.005 s) = 1.5 kg m/s JB = (150 N) (.010 s) = 1.5 kg m/s A. Force A B. Force B C. Both forces deliver the same impulse.
35 Stop To Think 9.1 Graph A is the force-versus-time graph for a hockey stick hitting a 160 g puck. Graph B is the force-versus-time graph for a golf club hitting a 46 g golf ball. Which force delivers the greater impulse? JA = (300 N) (.005 s) = 1.5 kg m/s JB = (150 N) (.010 s) = 1.5 kg m/s A. Force A B. Force B C. Both forces deliver the same impulse.
36 Momentum The more mass an object has, the more force is required to cause it to accelerate - Newton s 2 nd
37 Momentum The more mass an object has, the more force is required to cause it to accelerate - Newton s 2 nd
38 Momentum The more mass an object has, the more force is required to cause it to accelerate - Newton s 2 nd
39 Momentum The more mass an object has, the more force is required to cause it to accelerate - Newton s 2 nd
40 Momentum Rearranging the terms we find that
41 Momentum Rearranging the terms we find that Momentum is the product of the object s mass and velocity
42 Momentum Rearranging the terms we find that Momentum is the product of the object s mass and velocity Units of kg m/s
43 Momentum
44 Momentum The magnitude of an object s momentum is the product of the object s mass and speed
45 Momentum
46 Impulse-Momentum We saw that, where the right side is the change in the momentum of an object
47 Impulse-Momentum We saw that, where the right side is the change in the momentum of an object We know that the area under the force-versustime curve, or the product of the average force over the time interval it is applied, is the impulse
48 Impulse-Momentum We can deduce then, that impulse and momentum are related as
49 Impulse-Momentum We can deduce then, that impulse and momentum are related as
50 Impulse-Momentum We can deduce then, that impulse and momentum are related as The impulse-momentum theory states that an impulse delivered to an object causes the object s momentum to change
51 QuickCheck Question 9.1 The cart s change of momentum Δp x is A. 20 kg m/s B. 10 kg m/s C. 0 kg m/s D. 10 kg m/s E. 30 kg m/s
52 QuickCheck Question 9.1 The cart s change of momentum Δp x is A. 20 kg m/s B. 10 kg m/s C. 0 kg m/s D. 10 kg m/s E. 30 kg m/s Δp x = 10 kg m/s ( 20 kg m/s) = 30 kg m/s
53 QuickCheck Question 9.1 The cart s change of momentum Δp x is A. 20 kg m/s B. 10 kg m/s C. 0 kg m/s D. 10 kg m/s E. 30 kg m/s Δp x = 10 kg m/s ( 20 kg m/s) = 30 kg m/s Negative initial momentum because motion is to the left and v x < 0.
54 QuickCheck Question 9.1 The cart s change of momentum Δp x is A. 20 kg m/s B. 10 kg m/s C. 0 kg m/s D. 10 kg m/s E. 30 kg m/s Δp x = 10 kg m/s ( 20 kg m/s) = 30 kg m/s Negative initial momentum because motion is to the left and v x < 0.
55 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right E. 2.0 m/s right
56 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right E. 2.0 m/s right J x =
57 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right J x = E. 2.0 m/s right = 1 kg m/s
58 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right J x = E. 2.0 m/s right = 1 kg m/s J x = Δp x = m (vf - vi) vf = J x /m + vi
59 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right E. 2.0 m/s right = 1 kg m/s vf = J x /m + vi = (1 kg m/s)/(2.0 kg) + (0.5 m/s) = 1 m/s J x = J x = Δp x = m (vf - vi) vf = J x /m + vi
60 QuickCheck Question 9.2 A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object s speed and direction after the force ends? A m/s left B. At rest C m/s right D. 1.0 m/s right J x = E. 2.0 m/s right = 1 kg m/s vf = J x /m + vi = (1 kg m/s)/(2.0 kg) + (0.5 m/s) = 1 m/s J x = Δp x = m (vf - vi) vf = J x /m + vi
61 QuickCheck Question 9.4 A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for A. 1/4 s B. 1/2 s C. 1 s D. 2 s E. 4 s
62 QuickCheck Question 9.4 A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for A. 1/4 s B. 1/2 s C. 1 s D. 2 s E. 4 s Remember: Fnew =1/2 Fold
63 QuickCheck Question 9.4 A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for A. 1/4 s B. 1/2 s C. 1 s D. 2 s E. 4 s Remember: F 1/Δt Fnew =1/2 Fold
64 QuickCheck Question 9.4 A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for A. 1/4 s B. 1/2 s C. 1 s D. 2 s E. 4 s Remember: F 1/Δt Fnew =1/2 Fold Fnew Fold = 1/Δtnew 1/Δtold = Δtold =1/2 Δtnew Δtnew = 2 Δtold
65 QuickCheck Question 9.4 A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for A. 1/4 s B. 1/2 s C. 1 s D. 2 s E. 4 s Remember: F 1/Δt Fnew =1/2 Fold Fnew Fold = 1/Δtnew 1/Δtold = Δtold Δtnew =1/2 Δtnew = 2 Δtold
66 QuickCheck Question 9.5 A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. A. Greater than B. Equal to C. Less than D. Can t say. It depends on how big the force is.
