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Momentum and CollisionsSection 1 Preview Section 1 Momentum and ImpulseMomentum and Impulse Section 2 Conservation of MomentumConservation of Momentum Section 3 Elastic and Inelastic CollisionsElastic and Inelastic Collisions Section 4 Extra QuestionsExtra Questions

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Momentum and CollisionsSection 1 What do you think? Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. How are these features similar?

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Momentum and CollisionsSection 1 What do you think? What are some common uses of the term momentum? Write a sentence or two using the term momentum. Do any of the examples provided reference the velocity of an object? Do any of the examples reference the mass of an object?

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Momentum and CollisionsSection 1 Momentum Momentum (p) is proportional to both mass and velocity. A vector quantity SI Units: kg m/s

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Momentum and CollisionsSection 1 Momentum and Newton’s 2nd Law Prove that the two equations shown below are equivalent. F = ma and F = p/ t Newton actually wrote his 2nd Law as F = p/ t. –Force depends on how rapidly the momentum changes.

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Momentum and CollisionsSection 1 Impulse and Momentum The quantity F t is called impulse. –SI units: Nm or kgm/s Impulse equals change in momentum. –Another version of Newton’s 2nd Law –Changes in momentum depend on both the force and the amount of time over which the force is applied.

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Momentum and CollisionsSection 1 Click below to watch the Visual Concept. Visual Concept Impulse-Momentum Theorem

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Section 1Momentum and Collisions Changing momentum Greater changes in momentum( p) require more force (F) or more time ( t). A loaded truck requires more time to stop. –Greater p for truck with more mass –Same stopping force

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Momentum and CollisionsSection 1 Classroom Practice Problems A 1350 kg car has a velocity of 22.0 m/s to the north. When braking rapidly, it stops in 4.50 s. –What was the momentum of the car before braking? –What is the magnitude of the force required to stop the car? Answers: –2.97 x 10 4 kg m/s to the north –6.60 x 10 3 N

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Momentum and CollisionsSection 1 Stopping Time F t = p = mv When stopping, p is the same for rapid or gradual stops. Increasing the time ( t) decreases the force (F). –What examples demonstrate this relationship? Air bags, padded dashboards, trampolines, etc Decreasing the time ( t) increases the force (F). –What examples demonstrate this relationship? Hammers and baseball bats are made of hard material to reduce the time of impact.

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Momentum and CollisionsSection 1 Classroom Practice Problems A 65 kg passenger in a car travels at a speed of 8.0 m/s. If the passenger is stopped by an airbag in 0.75 s, how much force is required? –Answer: 6.9 x 10 2 N If the car does not have an air bag and the passenger is instead stopped in s when he strikes the dashboard, by what factor does the force increase? –Answer: F = 2.0 x 10 4 N so it is 29 times greater

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Momentum and CollisionsSection 1 Now what do you think? Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. –List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. –How are these features similar?

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Momentum and CollisionsSection 1 Now what do you think? How is momentum defined? How is Newton’s 2nd Law written using momentum? What is impulse? What is the relationship between impulse and momentum?

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Section 2Momentum and Collisions What do you think? Two skaters have equal mass and are at rest. They are pushing away from each other as shown. Compare the forces on the two girls. Compare their velocities after the push. How would your answers change if the girl on the right had a greater mass than her friend? How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

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Momentum and CollisionsSection 2 Momentum During Collisions When the bumper cars collide, F 1 = -F 2 so F 1 t = -F 2 t, and therefore p 1 = - p 2. The change in momentum for one object is equal and opposite to the change in momentum for the other object. Total momentum is neither gained not lost during collisions.

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Momentum and CollisionsSection 2 Conservation of Momentum Total momentum remains constant during collisions. The momentum lost by one object equals the momentum gained by the other object. Conservation of momentum simplifies problem solving.

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Momentum and CollisionsSection 2 Click below to watch the Visual Concept. Visual Concept Conservation of Momentum

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Momentum and CollisionsSection 2 Classroom Practice Problems A 62.0 kg astronaut on a spacewalk tosses a kg baseball at 26.0 m/s out into space. With what speed does the astronaut recoil? –Step 1: Find the initial momentum of both astronaut and baseball. Answer: zero because v i = 0 for both –Step 2: Since p i = 0, then p f, astronaut = -p f, baseball –Step 3: Substitute and solve for v f,astronaut Answer: m/s or cm/s Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.

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Momentum and CollisionsSection 2 Classroom Practice Problem Gerard is a quarterback and Tyler is a defensive lineman. Gerard’s mass is 75.0 kg and he is at rest. Tyler has a mass of 112 kg, and he is moving at 8.25 m/s when he tackles Gerard by holding on while they fly through the air. With what speed will the two players move together after the collision? Answer: 4.94 m/s

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Section 2Momentum and Collisions Now what do you think? Two skaters have equal mass and are at rest. They are pushing away from each other as shown. Compare the forces on the two girls. Compare their velocities after the push. How would your answers change if the girl on the right had a greater mass than her friend? How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

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Section 3Momentum and Collisions What do you think? Collisions are sometimes described as elastic or inelastic. To the right is a list of colliding objects. Rank them from most elastic to most inelastic. What factors did you consider when ranking these collisions? 1.A baseball and a bat 2.A baseball and a glove 3.Two football players 4.Two billiard balls 5.Two balls of modeling clay 6.Two hard rubber toy balls 7.An automobile collision

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Momentum and CollisionsSection 3 Perfectly Inelastic Collisions Two objects collide and stick together. –Two football players –A meteorite striking the earth Momentum is conserved. Masses combine.

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Momentum and CollisionsSection 3 Classroom Practice Problems An 2.0 x 10 5 kg train car moving east at 21 m/s collides with a 4.0 x 10 5 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision. –Answer: 7.0 m/s to the east Now calculate the kinetic energy of the two cars before and after the collision. Was kinetic energy conserved? –Answer: KE before = 4.4 x 10 7 J, KE after = 1.5 x 10 7 J KE is not conserved. It is less after the collision.

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Momentum and CollisionsSection 3 Inelastic Collisions Kinetic energy is less after the collision. –It is converted into other forms of energy. Internal energy - the temperature is increased. Sound energy - the air is forced to vibrate. Some kinetic energy may remain after the collision, or it may all be lost.

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Momentum and CollisionsSection 3 Elastic Collisions Objects collide and return to their original shape. Kinetic energy remains the same after the collision. Perfectly elastic collisions satisfy both conservation laws shown below.

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Section 3Momentum and Collisions Elastic Collisions Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of momentum? –v f,A = 2.0 m/s, v f,B = 2.0 m/s –v f,A = 0 m/s, v f,B = 4.0 m/s –v f,A = 1.5 m/s, v f,B = 2.5 m/s Answer: all three m = 0.35 kg v = 4.0 m/s v = 0 m/s

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Section 3Momentum and Collisions Elastic Collisions Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of kinetic energy? –v f,A = 2.0 m/s, v f,B = 2.0 m/s –v f,A = 0 m/s, v f,B = 4.0 m/s –v f,A = 1.5 m/s, v f,B = 2.5 m/s Answer: only v f,A = 0 m/s, v f,B = 4.0 m/s m = 0.35 kg v = 4.0 m/s v = 0 m/s

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Section 3Momentum and Collisions Click below to watch the Visual Concept. Visual Concept Types of Collisions

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Momentum and CollisionsSection 3 Types of Collisions

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Section 3Momentum and Collisions Now what do you think? To the right is a list of colliding objects. Rank them from most elastic to most inelastic. What factors did you consider when ranking these collisions? 1.A baseball and a bat 2.A baseball and a glove 3.Two football players 4.Two billiard balls 5.Two balls of modeling clay 6.Two hard rubber toy balls 7.An automobile collision

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Section 3Momentum and Collisions Preview Multiple Choice Short Response Extended Response

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Section 3Momentum and Collisions Multiple Choice, continued 2. The vector below represents the momentum of a car traveling along a road. The car strikes another car, which is at rest, and the result is an inelastic collision. Which of the following vectors represents the momentum of the first car after the collision? F. G. H. J.