67 QuickCheck Question 9.5 A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. Same force, same time same impulse Same impulse same change of momentum A. Greater than B. Equal to C. Less than D. Can t say. It depends on how big the force is.
68 QuickCheck Question 9.5 A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. Same force, same time same impulse Same impulse same change of momentum A. Greater than B. Equal to C. Less than D. Can t say. It depends on how big the force is.
69 QuickCheck 9.6 Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? 10 N A. Ball 1 B. Ball 2 C. Both balls have the same final speed.
70 QuickCheck 9.6 Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? Remember: Change in momentum is due to the impulse delivered which is the area under the curve. 10 N A. Ball 1 B. Ball 2 C. Both balls have the same final speed.
71 QuickCheck 9.6 Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? Remember: Change in momentum is due to the impulse delivered which is the area under the curve. Area = 0.2 kg m/s 10 N Area = 0.2 kg m/s A. Ball 1 B. Ball 2 C. Both balls have the same final speed.
72 QuickCheck 9.6 Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? Remember: Change in momentum is due to the impulse delivered which is the area under the curve. Area = 0.2 kg m/s 10 N Area = 0.2 kg m/s A. Ball 1 B. Ball 2 C. Both balls have the same final speed.
73 Impulse-Momentum
74 Impulse-Momentum 2 dimensions? components!
75 Impulse-Momentum Theory Tells us that the average force needed to stop an object is inversely proportional to the duration of the collision
76 Impulse-Momentum Theory Tells us that the average force needed to stop an object is inversely proportional to the duration of the collision
77 Impulse-Momentum Theory Tells us that the average force needed to stop an object is inversely proportional to the duration of the collision If the duration of the collision can be increased, the force of the impact will be decreased
78 Hedgehogs Hedgehogs have been observed to fall out of trees on purpose to get to the ground!
79 Hedgehogs Hedgehogs have been observed to fall out of trees on purpose to get to the ground! Their spines help cushion their fall by increasing the time it takes for the animal to come to rest when it falls off of a tree.
80 Momentum & Impulse
81 Total Momentum
82 Total Momentum If there is a system of particles moving, then the system as a whole has an overall momentum
83 Total Momentum If there is a system of particles moving, then the system as a whole has an overall momentum The total momentum of a system of particles is the vector sum of the momenta of the individual particles:
84 Impulse Approximation The impulse approximation states that we can ignore the small forces that act during the brief time of the impulsive force We consider only the momenta and velocities immediately before and immediately after the collisions
85 Solving Momentum and Impulse Problems
86 Example 9.3: Force in hitting a baseball A 150 g baseball is thrown with a speed of 20 m/s. It is hit straight back toward the pitcher at a speed of 40 m/s. The impulsive force of the bat on the ball has the shape shown in the figure. What is the maximum force F max that the bat exerts on the ball? What is the average force that the bat exerts on the ball?
87 Example 9.3: Force in hitting a baseball PREPARE We can model the interaction as a collision. The figure is a before-and-after visual overview in which the steps from Tactics Box 9.1 are explicitly noted. Because F x is positive (a force to the right), we know the ball was initially moving toward the left and is hit back toward the right. Thus we converted the statements about speeds into information about velocities, with (v x ) i negative.
88 Example 9.3: Force in hitting a baseball SOLVE We want to use the impulse-momentum theorem to find the mathematical solution:
89 Example 9.3: Force in hitting a baseball SOLVE We want to use the impulse-momentum theorem to find the mathematical solution: We know the velocities before and after the collision, so we can find the change in the ball s momentum:
90 Example 9.3: Force in hitting a baseball SOLVE We want to use the impulse-momentum theorem to find the mathematical solution: We know the velocities before and after the collision, so we can find the change in the ball s momentum:
91 Example 9.3: Force in hitting a baseball SOLVE The force curve is a triangle with height F max and width 0.60 ms. As in Example 9.1, the area under the curve is
92 Example 9.3: Force in hitting a baseball SOLVE The force curve is a triangle with height F max and width 0.60 ms. As in Example 9.1, the area under the curve is
93 Example 9.3: Force in hitting a baseball SOLVE The force curve is a triangle with height F max and width 0.60 ms. As in Example 9.1, the area under the curve is According to the impulse-momentum theorem, px = Jx, so we have
94 Example 9.3: Force in hitting a baseball SOLVE The force curve is a triangle with height F max and width 0.60 ms. As in Example 9.1, the area under the curve is According to the impulse-momentum theorem, px = Jx, so we have
95 Example 9.3: Force in hitting a baseball SOLVE Thus the maximum force is
96 Example 9.3: Force in hitting a baseball SOLVE Thus the maximum force is
97 Example 9.3: Force in hitting a baseball SOLVE Thus the maximum force is We find that the average force, which depends on the collision duration t = s, has the smaller value:
98 Example 9.3: Force in hitting a baseball SOLVE Thus the maximum force is We find that the average force, which depends on the collision duration t = s, has the smaller value:
99 Example 9.3: Force in hitting a baseball SOLVE Thus the maximum force is We find that the average force, which depends on the collision duration t = s, has the smaller value: ASSESS F max is a large force, but quite typical of the impulsive forces during collisions.
100 Conservation of Momentum The forces on the 2 balls have equal magnitude but opposite directions (Newton s 3 rd )
101 Conservation of Momentum The forces on the 2 balls have equal magnitude but opposite directions (Newton s 3 rd )
102 Conservation of Momentum The forces on the 2 balls have equal magnitude but opposite directions (Newton s 3 rd ) If the momentum of ball 1 increases, the momentum of ball 2 will decrease by the same amount
103 Conservation of Momentum The total momentum of the system is conserved
104 Conservation of Momentum The total momentum of the system is conserved The law of conservation of momentum states that there is no change in the total momentum of system experiencing internal forces, forces that act only between particles within a system
105 QuickCheck Question 9.7 You awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and same mass. You ve only time to throw one. Which will it be? Your life depends on making the right choice! A. Throw the Superball. B. Throw the ball of clay. C. It doesn t matter. Throw either.
106 QuickCheck Question 9.7 You awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and same mass. You ve only time to throw one. Which will it be? Your life depends on making the right choice! Larger Δp more impulse to door A. Throw the Superball. B. Throw the ball of clay. C. It doesn t matter. Throw either.
107 QuickCheck Question 9.7 You awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and same mass. You ve only time to throw one. Which will it be? Your life depends on making the right choice! Larger Δp more impulse to door A. Throw the Superball. B. Throw the ball of clay. C. It doesn t matter. Throw either.
108 QuickCheck Question 9.8 A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito B. The truck C. They have the same change of momentum. D. Can t say without knowing their initial velocities.
109 QuickCheck Question 9.8 A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito B. The truck C. They have the same change of momentum. D. Can t say without knowing their initial velocities. Momentum is conserved, so Δp mosquito + Δp truck = 0. Equal magnitude (but opposite sign) changes in momentum.
110 QuickCheck Question 9.8 A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum? A. The mosquito B. The truck C. They have the same change of momentum. D. Can t say without knowing their initial velocities. Momentum is conserved, so Δp mosquito + Δp truck = 0. Equal magnitude (but opposite sign) changes in momentum.
111 Law of Conservation of Momentum External forces are forces from agents outside the system
112 Law of Conservation of Momentum External forces are forces from agents outside the system They can change the momentum of the system
113 Law of Conservation of Momentum External forces are forces from agents outside the system They can change the momentum of the system An isolated system is a system with no net external force acting on it
114 Law of Conservation of Momentum The change in the total momentum is
115 Law of Conservation of Momentum The change in the total momentum is If the net force due to external forces is 0, then the change in the total momentum is 0
116 Law of Conservation of Momentum
117 Law of Conservation of Momentum The total momentum of a system after an interaction is equal to the total momentum before the interaction and is written as
118 Law of Conservation of Momentum The total momentum of a system after an interaction is equal to the total momentum before the interaction and is written as
119 In 2 Dimensions Since momentum is a vector, we can rewrite the law of conservation of momentum for an isolated system:
120 Solving Law of Conservation of Momentum Problems
121 Solving Law of Conservation of Momentum Problems
122 It Depends on the System Goal: choose a system with conserved momentum
123 It Depends on the System Goal: choose a system with conserved momentum If we choose just the person, there is a nonzero net force on the system
124 It Depends on the System Goal: choose a system with conserved momentum If we choose just the person, there is a nonzero net force on the system If we choose the system to be the person and the cart, the net force is zero and the momentum is conserved
125 Example 9.5: Speed of Ice Skaters pushing off Two ice skaters, Sandra and David, stand facing each other on frictionless ice. Sandra has a mass of 45 kg, David a mass of 80 kg. They then push off from each other. After the push, Sandra moves off at a speed of 2.2 m/s. What is David s speed?