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Section 3Momentum and Collisions Multiple Choice, continued 3. What is the momentum of a kg baseball thrown with a velocity of 35 m/s toward home plate? A. 5.1 kg m/s toward home plate B. 5.1 kg m/s away from home plate C. 5.2 kg m/s toward home plate D. 5.2 kg m/s away from home plate

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Section 3Momentum and Collisions Multiple Choice, continued Use the passage below to answer questions 4–5. After being struck by a bowling ball, a 1.5 kg bowling pin slides to the right at 3.0 m/s and collides head-on with another 1.5 kg bowling pin initially at rest. 4. What is the final velocity of the second pin if the first pin moves to the right at 0.5 m/s after the collision? F. 2.5 m/s to the left G. 2.5 m/s to the right H. 3.0 m/s to the left J. 3.0 m/s to the right

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Section 3Momentum and Collisions Multiple Choice, continued Use the passage below to answer questions 4–5. After being struck by a bowling ball, a 1.5 kg bowling pin slides to the right at 3.0 m/s and collides head-on with another 1.5 kg bowling pin initially at rest. 5. What is the final velocity of the second pin if the first pin stops moving when it hits the second pin? A. 2.5 m/s to the left B. 2.5 m/s to the right C. 3.0 m/s to the left D. 3.0 m/s to the right

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Section 3Momentum and Collisions Multiple Choice, continued 6. For a given change in momentum, if the net force that is applied to an object increases, what happens to the time interval over which the force is applied? F. The time interval increases. G. The time interval decreases. H. The time interval stays the same. J. It is impossible to determine the answer from the given information.

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Section 3Momentum and Collisions Multiple Choice, continued 8. Two shuffleboard disks of equal mass, one of which is orange and one of which is yellow, are involved in an elastic collision. The yellow disk is initially at rest and is struck by the orange disk, which is moving initially to the right at 5.00 m/s. After the collision, the orange disk is at rest. What is the velocity of the yellow disk after the collision? Think energy! F. zero G m/s to the left H m/s to the right J m/s to the right

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Section 3Momentum and Collisions Multiple Choice, continued Use the information below to answer questions 9–10. A kg bead slides on a straight frictionless wire and moves with a velocity of 3.50 cm/s to the right, as shown below. The bead collides elastically with a larger kg bead that is initially at rest. After the collision, the smaller bead moves to the left with a velocity of 0.70 cm/s. 9. What is the large bead’s velocity after the collision? A cm/s to the right B cm/s to the right C cm/s to the right D cm/s to the right

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Section 3Momentum and Collisions Multiple Choice, continued Use the information below to answer questions 9–10. A kg bead slides on a straight frictionless wire and moves with a velocity of 3.50 cm/s to the right, as shown below. The bead collides elastically with a larger kg bead that is initially at rest. After the collision, the smaller bead moves to the left with a velocity of 0.70 cm/s. 10. What is the total kinetic energy of the system after the collision? F 10 –4 J G 10 –4 J H 10 –4 J J 10 –4 J

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Section 3Momentum and Collisions Short Response 11. Is momentum conserved when two objects with zero initial momentum push away from each other?

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Section 3Momentum and Collisions Short Response, continued An 8.0 g bullet is fired into a 2.5 kg pendulum bob, which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6.0 cm. 13. What was the initial speed of the bullet? Show your work.

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Section 3Momentum and Collisions Short Response, continued Base your answers to questions 13–14 on the information below. An 8.0 g bullet is fired into a 2.5 kg pendulum bob, which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6.0 cm. 14. What will be the kinetic energy of the pendulum when the pendulum swings back to its lowest point? Show your work.

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Section 3Momentum and Collisions Extended Response 15. An engineer working on a space mission claims that if momentum concerns are taken into account, a spaceship will need far less fuel for the return trip than for the first half of the mission.Write a paragraph to explain and support this hypothesis.

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