126 Example 9.5: Speed of Ice Skaters pushing off PREPARE The two skaters interact with each other, but they form an isolated system because, for each skater, the upward normal force of the ice balances their downward weight force to make Thus the total momentum of the system of the two skaters is conserved. The figure shows a before-and-after visual overview for the two skaters. The total momentum before they push off is zero because both skaters are at rest. Consequently, the total momentum will still be 0 after they push off.
127 Example 9.5: Speed of Ice Skaters pushing off SOLVE Since the motion is only in the x-direction, we ll need to consider only x-components of momentum. We write Sandra s initial momentum as (p Sx ) i = m S (v Sx ) i, where m S is her mass and (v Sx ) i her initial velocity. Similarly, we write David s initial momentum as (p Dx ) i = m D (v Dx ) i. Both these momenta are zero because both skaters are initially at rest.
128 Example 9.5: Speed of Ice Skaters pushing off SOLVE We can now apply the mathematical statement of momentum conservation, Equation Writing the final momentum of Sandra as m S (v Sx ) f and that of David as m D (v Dx ) f, we have
129 Example 9.5: Speed of Ice Skaters pushing off SOLVE We can now apply the mathematical statement of momentum conservation, Equation Writing the final momentum of Sandra as m S (v Sx ) f and that of David as m D (v Dx ) f, we have
130 Example 9.5: Speed of Ice Skaters pushing off SOLVE Solving for (v Dx ) f, we find
131 Example 9.5: Speed of Ice Skaters pushing off SOLVE Solving for (v Dx ) f, we find David moves backward with a speed of 1.2 m/s. Notice that we didn t need to know any details about the force between David and Sandra in order to find David s final speed. Conservation of momentum mandates this result.
132 Example 9.5: Speed of Ice Skaters pushing off SOLVE Solving for (v Dx ) f, we find David moves backward with a speed of 1.2 m/s. Notice that we didn t need to know any details about the force between David and Sandra in order to find David s final speed. Conservation of momentum mandates this result. ASSESS It seems reasonable that Sandra, whose mass is less than David s, has the greater final speed.
133 Interactions Between Particles Two types of collisions
134 Interactions Between Particles Two types of collisions 1. Elastic - particles collide and separate from one another
135 Interactions Between Particles Two types of collisions 1. Elastic - particles collide and separate from one another 2. Inelastic - particles collide and stick to one another
136 Interactions Between Particles Two types of collisions 1. Elastic - particles collide and separate from one another 2. Inelastic - particles collide and stick to one another Explosions - particles move apart from one another in the opposite direction
137 Explosions! An explosion is when the particles of the system move apart after a brief, intense interaction; opposite of a collision
138 Explosions! An explosion is when the particles of the system move apart after a brief, intense interaction; opposite of a collision The forces are internal forces and if the system is isolated, the total momentum is conserved
139 QuickCheck Question 9.10 The two boxes are on a frictionless surface. They had been sitting together at rest, but an explosion between them has just pushed them apart. How fast is the 2-kg box going? A. 1 m/s B. 2 m/s C. 4 m/s D. 8 m/s E. There s not enough information to tell.
140 QuickCheck Question 9.10 The two boxes are on a frictionless surface. They had been sitting together at rest, but an explosion between them has just pushed them apart. How fast is the 2-kg box going? A. 1 m/s B. 2 m/s C. 4 m/s D. 8 m/s E. There s not enough information to tell.
141 Inelastic Collisions A perfectly inelastic collision is a collision in which the two objects stick together and move with a common final velocity
142 Inelastic Collisions A perfectly inelastic collision is a collision in which the two objects stick together and move with a common final velocity Examples include clay hitting the floor and a bullet embedding itself in wood
143 QuickCheck Question 9.11 The 1-kg box is sliding along a frictionless surface. It collides with and sticks to the 2-kg box. Afterward, the speed of the two boxes is A. 0 m/s B. 1 m/s C. 2 m/s D. 3 m/s E. There s not enough information to tell.
144 QuickCheck Question 9.11 The 1-kg box is sliding along a frictionless surface. It collides with and sticks to the 2-kg box. Afterward, the speed of the two boxes is A. 0 m/s B. 1 m/s C. 2 m/s D. 3 m/s E. There s not enough information to tell.
145 Momentum and Collisions in 2 Dimensions When the motion of the collisions occur in two dimensions, we must solve for each component of the momentum:
146 Momentum and Collisions in 2 Dimensions When the motion of the collisions occur in two dimensions, we must solve for each component of the momentum: In these collisions, the individual momenta can change but the total momentum does not.
147 Summary
148 Summary
149 Summary
150 Summary
151 Summary
152 Summary
153 Things that are due Reading Quiz #9 Due October 20, 2015 by 4:59 pm Homework #6 Due October 21, 2015 at 11:59 pm Reading Quiz #10 Due October 22, 2015 by 4:59 pm
154 QUESTIONS?
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